Feedback Solution to Optimal Switching Problems with Switching Cost

Many real-world control problems can be classified as switching problems in the sense that the system subject to control is comprised of several different modes (sometimes called subsystems) and at each instant only one of the modes can be active. A basic example of such a system is a plant equipped with on-off actuators [1]. The solution to such problems includes a switching schedule which determines the number of switching, the switching instants, and the order of the active subsystems. The developments in the field of optimal switching can be divided into different categories, two of which are nonlinear programming based methods and discretization based methods. Nonlinear programming based methods utilize the gradient of the cost with respect to the switching instants to calculate local optimal switching times using nonlinear programming [2]-[9]. In these methods, the sequence of active subsystems, known as the mode sequence, is typically selected a priori. The problem is then simplified to determining the switching instants between the modes. Discretization based methods, however, discretize the state and input space to end up with a finite number of choices [10], [11]. Among the intelligent approaches to the problem, genetic algorithm and neural networks were used in Refs.