Recent technological innovations have caused a considerable interest in the study of dynamical processes having a heterogeneous continuous and discrete nature. Such hybrid systems are characterized by the interaction of continuous parts, governed by differential or difference equations, and by discrete parts, described by finite state machines, if-then-else rules, propositional and temporal logic. Hybrid systems switch between many operating modes where each mode is governed by its own characteristic dynamical laws. Mode transitions are triggered by variables crossing specific thresholds (state events), by the elapse of certain time periods (time events), or by external inputs (input events). Typical hybrid systems are embedded systems, constituted by dynamical components governed by logical/discrete decision components. Application areas of hybrid systems include automotive, manufacturing, communication networks, aerospace, robotics, traffic control, and chemical processes. Hybrid systems require interdisciplinary approaches exploiting formal methods in computer science, control theory, operations research.
General theories and tools for controller synthesis, verification, stability and performance analysis of hybrid systems are still under continuous development, which makes hybrid systems an exciting area for researchers in control.
Recently, it was demonstrated that advanced control algorithms, such as model predictive control (MPC), yield hybrid control laws. Current research in this area deals with approximation of MPC control laws via simpler, hybrid feedback laws that can meet real-time specifications for high-tech applications, such as automotive, aerospace and power electronics.
The main scientific events related to hybrid systems are the "Hybrid Systems: Computation and Control" (HSCC) Conference, and the "Analysis and Design of Hybrid Systems" (ADHS) Conference. In addition, several invited sessions are organized routinely at major control conferences, such as the IEEE Conference on Decision and Control. Another scientific event relevant to hybrid systems is the “International Workshop on Nonlinear Model Predictive Control” (NMPC), where a special focus is dedicated to synthesis and implementation of piecewise affine hybrid control laws.
To learn more about the subject of hybrid systems, didactic material is available from the two schools 1st HYCON PhD School on Hybrid Systems and 2nd HYCON PhD School on Hybrid Systems. Furthermore, a comprehensive overview of hybrid dynamics and control theory is available within the April 2009 issue of the IEEE Control Systems Magazine.
For more information about academic and industrial research groups currently active on hybrid systems and additional technical resources please visit the web page (an updated version of the HYSCOM website is under construction) http://www.dii.unisi.it/~hybrid/ieee.