Efficient approximate robust MPC based on quad-tree partitioning

Recently, the approximate solutions to the infinite horizon min-max model predictive control with a time-varying terminal cost and constraint have been explicitly characterized in the form of a piecewise affine (PWA) state feedback law defined on an orthogonal partition of the state-space [13]. The advantage of this formulation is the reduction in on-line computational complexity which amounts to the evaluation of a PWA function in the control unit. This paper extends the authors work in [13]. In order to accommodate a wider class of systems, a nominal performance cost is chosen to substitute the "worst-case" one in the existing MPC technique. Robust exponential stability of the controller is established by means of satisfaction of certain linear matrix inequalities (LMIs). The proposed approach is applied to control a current loop of a permanent-magnet synchronous motor (PMSM) and an uncertain double integrator.