A combined multi-parametric and dynamic programming approach for model predictive control of hybrid linear systems

This work presents a methodology to derive explicit control laws for hybrid linear systems. The proposed method employs multi-parametric and dynamic programming techniques to dissemble the original MPC formulation into a set of smaller problems, which can be efficiently solved using suitable multi-parametric mixed integer programming algorithms. The solution comprises the envelope of explicit piece-wise affine control laws defined over a set of convex critical regions. The proposed developments are demonstrated in an example of the optimal control of a piece-wise affine system with a quadratic objective function.