Abstract:

The classical Lyapunov and Bellman equations, and inequalities, are cornerstone objects in linear systems theory. These equations, and inequalities, are concerned with convex quadratic functions verifying stability in cases of the Lyapunov equation and inequalities as well as optimality and stability in cases of the Bellman equation and inequalities. Rather peculiarly, prior to my work in the area, very little had been known about the related Lyapunov and Bellman equations, and inequalities, within the space of the Minkowski functions of nonempty convex compact subsets containing the origin in their interior. My recent research has provided complete characterizations of the solutions to the Lyapunov and Bellman equations, and inequalities, within the space of the Minkowski functions, referred to as the Minkowski–Lyapunov and Minkowski–Bellman equations, and inequalities, respectively. The talk reports key results underpinning the study of these fundamental equations and inequalities and their generalizations. The talk also renders strong evidence of topological flexibility and theoretical correctness of the developed frameworks and consequent advantages over the traditional Lyapunov and Bellman equations and inequalities.

Speaker Bio:

Saša V. Raković received the Ph.D. degree in Control Theory from Imperial College London. His Ph.D. research was awarded the Eryl Cadwaladr Davies Prize 2005 as the best PhD thesis in the EEE Department of Imperial College. Saša V. Raković has been affiliated with several well known international universities, including, inter alia, Imperial College London, ETH Zürich, Oxford University, UMD at College Park, UT at Austin and Texas A&M University at College Station. He is currently a full Professor at Beijing Institute of Technology, Beijing. His research interests and activity span broad areas of artificial intelligence, autonomy, controls, dynamics, systems, applied mathematics, optimization, and set-valued analysis. His research is driven by mathematical problems that belong to the intersection of artificial intelligence, controls, dynamics, systems, and optimization. Saša V. Raković has, together with William S. Levine, edited a well-received “Handbook of Model Predictive Control” published by Springer Nature. Saša V. Raković has authored 120 publications, most of which are highly cited (i.e., about 8000 citations according to Google Scholar) and are published in leading international journals and proceedings of key conferences in the fields of control theory and engineering. Saša V. Raković’s research has made contributions to theory, computation, and implementation of conventional, robust and stochastic model predictive control, and he is best known as one of the key contributors to the tube model predictive control framework.