An MPC scheme with guaranteed stability for linear singularly perturbed systems

In this paper the formulation and stability of a double-layer model predictive control algorithm is presented. This control scheme guarantees the stability of the closed-loop system, for regulating a stabilizable linear singularly perturbed system to the steady-state. The controller has a two-level hierarchical structure acting on the two different time scales of the system. On each level, the controller has a quasi-infinite horizon structure: The objective function to be minimized in both cases consists of an integral squared error over a finite horizon plus a quadratic terminal state cost. Furthermore the optimization problem includes a terminal inequality constraint, that forces the final state into a predefined neighborhood of the origin, where the cost-to-go is upper bounded by the terminal state cost. The approach aims at reducing the computational load and the ill-conditioning for stiff problems.