Set membership approximation of discontinuous nonlinear model predictive control laws

In this paper, the use of Set Membership (SM) methods is investigated, in order to derive off-line an approximation of a discontinuous nonlinear model predictive control (NMPC) law. The approximating function can then be evaluated on-line, instead of solving the nonlinear program embedded in the NMPC scheme. This way, a significant decrease of computational times may be obtained, thus allowing the application of NMPC also to systems with “fast” dynamics. It is shown that the knowledge of the discontinuities is needed to achieve an approximated controller with arbitrarily small approximation error. By exploiting such a knowledge, SM techniques already developed for the case of continuous NMPC laws are generalized in order to approximate discontinuous ones. The stability of the origin of the closed loop system with the approximated control law is analyzed, and a numerical example is employed to illustrate the features of the proposed approach.