Optimal control of constrained piecewise affine systems with state- and input-dependent disturbances∗

Finite horizon optimal control of piecewise affine systems with a piecewise affine (1-norm or ∞-norm) stage cost and terminal cost is considered. Provided the respective constraint sets are given as the unions of polyhedra, it is shown that the partial value functions and partial optimal control laws are piecewise affine on a polyhedral cover of the set of states that can be steered, by an admissible control policy, to a terminal set of states in a finite number of steps. Existing results only consider the case of systems without disturbances, or systems with disturbances that are independent of the state and input. This paper extends these results to the case where the disturbance is dependent on the state and input.

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