Optimizing Online Control of Constrained Systems with Switched Dynamics

This paper studies the online control of switched systems over a finite time horizon subject to time-varying constraints on the continuous states and bounded input set. The formulation leads to optimization problems of the class mixedinteger nonlinear programming (MINLP), which is known to be computationally hard. This paper proposes a method to approximate the optimal solution while keeping the computational effort low enough, to enable real-time applicability for many systems. The main idea is to use heuristics based on the value function for relaxed sub-problems to prune the tree encoding the possible sequences of discrete choices (i.e. the selected continuous dynamics) over a prediction horizon. Numeric tests show that the times for computation are drastically below those for standard MINLP solution in the vast majority of cases, while good approximations of the optimal solutions are obtained.