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.