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Reachability analysis of dynamic programming based controlled systems: An extended algorithm

This paper extends the algorithm proposed in [1]. In [1], the numerical approximation of the solution of dynamic programming problems is used as a candidate Lyapunov function VL(x), in order to prove convergence of the closed loop system to a given target. That is done in the framework of sampled data systems. The described algorithm provides only a sufficient condition, which in many cases is not verified due to the deviations introduced by the approximations. In this paper, the previous algorithm is extended in order to compute the decrease in the candidate Lyapunov over multiple sampling periods, i.e., VL(x(k + n)) - VL(x(k)), with n ϵ N. Thus, it is expected that the verification procedure becomes more robust with respect to the deviations introduced by the numerical approximation of the control law and candidate Lyapunov function. The core of the algorithm is based on linear programming with polytopic convex constraints.