Distinguished Lecturers Program

Program Description

The Control Systems Society is continuing to fund a Distinguished Lecture Series.

The primary purpose is to help Society chapters provide interesting and informative programs for the membership, but the Distinguished Lecture Series may also be of interest to industry, universities, and other parties.

The Control Systems Society has agreed to a cost sharing plan which may be used by IEEE Chapters, sections, subsections, and student groups. IEEE student groups are especially encouraged to make use of this opportunity to have excellent speakers at moderate cost.

At the request of a Society Chapter, (or other IEEE groups as mentioned above), a lecture will be scheduled at a place and time that is mutually agreeable to both the Chapter and the Distinguished Lecturer. Eighty percent (80%) of the funds for the normal travel expenses for a lecture will be paid by the Society, the remaining travel expenses will be provided by the chapter. Lecturers will receive no honorarium. Note that the group organising the lecture must have some IEEE affiliation and the lecture must be free to attend by IEEE members.

The society will provide 80% of the expenses for qualified users of the program up to a maximum limit of $1000 for within a continent visit to be paid by the society and $2000 if the trip travels internationally. The speakers are geographically distributed so that this limit should be adequate for the trips to any part of the world. Travel outside of North America is encouraged provided that the society is not expected to spend in excess of $2000.

Procedures

When you wish to use this program, you may contact the speaker directly to make arrangements, however you must notify the Control Systems Society Coordinator in order that he may be aware of and agree to the planned visit. Once the trip has taken place the speaker should then request (by letter and appropriate expense receipts) that he/she be reimbursed for the remaining expenses through the Society Treasurer. The inviting chapter pays the speaker the additional costs. Procedures for unusual situations (such as when the speaker has other business on the trip) should be cleared through the Society Coordinator.

Society Coordinator

  • Headshot Photo
    Ian Petersen
    CSS Board of Governors, term ending 31 December 2013 (elected); Distinguished Lecturers Chair; TCST Associate Editor

Distinguished Lecturers

Bassam Bamieh Headshot Photo
Bassam Bamieh
Distinguished Lecturer

Distributed Control in Large Actuator/Sensor Arrays

Abstract: Control systems with large arrays of sensors and actuators are increasingly common in several applications such as fluid low control, process control, smart structures, and arrays of Micro-Electro-Mechanical (MEMS) devices. These are systems where distributed arrays of sensors and actuators interact with media described by partial differential equations. We address the important issues of controller design, controller architecture and the communication requirements between sensors and actuators in such arrays.

We consider a special (but common) class of such systems which posses spatio-temporal invariant dynamics, and show that optimal controllers inherit this invariance property.  We show how one can use multidimensional transform techniques to constructively design quadratically optimal (i.e. H2 or H-infinity) distributed controllers by solving parameterized families of Ricatti equations. It turns out that such optimal controllers have an inherent degree of localization or semi-decentralization. The implications for controlled actuator/sensor arrays will be discussed. We illustrate these concepts with an example of controlling arrays of capacitively actuated micro-cantilevers.

Modeling and Control of Shear Flow Turbulence

Abstract: The problem of describing transition and turbulence in wall bounded shear flows such as pipes, channels and boundary layers is an important and old problem in Hydrodynamic Stability. This type of turbulence is responsible for a significant portion of the drag on marine and aeronautical vehicles. Recently, a new theory of transition has emerged that appears to be in much better agreement with experiments than classical hydrodynamic stability. We review this theory and show the surprising parallels it has with the central notions of robust control theory. We show how tools like robust stability analysis, input-output norms and singular value plots describe transition and turbulent flow structures with surprising fidelity. It thus appears that in the technologically important case of wall bounded shear flows, transition is not so much a problem of linear or nonlinear instability, but rather of robustness to ambient uncertainty. This characterization of turbulence in terms of system theoretic norms and stability margins allows for a nice framework for its control. We will show how skin friction drag reduction problems can be recast as:

  1. they apply to general nonlinear systems with disturbances;
  2. we obtain explicit (often non-conservative) bounds on the maximal allowable transmission interval that guarantee stability; and
  3. we show that this approach is valid for a wide range of network protocols. This provides a flexible framework for design of NQCS, NCS and/or QCS that is amenable to various extensions and modifications, such as a treatment of dropouts and stochastic protocols, combined controller/protocol design, and so on.

José C. Geromel Headshot Photo
José C. Geromel
Distinguished Lecturer

Linear Filtering under Parameter Uncertainty and Delay

This talk aims at presenting filter design methodologies to deal with plants subject to parameter uncertainty and constant time-delay. After a brief discussion on relevant aspects of the problem under consideration as, for instance, convexity and computational difficulties, the conservativeness of the solution is evaluated in terms of the minimum guaranteed estimation error norm, based on a quality certificate determined from the equilibrium solution of a min-max problem. Constant time-delay is handled from a finite dimension comparison system well adapted to deal with frequency domain performances. The talk ends with a discussion on the possible application of the filter design methodology to networked systems described through an appropriate model based on Markov chains.

