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.@en

This paper addresses the infinite-horizon optimal control problem for max-plus linear systems where the considered objective function is a sum of discounted stage costs over an infinite horizon. The minimization problem of the cost function is equivalently transformed into a maximization problem of a reward function. The resulting optimal control problem is solved based on an optimistic planning algorithm. The control variables are the increments of system inputs and the action space is discretized as a finite set. Given a finite computational budget, a control sequence is returned by the optimistic planning algorithm. The first control action or a subsequence of the returned control sequence is applied to the system and then a receding-horizon scheme is adopted. The proposed optimistic planning approach allows us to limit the computational budget and also yields a characterization of the level of near-optimality of the resulting solution. The effectiveness of the approach is illustrated with a numerical example. The results show that the optimistic planning approach results in a lower tracking error compared with a finite-horizon approach when a subsequence of the returned control sequence is applied.@en