Set Membership approximation of discontinuous NMPC laws

In this paper, the use of set membership (SM) approximation methods is investigated, in order to derive a fast implementation of discontinuous nonlinear model predictive control (NMPC) laws. It is shown that the knowledge of the discontinuities is needed in order to achieve an approximated controller with guaranteed and arbitrary small approximation error. Exploiting such a knowledge, SM techniques already developed in previous works for the continuous case are generalized to approximate discontinuous NMPC. Thus, the proposed techniques can be applied to a very general class of predictive control laws, since neither convexity of the optimal cost function nor continuity of the exact NMPC law are assumed. The stability of the closed loop system with the approximated control law is also analyzed. An inverted pendulum example is employed to show the effectiveness of the proposed approach.