Switched Linear Systems Analysis and Control Design

In this talk, several aspects involving switched linear systems are presented. They are divided in two main streams characterized by considering the switching signal either as an exogenous perturbation to be attenuated or a control action to be adequately designed. The talk starts by introducing basic concepts on stability, performance calculation and switching control design based on a min-type Lyapunov function. The relevance of the proposed switching control scheme is discussed by introducing the concept of control consistency that requires performance improvement when compared to the ones of each isolated subsystems. This aspect makes clear the importance of switching systems in both theoretical and practical application frameworks. The talk ends with two examples of application of this methodology in LPV systems and DC-DC converters control design.

Joao P. Hespanha Headshot Photo
Joao P. Hespanha
Distinguished Lecturer

Switched Systems: Mixing Logic with Differential Equations

As computers, digital networks, and embedded systems become ubiquitous and increasingly complex, one needs to understand the coupling between logic-based components and continuous physical systems. This prompted a shift in the standard control paradigm-in which dynamical systems were typically described by differential or difference equations-to allow the modeling, analysis, and design of systems that combine continuous dynamics with discrete logic. This new paradigm is often called hybrid or switched control.

This talk deals precisely with systems that result from the interconnection of differential equations with logic-based decision rules. Such systems are hybrid in the sense that some of the variables that describe their behavior take continuous values (e.g., the state of a differential equation) whereas others take discrete values (e.g., a Boolean value, or the state of a finite automaton). We are particularly interested in switched system. These are systems for which the continuous dynamics are effectively determined by the values of one or more discrete variables.

In the talk, we present several mathematical tools that have been developed to understand the behavior of switched systems. These tools are introduced in the context of specific applications where both logic and differential equations arise naturally. We draw these examples from areas as diverse as computer networks, vision-based robotics, and adaptive control. The goal of this talk is twofold: (i) demonstrate that switched systems are ubiquitous and of significant practical application, and (ii) show that a unified theory of switched systems is becoming available.

Stochastic hybrid models in biology: Modeling and analysis

The time evolution of chemically reacting molecules is sometimes modeled using a stochastic formulation, which takes into account the inherent randomness of molecular motion. This formulation is especially useful for complex reactions inside living cells, where small populations of key reactants can set the stage for significant stochastic effects. In this talk, we show how Stochastic Hybrid Systems can be used to construct stochastic models for chemical reactions.

Hybrid systems combine continuous-time dynamics with discrete modes of operation. The states of such system usually have two distinct components: one that evolves continuously, typically according to a differential equation; and another one that only changes through instantaneous jumps. To model chemical reactions, we actually need Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events, much like transitions between states of a continuous-time Markov chains. However, the rate at which transitions occur is allowed to depend on both the continuous and the discrete states of the SHS.

Several tools are available to analyze SHSs. Among these, we discuss the use of the extended generator, infinite-dimensional moment dynamics, and finite-dimensional truncations by moment closure. The application of these tools is illustrated in the context of modeling the evolution of populations of molecules undergoing a system of chemical reactions.

Communication constraints in networked control systems

Networked Control Systems (NCSs) are spatially distributed systems for which the communication between processes, sensors, actuators, and/or controllers is supported by a digital communication network. This type of systems exhibits several characteristics that make them unique from a control perspective.

In this talk we address the effect of limited communication bandwidth and network latency in the overall performance of a closed-loop NCS. Not surprisingly, there is a trade-off between the amount of communication resources utilized and the control performance achievable. For prototypical examples (linear processes and quadratic costs) we construct optimal communication logics that achieve optimal performance with minimal communication. The effect of network latency is also investigated in this context.

John Lygeros Headshot Photo
John Lygeros
Distinguished Lecturer

Stochastic model predictive control

Abstract: In recent years Model Predictive Control (MPC) has emerged as a powerful methodology for on-line control of complex systems. The central idea is to formulate a finite horizon optimal control problem based on a model of the system dynamics. The optimal control problem is then solved (either on-line, using numerical optimization tools, or off-line, using multi-parametric programming), the initial part of the optimal input sequence is applied, a measurement of the state is taken and the process is repeated. The periodic state measurements provide the feedback necessary to make the process robust against disturbances, including errors in the system model used in the optimization. Over the years, MPC for deterministic systems has become a mature technology, with countless applications in a wide range of domains. More recently, robust MPC (where the system model includes bounded, worst case uncertainty) has also flourished, exploiting advances in robust optimization. In comparison, MPC for systems with stochastic, potentially unbounded uncertainty has received relatively little attention. Dealing with stochastic uncertainty is important, since it will allow the MPC methodology to extend to application areas such as finance, air traffic management, and insurance, which naturally lend themselves to an MPC approach but also naturally involve stochastic models. The extension of MPC to stochastic systems poses several challenges, both conceptual and practical: How should state constraints be interpreted in the finite and infinite horizon context, how can input constraints be enforced, what cost functions and policies should one consider for the optimal control problem, under what conditions are the resulting optimization problems convex, etc. In this talk we highlight these challenges and outline methods that can be used to overcome them.

Randomized optimization of deterministic and expected value criteria.

