University of Cambridge > Talks.cam > CUED Control Group Seminars > Minkowski, Lyapunov, and Bellman: Inequalities and Equations for Stability and Optimal Control

Minkowski, Lyapunov, and Bellman: Inequalities and Equations for Stability and Optimal Control

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The algebraic 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 case of Lyapunov equation and providing optimality in case of Bellman equation. Rather peculiarly, very little had been known about Lyapunov and Bellman equations, and inequalities, within space of Minkowski functions of nonempty convex compact subsets containing the origin in their interior prior to my work in the area. Key results of my related research on these fundamental problems have provided characterization of solutions to both Lyapunov and Bellman equations within space of Minkowski functions, referred to as the Minkowski–Lyapunov and Minkowski–Bellman equations. The talk outlines key results underpinning these two fundamental equations and related inequalities, and draws parallel to classical results on algebraic Lyapunov and Bellman equations and inequalities.

This talk is part of the CUED Control Group Seminars series.

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