Strongly convex attainable sets and low complexity finite-state controllers

We present several novel results related to the concept of strong convexity, culminating in sufficient conditions for attainable sets of continuous-time nonlinear dynamical systems to be strongly convex. Based on these results, we propose a method to over-approximate attainable sets by intersections of supporting balls, which greatly improves upon the accuracy of previously proposed approximations based on supporting halfspaces. The latter advantage can be exploited, for example, when the method is used in algorithms that compute discrete abstractions of continuous plants. As we demonstrate by an example, the design of finite-state controllers can then be based on coarser state space quantizations, which directly translates into a reduced complexity of the controllers.