Learning-based control paradigms have seen many success stories with autonomous systems in recent years. A typical architecture in these systems involves layers for perception, planning and control, wherein each of these layers uses different tools and metrics for assessing robustness and performance. For example, the planners -- that use vision-based sensors to update the navigation and motion planning -- operate largely relying on distributionally robust stochastic optimal control, whereas the low-level controller can be a deterministic controller with its conventional gain and phase (time-delay) margin. We present a new analysis framework for addressing this ontology challenge inherent to autonomous systems. We derive distributional robustness guarantees for deterministic L1 adaptive controllers that can be used by any stochastic planner without facing a language barrier. The combined planner-controller framework can serve as foundation for development of certificates for V&V of learning-enabled systems. An overview of different projects at our lab that build upon this framework will be demonstrated to show different applications. 

The robust learning of dynamical systems is crucial for safety-critical applications, such as power systems and autonomous systems. The control theory has a rich literature on system identification and optimal control in the case when the system is subject to non-adversarial and mostly Gaussian disturbance. However, there is a pressing need to develop learning and control techniques for systems whose inputs are under adversarial attacks, meaning that the system operates in a hostile environment. The main challenge is that the classic results relying on closed-form solutions for least-square estimators and LQR/LQG are no longer valid, and it is essential to design non-smooth estimators and controllers with no closed-form solutions in presence of adversarial attacks. In this talk, we discuss the recent advances in the area and focus on the problem of learning an unknown nonlinear dynamical system subject to adversarial disturbance/input. We develop a non-smooth estimator and show that the correct dynamics of the system can be learned in finite time no matter how severe the attack is as long as the learning period is longer than some threshold. We then study optimal control for systems in hostile environments

Nonlinearity appears in many areas of machine learning (ML), such as deep learning, reinforcement learning, graphical models, and adversarial ML. Given the large-scale nature and complexity of ML problems, nonlinearity has often been handled by heuristic techniques. These methods are behind the major successes of artificial intelligence in the past decade, but they lack mathematical guarantees. This has limited the applications of these methods to safety-critical systems, such as power systems and transportation systems. In this talk, we develop a set of computational tools with mathematical guarantees for various nonlinear problems, with applications to ML and energy. First, we work through the notions of restricted isometry property (RIP) and spurious solutions to understand when the best (global) solution of a nonlinear learning or optimization problem can be found via local search techniques. We discuss the limitations of RIP and introduce a variant of this notion that can be applied to a much broader set of problems, formulated as matrix sensing over graphs. We demonstrate the results on the state estimation problem for power systems and show how much data should be collected to break down the complexity of the underlying learning problem in power systems. We then study the problem of learning a model under adversarial attacks on the data using the notion of graphical mutual incoherence, and as an example we use our results to design the first vulnerability map of the U.S. power grid.

Power systems around the world are being modernized to address environmental concerns, reduce costs, and guarantee access to electricity all the time.  Four main criteria for this upgrade are efficiency, reliability, resiliency and sustainability. Recent advances in various technologies are the key enablers for this modernization. Nevertheless, such physical systems are becoming overwhelmingly large-scale and stochastic with highly complex dynamics, coupled with millions of human interactions. The design and operation of these systems needs major innovations in computational techniques. In this talk, we first discuss some major challenges behind the modernization of power grids and explain why addressing them involves many different fields. Then, we focus on three topics of optimization, learning, and control for power systems, which all need major revolutions in computational techniques. We study how recent advances in AI and machine learning can assist with addressing some of these challenges. We offer case studies on the grids for California, Texas, and different parts of Europe. 

Rehabilitation robotics leverages the principle of "practice makes perfect" by using repetitive task-based exercises to facilitate motor re-learning and functional recovery, particularly in poststroke rehabilitation. Rooted in neurocognitive rehabilitation theories, robot-assisted therapies provide tailored, intensive training routines that meet individual patient needs. Learning control (LC) strategies, originally developed in 1978 to achieve high tracking performance in industrial applications, offer a compelling framework for controller designs in this field. Unlike traditional control methods, LC algorithms improve performance over time by utilizing information from previous iterations. This talk highlights recent advances in LC designs and illustrates how various LC algorithms effectively address the unique challenges posed by rehabilitation robotics. Additionally, it explores future opportunities for integrating learning control into rehabilitation systems and outlines key research questions for advancing control theory in this critical area.

Extremum Seeking Control (ESC) is a control method designed to determine and maintain the extremum (maximum or minimum) value of a function in real time. Since its invention in 1922, ESC has undergone significant theoretical developments and has been applied in various domains, such as maximizing power generation from wind turbines. This talk will begin by revisiting the history of extremum seeking control and explaining the fundamentals of how ESC functions. It will then delve into recent advancements, including several design frameworks. The final section will specifically focus on model-guided ESC in human-prosthetic interfaces. This innovative application utilizes model-based approaches to enhance the interaction between humans and prosthetic devices, aiming to improve both performance and user experience.

