Trade-offs between precision and computation horizon in real-time optimal control of switched systems

In this paper the problem of real-time optimal control is considered. In particular, we will study dynamical systems that switch between different modes at controlled switching times. Ideally, one would want the switching controller to provide sufficiently good values for the switching times at every instant of time. However, due to the limited computational resources available in many real-time applications, questions concerning trade-offs between the computation horizon and the precision of the solution arise naturally. These trade-offs constitute the main focus of this paper, and a solution will be provided based on the minimization of a conservative bound on the error between the true gradient and the gradient obtained in real-time