Abstract: Simulated annealing, Markov Chain Monte Carlo, and genetic algorithms are all randomized methods that can be used in practice to solve (albeit approximately) complex optimization problems. They rely on constructing appropriate Markov chains, whose stationary distribution concentrates on "good" parts of the parameter space (i.e. near the optimizers). Many of these methods come with asymptotic convergence guarantees, that establish conditions under which the Markov chain converges to a globally optimal solution in an appropriate probabilistic sense. An interesting question that is usually not covered by asymptotic convergence results is the rate of convergence: How long should the randomized algorithm be executed to obtain a near optimal solution with high probability? Answering this question would allow one to determine a level of accuracy and confidence with which approximate optimality claims can be made as a function of the amount of time available for computation. In this talk we present some new results on finite sample bounds of this type, primarily in the context of stochastic optimization with expected value criteria using Markov Chain Monte Carlo methods. The discussion will be motivated by the application of these methods to collision avoidance in air traffic management and parameter identification for biological systems.

Stochastic hybrid systems: From theory to applications.

Abstract: The term stochastic hybrid systems defines a class of control systems that involve the interaction of continuous dynamics, discrete dynamics and probabilistic uncertainty. Over the last decade stochastic hybrid systems have emerged as a powerful modeling paradigm in a wide range of application areas. This talk will provide an overview of recent developments in this rapidly evolving field of research. We will present the theoretical foundations and challenges of stochastic hybrid systems. We will also outline computational methods that can be used to analyze and control such systems, based primarily on randomized algorithms. The discussion will be motivated by applied modeling, analysis and control problems from the areas of systems biology and air traffic management.

Air traffic management: Challenges and opportunities for automatic control.

Abstract: Increasing levels of traffic are pushing the current Air Traffic Management (ATM) system to its limits. It is widely recognized that safely accommodating this increase in demand will require (in addition to technological advances) operational changes as well as novel, advanced decision support algorithms to assist the human operators. The operation of ATM is characterized by a hierarchy of tasks, which are exceptional benchmarks for control methodologies aiming to tackle complexity. Ongoing control research in the area of ATM includes large scale and distributed optimization for the management of traffic flows, innovative filtering, prediction and control methods for collision avoidance, systems methods for improving the situational awareness of human operators, optimal control for the design of safe coordination maneuvers, etc. In addition, models and simulation tools covering all levels of ATM are being developed, either to test and validate new methods, or to perform risk assessment for existing operations. This talk will highlight the problems and challenges that ATM poses for control engineers and outline advanced control and filtering methods that have been developed to improve the accuracy of aircraft trajectory prediction, detect potential safety problems, and compute maneuvers to resolve them.

Dragan Nesic Headshot Photo
Dragan Nesic
Distinguished Lecturer

Analysis and design of extremum seeking controllers

Abstract: Design of engineered systems whose operation is "best" or "optimal" in some sense is increasingly important due to a range of socio-economic and environmental problems that we are facing at the dawn of the 21st century, such as the climate change and increased competition in a global market. While still attracting a considerable research attention, optimal control methods can be regarded as classical and in certain areas, such as linear quadratic control, they are very well developed and understood. An underlying assumption in the classical control literature is that both the plant model and the cost to optimize are known to the engineer designing the system. However, surprisingly many engineering systems do not satisfy this basic assumption and, hence, classical optimization methods are often not directly applicable.

Extremum seeking is an optimal control approach that deals with situations when the plant model and/or the cost to optimize are not available to the designer but it is assumed that measurements of plant input and output signals are available. Using these available signals, the goal is to design a controller that dynamically searches for the optimizing inputs. This method was successfully applied to biochemical reactors, ABS control in automotive brakes, variable cam timing engine operation, electromechanical valves, axial compressors, mobile robots, mobile sensor networks, optical fibre amplifiers and so on. Interestingly, some bacteria (such as the flagella-actuated E. Coli) and swarms of fish collectively search for food using extremum seeking techniques. This presents opportunities for research cross-fertilization between control engineering and biology.

While extremum seeking is an old topic, local stability of a class of extremum seeking controllers was proved for the first time by Krstic and Wang in 2000. Subsequently, Popovic and Teel proposed an alternative framework for extremum seeking and provided corresponding stability proofs. We present an extension of stability results by Krstic and Wang for a simplified extremum seeking scheme and show that the scheme yields semi-global extremum seeking under appropriate assumptions if the controller parameters are tuned appropriately. An interesting trade-off between the size of domain of attraction and the speed of convergence of the scheme is uncovered. The scheme works in essence as a steepest descent method and we also provide a strategy and conditions under which it yields global stability in presence of local extrema. Flexibility of the choice of dither in the scheme is also discussed and its effect on the convergence speed is explained. We use recent results on singular perturbations and averaging in the stability analysis. Examples of application of our scheme and Teel and Popovic approach are presented respectively for biochemical reactors and Raman optical amplifiers. 

A unified approach to analysis and design of quantized and networked control systems

Abstract: Emerging control applications, such as drive-by-wire cars, often require some control loops to be closed over a network. Motivation for using this set-up comes from lower cost, ease of maintenance, great flexibility, as well as low weight and volume. This motivates research into control systems in which one or several control loops are closed via a network.

