Optimal control of uncertain piecewise affine/mixed logical dynamical systems

This paper proposes an approach to extend the mixed logical dynamical modelling framework for synthesizing robust optimal control actions for constrained piecewise affine systems subject to bounded additive input disturbances. Rather than using closed-loop dynamic programming arguments, robustness is achieved here with an open-loop optimization strategy, such that the optimal control sequence optimizes nominal performance while robustly guaranteeing that safety/performance constraints are respected. The proposed approach is based on the robust mode control concept, which enforces the control input to generate trajectories such that the mode of the system, at each time instant, is independent of the disturbances.