Near-optimal control with adaptive receding horizon for discrete-time piecewise affine systems

We consider the infinite-horizon optimal control of discrete-time, Lipschitz continuous piecewise affine systems with a single input. Stage costs are discounted, bounded, and use a 1 or ∞-norm. Rather than using the usual fixed-horizon approach from model-predictive control, we tailor an adaptive-horizon method called optimistic planning for continuous actions (OPC) to solve the piecewise affine control problem in receding horizon. The main advantage is the ability to solve problems requiring arbitrarily long horizons. Furthermore, we introduce a novel extension that provides guarantees on the closed-loop performance, by reusing data (“learning”) across different steps. This extension is general and works for a large class of nonlinear dynamics. In experiments with piecewise affine systems, OPC improves performance compared to a fixed-horizon approach, while the data-reuse approach yields further improvements.