Currently, there are two distinct approaches to modelling the effects of the network in such systems. The first approach assumes that only a finite number of bits can be transmitted over the network at any transmission instant and the sensor/actuator values need to be appropriately quantized before they are sent over the network. We refer to such systems as quantized control systems (QCS). In another approach, network transmits sensor/actuator values in packets and it is assumed that packets are large enough to ignore quantization effects. In this case we can regard the network as a serial communication channel that transmits signals from many sensors/actuators in the control system. The main issue in such systems is that the serial communication channel has many \x{201C}nodes\x{201D} (groups of sensors and actuators) where only one node can transmit its value at any transmission time and, hence, access to the channel needs to be scheduled in an appropriate manner for a proper operation of the system. Such systems are often referred to in the literature as networked control systems (NCS).

While QCS and NCS deal with very similar issues, these systems have been treated separately in the literature with little cross-fertilization. Our goal is to present a unified approach to analysis and design of networked and quantized control systems (NQCS) that combine time scheduling and quantization. In particular, we present an emulation controller design approach where, in the first step, we design a controller ignoring the network and, in the second step, we implement the designed controller over the network with sufficiently fast transmissions and a given protocol. Our results have several features:

Analysis and design of nonlinear sampled-data control systems

Abstract: In the vast literature on nonlinear control design, an area that has received scant attention is sampled-data control. In this problem, a continuous time plant is typically controlled by a discrete-time feedback algorithm. A sample and hold device provides the interface between continuous time and discrete-time.

One way to address sampled-data control is to implement a continuous time control algorithm with a sufficiently small sampling period (i.e. emulation). However, the hardware used to sample and hold the plant measurements or compute the feedback control action may make it impossible to reduce the sampling period to a level that guarantees acceptable closed-loop performance. In this case, it becomes interesting to investigate the application of sampled-data control algorithms based on a discrete-time model of the process. Note that even if the continuous-time model of a nonlinear plant is known to the designer, we typically can not compute analytically an exact discrete-time model and, hence, a more realistic approach is to base the controller design on an approximate discrete-time model of the plant (e.g. Euler).

We present an overview of our work on sampled-data nonlinear systems. First, we discuss a framework for controller design for sampled-data nonlinear systems via their approximate discrete-time models that we proposed. Our conditions are very general and we illustrate with examples that if some of these conditions are relaxed it may happen that the controller stabilizes the approximate model of the plant but it destabilized the exact model for all positive sampling periods. Our results adapt the notion of "consistency" from the numerical analysis literature and exploit it in our conditions and proofs. A range of controller design methods can be developed within our framework and we present a backstepping design for strict feedback systems as an illustration. Then, we investigate different techniques for emulation and continuous-time controller redesign for sampled-data implementation. Several examples illustrate the generality and flexibility of our approach. Moreover, they illustrate that the discrete-time designs typically outperform the emulation designs in simulations.

Fernando Paganini Headshot Photo
Fernando Paganini
Distinguished Lecturer

Network control through distributed optimization – A Tutorial

Today’s Internet is a gigantic, complex communications infrastructure, shared by end-to-end connections which compete for the bandwidth resources. What is the resulting allocation? The answer is highly dependent on multiple automatic control mechanisms embedded in the network protocols, which dynamically adjust flow rates, routing, medium access, etc., making the Internet probably the largest scale artificial control system in operation. Is there any hope for a mathematical analysis or synthesis at this huge scale? Research over more than a decade has shown that substantial progress is possible by casting the problem in the language of economic theory and convex optimization. These tools combine with methods of dynamics and control to provide useful insights into current behavior, and design proposals with provable performance at multiple protocol layers. In this talk we will give a tutorial overview of this field of research.


Stability and fairness in the control of network connections

Users of the Internet establish end-to-end connections to support data transfers. The traffic rates obtained by these connections are the result of a global resource allocation involving multiple layers of control: flow control, routing, medium access control, and physical layer adaptation. Research over more than a decade has provided mathematical models that help understand the stability and fairness of this allocation among connections.

The generation of connections is, however, itself a dynamic process, and therefore also subject to stability and fairness concerns. One model of connection dynamics is in the realm of queueing theory, where connections are generated randomly between the many network endpoints, bringing a certain random file size to be transported. In this talk we will discuss recent results that characterize the stability region of this queueing system, for general file-size distributions commonly observed in practice.

Another viewpoint for the generation of connections is as a strategic game: users can actively generate parallel connections to obtain a higher share of the underlying bandwidth resources, making fairness between connections a moot point. This behavior indeed occurs with certain greedy applications, and if generalized can have negative consequences. In this talk we will advocate for a ``user-centric" notion of fairness, where fairness is framed in terms of aggregate rates per user, and propose admission control mechanisms to achieve this allocation in a distributed way across a network.


Headshot Photo
Lucy Y. Pao
Distinguished Lecturer

Combined Feedforward/Feedback Control of Flexible Structures, with Applications Ranging from Atomic Force Microscopes to Megawatt Wind Turbines

Abstract: In the past, manipulators, machine tools, measurement and many other systems were designed with rigid structures and operated at relatively low speeds. With an increasing demand for fuel efficiency, smaller actuators, and speed, lighter weight materials are now often used in the construction of systems, making them more flexible. Flexible structures are also prevalent in space systems where lightweight materials are necessitated for fuel efficiency when carrying the structures into space. Achieving high-performance control of flexible structures is a difficult task, but one that is now critical to the success of many important applications, ranging from the shuttle remote manipulator system, satellites, wind turbines, robot manipulators, gantry cranes, disk drives, to atomic force microscopes. The unwanted vibration that results from maneuvering a flexible structure often dictates limiting factors in the performance and lifespan of the system.

