Model predictive control for continuous piecewise affine systems using optimistic optimization

This paper considers model predictive control for continuous piecewise affine (PWA) systems. In general, this leads to a nonlinear, nonconvex optimization problem. We introduce an approach based on optimistic optimization to solve the resulting optimization problem. Optimistic optimization is based on recursive partitioning of the feasible set and is characterized by an efficient exploration strategy seeking for the optimal solution. The advantage of optimistic optimization is that one can guarantee bounds on the suboptimality with respect to the global optimum for a given computational budget. The 1-norm and ∞-norm objective functions often considered in model predictive control for continuous PWA systems are continuous PWA functions. We derive expressions for the core parameters required by optimistic optimization for the resulting optimization problem. By applying optimistic optimization, a sequence of control inputs is designed satisfying linear constraints. A bound on the suboptimality of the returned solution is also discussed. The performance of the proposed approach is illustrated with a case study on adaptive cruise control.