Approximate off-line receding horizon control of constrained nonlinear discrete-time systems

The present paper concerns the design of approximate off-line model predictive control laws for nonlinear discrete-time systems subject to hard constraints on state and input variables. The possibility to obtain an approximate receding horizon control law by performing off-line optimization, leads to a dramatic reduction of the real-time computational complexity with respect to on-line algorithms, and allows the application of the developed control technique to plants with fast dynamics, that require small sampling periods. The main feature of the proposed approximation scheme consists in the possibility to cope with possibly discontinuous state-feedback control laws, while guaranteeing the fulfillment of hard constraints on state and input variables despite the perturbations due to the use of an approximate controller. Finally, the resulting closed-loop system is shown to be input-to-state-stable with respect to the approximation-induced perturbations.