We will discuss combined feedforward and feedback architectures and algorithms for controlling flexible structures. Depending upon the particular performance goals, such as tracking accuracy in a trajectory following task or rapid settle time for a point-to-point motion, there are different requirements for the controller. In many applications, the actuators and sensors are separated by the flexible structure, leading to nonminimum phase characteristics that are challenging for control. Over the last few decades, many feedback and feedforward control methods have been developed for flexible structures. We will overview and compare several of these control methods and highlight recent developments and results. We will also present advances in a few application areas that have been achieved through better control of inherent flexible structures. Finally, we shall close by discussing a number of future challenges.

Multisensor Fusion Algorithms for Tracking Applications, with Applications Ranging from Tracking Ground Vehicles to Aerial Vehicles to Satellites

Abstract: In many applications, such as tactical defense, unmanned aerial vehicles, and mobile robotics, multiple sensors are used to track objects and assess the environment. Multiple sensors provide large amounts of data with which to detect, track, and identify targets of interest. Using different types of sensors to obtain information allows the strengths of one sensor type to compensate for the weaknesses of another and further provides redundance, therefore increasing system robustness.

In this talk, we will review a few multisensor fusion algorithms for tracking applications that combine measurements from multiple sensors in a consistent manner. We will then discuss some selected recent research results in developing effective methods of managing sensor resources, deriving and extending sensor fusion algorithms for distributed processing architectures, developing techniques that allow complex multisensor fusion algorithms to be evaluated and compared efficiently, and formulating methods for detecting track loss in the absence of truth data.

Haptic Interfaces: Making Touch Interfaces More Interactive

Abstract: Haptic interfaces enable users to feel, touch, and manipulate remote or virtual objects, and as such, haptic interfaces can facilitate human-computer and human-machine interaction in a wide range of applications ranging from scientific visualization to teleoperation to laparoscopic surgery. In this talk, we will give examples of haptic interfaces from around the world, including those we have developed in our own lab. Limitations and capabilities of current haptic interfaces will be discussed. We will also outline a number of applications of haptic interfaces, ranging from low-end applications (vibrotactile mice, joysticks) to high-end applications (medical/rehabilitation, scientific visualization). Throughout the talk, we will highlight some of our work in two areas: (1) investigating the use of haptic interfaces for scientific visualization of complex multi-dimensional data, as well as (2) developing low-cost yet high-quality multi-degree-of-freedom haptic interfaces in the hopes of expanding haptic interfaces to an even broader range of applications.

Carsten W. Scherer Headshot Photo
Carsten W. Scherer
Distinguished Lecturer

Linear Matrix Inequalities in Control - A Tutorial

Semi-definite programming has grown into an important computational tool for attacking problems in all areas of control. In this overview we discuss the basic ideas how to translate stability, performance and robust performance objectives into the framework of linear matrix inequalities. Throughout the presentation particular emphasis is put on an investigation of those system interconnection structures that are amenable to convex optimization for controller design.

Robust Estimator Design by Convex Optimization

Estimators serve to reconstruct information about the internal behavior of a dynamical systems on the basis of measurements that are corrupted by noise. Based on a tutorial introduction of classical Kalman filtering, we review the relevance of optimal estimator synthesis for modern control applications. This serves as a foundation for illustrating the key steps in translating optimal estimator synthesis into a semi-definite program. In practical applications, models of dynamical systems are never precise. In the last part of the talk we will demonstrate how various types of system-model mismatches can be captured by robust semi-definite programming or by integral quadratic constraints.

Matrix Sum-of-Squares Relaxations in Robust Control

Various interesting optimization based controller synthesis problems can be translated into semi-definite programs which can in turn be solved rather efficiently. In this tutorial presentation we motivate why linear matrix inequalities naturally appear if addressing question of stability and performance for linear control systems. If parameters describing the optimization problems are not precisely known, it is argued why it is required to solve so-called robust linear matrix inequalities. In the more technical part of the presentation we will reveal how to systematically construct approximations of robust linear matrix inequalities on the basis of so-called sum-of-squares decompositions (related to Hilbert's famous 17th problem), with the benefit of allowing to arbitrarily reduce the relaxation error.

Rodolphe Sepulchre Headshot Photo
Rodolphe Sepulchre
Distinguished Lecturer

Consensus in Nonlinear Spaces

Consensus problems have attracted significant attention in the control community over the last decade. They act as a rich source of new mathematical problems pertaining to the growing field of cooperative and distributed control. The talk focuses on consensus problems whose underlying state-space is not a linear space, but instead a highly symmetric nonlinear space such as the circle and several other relevant generalizations. A geometric approach is shown to highlight the connection between several fundamental models of consensus, synchronization, and coordination, to raise significant global convergence issues not captured by linear models, and to be relevant for a number of engineering applications, including the design of coordinated motions in the plane or in the three-dimensional space.  Finally, nonlinear considerations on the original consensus problem defined in the positive orthant shed light on the special role of nonquadratic Lyapunov functions in this framework.

