Stabilizing predictive controller for singular systems

Developing the model predictive controllers (MPC) for singularly perturbed systems is an important and challenging problem. In this paper we derive sufficient conditions for exponentially stabilizing MPC for a family of singularly perturbed liner time-varying (LTV) systems. A min-max MPC approach is employed to compute the optimal time-varying input vector subject to constraints and uncertainties. More specifically, the set of admissible control signals is calculated by minimizing the upper bound of a cost function along the finite horizon for the worst case scenario with respect to the input uncertainties. The optimality itself does not necessarily imply stability. Therefore, the purpose of this paper is twofold. First we derive the conditions that would guarantee the stability of the multi-scales dynamics. Second, the stability conditions are introduced into the optimization problem to compute the input signal in optimization performed over the defined set of constraints.