Constrained Quadratic Control of Discrete-Time Piecewise Affine Systems

An increasing sequence of symbolic models of the piecewise affine plant are obtained in the order of increasing fidelity. Each of these models leads to a dynamic programming-like synthesis condition for a stabilizing state-feedback controller that satisfies a quadratic performance bound for the plant. The synthesis condition accommodates the user's willingness to trade off the size of the stable invariant set and the length of the decision horizon against computational complexity, and yet is capable of approaching the optimal performance in the limit as the user spends increasing amounts of computation.