Rank-preserving optimization on the cone of positive semidefinite matrices: a geometric approach

The talk is an introduction to a recent computational framework for optimization over the set of fixed rank positive semidefinite matrices. The foundation is geometric  and the motivation is algorithmic, with a bias towards low-rank computations in large-scale problems.  Special attention is given to  two quotient riemannian geometries that are rooted in classical matrix factorizations and that  lead to rank-preserving efficient computations in the cone of symmetric positive definite matrices. The field of applications is vast, and the talk surveys recent developments that illustrate the potential of the approach in large-scale computational problems encountered in control, optimization, and machine learning.  The talk is introductory and requires no particular background in riemannian geometry.

Algorithmic challenges in an information-rich age

Modern scientific exploration is increasingly based on distributed technologies. Those include extremely large telescopes made of thousand individual mirrors, sensor networks sharing hundreds of spatially distributed measurements in the ocean, microarrays allowing for the simultaneous measurement of thousands gene expressions in a single cell,  or the simultaneous acquisition of thousands of diffusion tensors (one per voxel) in brain imaging.

Distributed technologies overcome fundamental hardware limitations at the price of formidable computational challenges. Those challenges raise new algorithmic questions that involve a mix of statistical, machine learning, and optimization tools.

This non-technical talk illustrates some of these challenges and open questions through a journey across three concrete research projects, suggesting that geometry plays a fundamental role in making those computational problems tractable.

Sarah Spurgeon Headshot Photo
Sarah Spurgeon
Distinguished Lecturer

Sliding mode control: from theory to application

Sliding mode control is a practically realisable nonlinear control strategy which yields robust performance in the presence of uncertainty. Interesting properties result from allowing the control signal to switch; for example, total invariance of the system response to a substantial class of parameter variations and external disturbance signals is possible. Dynamic performance requirements are met by prescribing a dynamic system which exhibits the ideal performance required from the plant. An appropriate discontinuous control signal is then selected to ensure the trajectories of the system of interest find this ideal dynamics attractive. This lecture will first provide an introduction to the basic properties of sliding mode control. The sliding mode controller design paradigm will be reviewed and it will be shown how designers can select the ideal performance for given problem classes and how the control can be selected to ensure the ideal dynamics is attained and maintained. The lecture will briefly review certain topics of current research interest in the sliding mode control research community including providing a brief introduction to the higher order sliding mode control concept. In conclusion, the results of recent implementation studies will be presented to demonstrate both the practical issues associated with controller implementation and the merit of the proposed approach.

On discontinuous observers: from basic properties to a robust fault detection and condition monitoring tool

Historically the sliding mode technique developed as a robust control method being characterised by a suite of feedback control laws and a decision rule. The decision rule, termed the switching function, has as its input some measure of the current system behaviour and produces as an output the particular feedback controller which should be used at that instant in time. The concept of sliding mode observers came later. These observers have unique properties, in that the ability to generate the so-called sliding motion on the error between the measured plant output and the output of the observer ensures that a sliding mode observer produces a set of state estimates that are precisely commensurate with the actual output of the plant. It is also the case that analysis of the average value of the applied observer injection signal, the so-called equivalent injection signal, contains useful information about the mismatch between the model used to define the observer and the actual plant. These unique properties, coupled with the fact that the discontinuous injection signals which were perceived as problematic for many control applications have no disadvantages for software-based observer frameworks, have generated a ground swell of interest in sliding mode observer methods in recent years. This lecture presents an overview of both linear and non-linear sliding mode observer paradigms. The use of the equivalent injection signal in problems relating to fault detection and condition monitoring is demonstrated. A number of application specific results are also described.

Maria Elena Valcher Headshot Photo
Maria Elena Valcher
Distinguished Lecturer

Stability and stabilizability of discrete-time switched systems with positivity constraints

A discrete-time positive switched system (DPSS) consists of a  family of positive state-space models  and a switching law, specifying when and how the switching among the various models takes place. These systems  have some interesting practical applications: they have been adopted for describing networks employing TCP and other congestion control applications, for modeling consensus and synchronization problems, and, quite recently, for describing the viral mutation dynamics under drug treatment.
  
As for  the broader classes of  hybrid and switched systems, stability and stabilizability properties have been the two  major issues to   attract the researchers' attention. Clearly, all results so far  obtained for general  discrete-time switched systems hold true for DPSS's.
 In particular, the asymptotic stability of a DPSS switching into a finite set of matrices, say A, is equivalent to the fact that the joint spectral radius  of A, is smaller than 1.

Even if  a number of algorithms was proposed to evaluate the joint spectral radius of a set of matrices in quite general conditions, research efforts about stability and henceforth about stabilizability have also taken alternative directions and focused on  different approaches.The most popular approach to the investigation of stability and stabilizability is undoubtedly the one based on common Lyapunov functions or multiple Lyapunov functions.

In this talk we concentrate our attention on discrete-time positive switched systems, and we investigate in detail stability and stabilizability properties for them. We propose several sufficient conditions for testing stability, based on the existence of special classes of common Lyapunov functions, and we mutually relate them, thus proving that if a linear copositive common  Lyapunov function can be found, then a quadratic positive definite common Lyapunov  function can be found, too, and this latter, in turn, ensures the existence of a   quadratic copositive common Lyapunov  function.

