Approximate off-line receding horizon control of constrained nonlinear discrete-time systems: Smooth approximation of the control law

In this work, the off-line approximation of state-feedback nonlinear model predictive control laws by means of smooth functions of the state is addressed. The idea is to investigate how the approximation errors affect the stability of the closed-loop system, in order to derive suitable bounds which have to be fulfilled by the approximating function. This analysis allows to conveniently set up the characteristic parameters of some techniques such as Neural Networks which can be used to implement the control law, in order to render the system Input-to-State Practically Stable while satisfying, in addition, hard constraints on the trajectories; both the amount of data storage and the computational time result strongly reduced with respect to Nearest Neighbor or Set Membership approaches, which have been recently proposed to obtain effective off-line approximation of nonlinear MPC. The provided simulations confirm the validity of the method.