Patchy approximate explicit model predictive control

Multiparametric quadratic programming (MPQP) can be used to construct an off-line solution to constrained linear model predictive control. The result is a piecewise linear state feedback defined over polyhedral cells of the state space. However, with high dimensional problems, coding and implementation of this solution may be very burdensome for the available hardware, due to the high number of polyhedral cells in the state space partition. In this paper we provide an algorithm to find an approximate solution to MPQP, which is obtained by linear interpolation of the exact solution at the vertices of a feasible set and the solution of linear quadratic(LQ) problem. Based on a patchy control technique, we assure robust closed loop stability in the presence of additive measurement noise despite the presence of discontinuities at the switch between the regions in the state space partition.