Stabilizability is also introduced and characterized. It is shown that if a DPSS is stabilizable, it can be stabilized by means of a periodic switching sequence, which asymptotically drives to zero  every positive initial state.  Conditions for  the existence of state-dependent stabilizing switching laws, based on the values of  a  copositive (linear/quadratic) Lyapunov function,  are investigated and related to  each other. Interestingly enough, the mutual relationship between the various conditions for the existence of these special Lyapunov functions are very close to the analogous ones obtained for the stability characterization.

A behavioral approach to dead-beat control

As first suggested in the pioneering papers by Jan C. Willems, the behavioral approach provides the  natural framework where control problems can be addressed in the utmost generality and without any a priori assumption regarding input/output partition and feedback connection.  Indeed, in this setting, the control target is that of restricting the behavior trajectories to a subset of "good ones" and this goal is achieved by interconnection, namely by constraining either all or a subset of the system variables to obey an additional family of 
laws, which represent the controller laws.
 
Starting from these inspiring contributions, there has been quite a number of papers on the control within the behavioral framework. In these papers two fundamental control set-ups have been explored: the full interconnection case and the partial interconnection case.
In the former, it is assumed that all variables are the target of the control problem (for instance, the stabilization problem) and at the same time they are all available for interconnection. In the latter, the system variables are partitioned in two (or possibly more) groups, by distinguishing between  to be controlled variables, which are the object of the control specifications, and control variables, which are the means through which the control target is achieved. Indeed, the controller achieves the desired result by restricting the behavior of the control variables which are the only ones available for interconnection.

In this talk we explore the dead-beat control (DBC) problem for discrete-time behaviors  defined on Z+. In investigating this problem, we take a perspective that differs both from the full interconnection and from the partial interconnection set-ups, in that we assume that only the to be controlled variable must be "driven to zero in a finite number of steps", but the control laws restrict the evolutions of  all the variable. So, there is  full interconnection for control purposes, but  the control target is just the to be controlled variable.

The investigation of the DBC problem under this perspective requires to introduce new concepts of controllability and of zero-controllability. Consistently, it will turn out that the possibility of designing DBC's with good properties (admissibility or regularity) is just equivalent to the zero-controllability property.  Special attention will be devoted to the class of minimal DBC's, by this meaning DBC's with the least number of rows, for which a parametrization will be provided. Such parametrization is quite complex, as it resorts both to polynomial and to rational parameters, under the constraint that the obtained result is polynomial. Open problems will be illustrated.

Mathukumalli Vidyasagar Headshot Photo
Mathukumalli Vidyasagar
Distinguished Lecturer

Predicting Extreme Events in Finance, Internet Traffic, and Weather: Use of Heavy-Tailed Distributions

As far back as 1963, Beniot Mandelbrot (who sadly passed away just a few weeks ago) pointed out that asset price movements in the real world don't follow the Gaussian distribution.  Instead they are "heavy-tailed" -- that is, they display a kind of self-similarity and scale-invariance.  Since then, similar patterns have been observed in extreme weather such as rainfall, and more recently, in Internet traffic.  Recent research in "pure" probability theory shows that heavy-tailed random variables have some very unusual properties.  For instance, if we average many observations of such variables, the averages move in a few large bursts instead of moving smoothly.  Such behavior has indeed been observed in the stock market.

The pervasiveness of heavy-tailed distributions in so many diverse arenas has implications for modeling, and risk mitigation. How do we design Internet traffic networks and storage servers if the volume of traffic is heavy-tailed?  How do we hedge our equity positions if asset prices move in a heavy-tailed manner? 

In this talk I will describe the issues involved through a combination of intuitive arguments, visualizations, and formal mathematics.  My hope is to inspire practicing engineers to become familiar with this fascinating class of models, and theoretical researchers to study the many open problems that still remain.

Changyun Wen Headshot Photo
Changyun Wen
Distinguished Lecturer

Adaptive Actuator Failure Compensation Control of Uncertain Nonlinear Systems with Guaranteed Transient Performance

Abstract

In order to accommodate actuator failures which are uncertain in time, pattern and value, two adaptive backstepping control schemes for parametric strict feedback systems are presented. Firstly a basic design scheme on the basis of existing approaches is considered. It is analyzed that, when actuator failures occur, transient performance of the adaptive system cannot be adjusted through changing controller design parameters. Then, based on a prescribed performance bound (PPB) which characterizes the convergence rate and maximum overshoot of the tracking error, a new controller design scheme is given. It is shown that the tracking error satisfies the prescribed performance bound all the time. Simulation studies also verify the established theoretical results that the PPB based scheme can improve transient performance compared with the basic scheme, while both ensure stability and asymptotic tracking with zero steady state error in the presence of uncertain actuator failures.

