Reachability computations for constrained discrete-time systems with state-and input-dependent disturbances

This paper presents new results that permit the computation of the set of states that can be robustly steered, using state feedback, to a given target set in a finite number of steps. It is assumed that the system is discrete-time, nonlinear, time-invariant and subject to mixed constraints on the state and input. A persistent disturbance, dependent on the current state and input, acts on the system. The results in this paper generalize previously published results that are not able to address state-input dependent disturbances. The application of the results to the computation of the maximal robustly controlled invariant set is briefly discussed. It is shown how polyhedral algebra, linear programming and computational geometry may be employed for set computations relevant to the analysis of linear and piecewise affine systems with additive state disturbances. Some simple examples are given to demonstrate that convexity of the robustly controllable sets cannot be guaranteed even if all relevant sets are convex and the system is linear.