On-Line Optimization of Switched-Mode Dynamical Systems

This paper considers an optimization problem in the setting of switched-mode hybrid dynamical systems, where the control variable (independent variable) consists of the mode-switching times, and the performance criterion is a cost functional defined on the system´s state trajectory. The system is deterministic, nonlinear, and autonomous, and its state variable cannot be measured and hence it has to be estimated. We propose an on-line, Newton-like optimization algorithm that recomputes the control variable by attempting to optimize the cost-to-go at equally-spaced epochs. The main result concerns the algorithm´s convergence rate, which can vary from sublinear to quadratic depending on its computing rate and the state estimation error.