We consider data-driven methods for modeling discrete-valued dynamical systems evolving over networks. The spread of viruses and diseases, the propagation of ideas and misinformation, the fluctuation of stock prices, and correlations of financial risk between banking and economic institutions are all examples of such systems. In many of these systems, data may be widely available, but approaches to identify relevant mathematical models, including the underlying network topology, are not widely established or agreed upon. Classic system identification methods focus on identifying continuous-valued dynamical systems from data, where the main analysis of such approaches largely focuses on asymptotic properties, i.e., consistency. More recent identification approaches have focused on sample complexity, i.e., how much data is needed to achieve an acceptable model approximation. In this talk, we will discuss the problem of identifying a mathematical model from data for a discrete-valued, discrete-time dynamical system evolving over a network. Specifically, under maximum likelihood estimation approaches, we will demonstrate guaranteed consistency conditions and sample complexity bounds. Applications to the aforementioned examples will be further discussed as time allows.

The study of epidemic processes has been of interest over a wide range of fields for the past century, including in mathematical systems, biology, physics, computer science, social sciences and economics. Recently there has been renewed interest in the study of epidemic processes focused on the spread of viruses over networks, motivated not only by recent outbreaks of infectious diseases, but also by the rapid spread of opinions over social networks, and the security threats posed by computer viruses. In this talk we will discuss modeling and convergence analysis results for epidemic processes over both static and time-varying networks, with the goal being to elucidate the behavior of such spread processes. Multi-strain models, and issues arising from epidemic modeling and prediction based on the use of data from ongoing viral outbreaks will also be discussed as time allows. Simulation results and potential mitigation actions will be reviewed to conclude the talk.

We consider the problem of clustering data sets where the data points are dynamic, or essentially time-varying. Our approach is to incorporate features of both the deterministic annealing algorithm as well as control theoretic methods in our computational solution. Extensions of our method can be made to the problem of aggregating time-varying graphs, for which we have developed a quantitative measure of dissimilarity that allows us to compare directed graphs of differing sizes. In this talk, an overview of our dynamic clustering algorithm will be given, along with some analysis of the algorithm properties. We will conclude with a few highlighted applications, and further extensions as time allows.

Evolutionary dynamics in large populations of decision-making autonomous agents have become a powerful model to study complex interactions in natural, social, economic and engineering systems. In this talk I focus on showing how evolutionary game theoretic models can be studied using systems and control theory. We look into how feedback actions can be incorporated and demonstrate that the closed-loop population dynamics may exhibit drastically different collective outcomes.

Team movement control, including navigation and path-following, are fundamental functions for mobile robots carrying out environmental monitoring and sampling tasks. New challenges arise when control algorithms have to be designed for a team of robots with limited communication capacity and the environment may contain obstacles. In this talk, I show how to design guiding vector fields to enable motion coordination among robots; I also show how to construct composite guiding vector fields to avoid colliding with obstacles of arbitrary shapes. Both theoretical guarantees and experimental validations are discussed for practical scenarios.

Distributed control is a classical research topic. While a rich theory is available, some assumptions such as availability of subsystem dynamics and topology and the subsystems following the prescribed controllers exactly have proven difficult to remove. An interesting direction in recent times to get away from these assumptions has been the utilization of learning for control. In this talk, we consider some problems in control design for distributed systems using learning. Our core message is that utilizing control-relevant properties in learning algorithms can not only guarantee concerns such as stability, performance, safety, and robustness that are important in control of physical systems, but also help with issues such as data sparsity and sample complexity that are concerns during the implementation of learning algorithms.

Fluid-like models, such as the Lighthill-Whitham-Richards (LWR) model and their discretizations like Daganzo’s Cell Transmission Model (CTM), have proven successful in modeling traffic networks. In general, these models are not linear; they employ discontinuous dynamics or nonlinear terms to describe phenomena like shock waves and phantom jams. Given the complexity of the dynamics, it is not surprising that the stability properties of these models are not yet well characterized. Recent results have shown the existence of a unique equilibrium in the free flow regime for certain classes of networks modeled by the CTM; however, these results restrict inflows to the system to be bounded or constant. Further, it is of interest to understand the system behavior in congested regimes since links in various practical networks are often congested.

Many learning algorithms have been proposed for design of control policies in cooperative and competitive multi-agent systems. We explore the robustness of some such algorithms to the presence of strategic agents. First, we show that some recently proposed multi-agent reinforcement learning algorithms are vulnerable to being hijacked by even one agent that prioritizes individual utility function over the team utility function and propose a way to make the algorithms robust to such attacks. Then we consider a game set up in which agents are employing a fictitious play-based learning algorithm and show that an agent can move the game to a more favorable equilibrium by deviating from the prescribed algorithm.

This lecture will survey the area of quantum control engineering. It will discuss models for quantum systems using both the Schrodinger and Heisenberg pictures of quantum mechanics including finite level quantum systems and continuous linear quantum systems. It will also discuss the open loop quantum control of quantum systems including robust and learning based approaches. In addition, it will discuss closed loop approaches to quantum control including measurement based feedback control and quantum filtering along with coherent quantum feedback control in which the controller is also a quantum system. In the area of coherent control of quantum linear quantum systems, it will discuss quantum H-infinity control, quantum LQG control and coherent quantum observers and coherent quantum state estimation. The lecture will also cover the quantum Kalman decomposition. Applications in the areas of quantum optics and quantum electromechanical systems will be presented.

This lecture presents a survey of some of the main results in the theory of negative imaginary systems. The lecture also presents some applications of negative imaginary systems theory in the design of robust controllers. In particular, the lecture concentrates on the application of negative imaginary systems theory in the area of control of atomic force microscopes.