Adaptive Compensation for Infinite Number of Actuator Failures or Faults

Abstract

In most of the existing results on adaptive control of systems with actuator failures, only the cases with finite number of failures are considered. It is assumed that one actuator may only fail once and the failure mode does not change afterwards.  In this talk, we shall consider how to deal with the problem of accommodating infinite number of actuator failures or faults in controlling uncertain nonlinear systems based on adaptive backstepping technique. With a newly proposed scheme, it is shown that all closed-loop signals are ensured bounded. The performance of the tracking error in the mean square sense with respect to the frequency of failure/fault pattern changes is also established. Moreover, asymptotic tracking can be achieved when the total number of failures and faults is finite. The effectiveness of the proposed scheme is verified in an aircraft application through simulation studies.

Decentralized Adaptive Control

Abstract

In the control of uncertain complex interconnected systems, decentralized adaptive control technique is an efficient and practical strategy to be employed for many reasons such as ease of design, familiarity, difficulty in information exchanging between subsystems and so on. In this context, a local controller using only local information is designed for each subsystem while guaranteeing the stability and performance of the overall system. However, simplicity of the design makes the analysis of the overall system quite difficult, especially when adaptive control approaches are employed to handle system uncertainties. Some results in the area will be covered in the following two parts:  

Part 1 Decentralized Adaptive Control based on Conventional Approaches.

In this part, how to establish the stability for decentralized adaptive control systems without relative degree constraints on subsystems will be presented.

 Part 2 Decentralized Adaptive Control Based on Backstepping Approches

In this part, decentralized adaptive control using backstepping technique will be considered for interconnected systems with both input and output dynamic interactions. To clearly illustrate the approaches, we will start with linear systems and then extend the results to nonlinear systems. The L2 and L1 norms of the system outputs are also established as functions of design parameters. This implies that the transient system performance can be adjusted by choosing suitable design parameters.

Lihua Xie Headshot Photo
Lihua Xie
Distinguished Lecturer

Minimum Data Rate and Channel Capacity for Stabilization of Linear Systems over Lossy Networks

One of the main challenges in networked control systems is the analysis and synthesis of control over limited rate feedback channels. The problem of minimum data rate for stabilization of linear systems has attracted significant interest in the past decade and it is now well known that under perfect communications the minimum data rate is related to the unstable engenvalues of the open-loop system. Another important issue in networked control is the uncertainties induced by the network such as packet losses. In this lecture, we shall discuss the minimum data rate for mean square stabilization over lossy networks. The packet losses process is modeled as an i.i.d. or Markov process. We show that the minimum data rate can be explicitly given in terms of the unstable eigenvalues of the open-loop system and the packet loss rate for the i.i.d. case or the transition probabilities of the Markov chain for the Markovian packet losses case. The number of additional bits required to counter the effect of the packet losses on stabilizability is completely quantified.  We shall also discuss the problem of minimum channel capacity for mean square stabilization of linear systems.

State Estimation over Rate limited Uncertain Channels

The problem of estimation and control over a communication network has attracted recurring interests in recent years due to the fact that there are more and more applications where communication networks are used to connect  sensors, controllers and actuators. While having many advantages of using communication works for transmitting data/signals, the limited data rate and network uncertainties such as packet losses pose significant challenges for analysis and design. In particular, in wireless sensor networks, power consumption is a critical design factor and communications cost much more energy as compared with computation. As such, there is a clear motivation for minimizing the communications. In this lecture, we shall discuss issues of quantized estimation and stability of Kalman over lossy channels. For the quantized estimation problem, we focus on how to jointly design quantizer and estimator to minimize the mean square estimation error. Under the Gaussian assumption of the predicted density, the quantized MMSE filter is shown to have a similar form as the Kalman filter with the raw measurement simply replaced by its quantized version. Quantization effects are explicitly quantified in terms of the number of quantization levels and quantization thresholds. The stability of the quantized estimator in relation to the system dynamics is examined. We then discuss the stability of Kalman filtering over a network subject to random packet losses, which are modeled by a time-homogeneous ergodic Markov process. Necessary and sufficient conditions for stability of the mean estimation error covariance matrices are derived by taking into account the system structure. Stability criteria are expressed by simple inequalities in terms of the largest eigenvalue of the open loop matrix and transition probabilities of the Markov process. Their implications and relationships with related results in the literature are discussed.

Network Topology and Communication Data Rate for Consensusability of Multi-agent Systems

Multi-agent cooperation involves a collection of decision-making components with limited processing, limited sensing and limited communications capabilities, all seeking to achieve a collective objective. Well known examples include mobile sensor networks for environment monitoring and surveillance and multi-UAV (unmanned aerial vehicle) formation flight. The distributed nature of information processing, sensing and actuation makes these applications a significant departure from the traditional centralized control system paradigm. In this lecture, we shall discuss the joint effects of agent dynamic, network topology and communication data rate on the consensusability  of linear discrete-time multi-agent systems. Neglecting the finite data rate constraint, a necessary and sufficient condition for consensusability under a set of distributed control protocols is given which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the communication  graph affect consensusability. The result is established by solving a discrete-time simultaneous stabilization problem. A lower bound of the optimal convergence rate to consensus, which is shown to be tight for some special cases, is given as well. The consensus problem under a finite communication data rate is also investigated. We shall present a systematic approach to the design of encoder, decoder and control protocol to achieve the exact consensus. The consensus convergence rate in relation to the bit rate, network synchronizability and the size of the network is established. The implementation of the algorithm on a real multi-robot system as well as on a virtual platform will be demonstrated.