Globally robust explicit model predictive control of constrained systems exploiting SVM-based approximation

This paper presents a systematic method to address the reduction of online computational complexity and infeasibility problem of explicit model predictive control for constrained systems under external disturbance. In feasible state space, in order to avoid the expensive database searching procedure, support vector machine-based approximation is proposed to yield a novel unified explicit optimal control law rather than a piecewise affine one developed by explicit model predictive control. In infeasible state space, through constructing finite maximum control invariant sets around fictitious equilibrium points, a reachable controller is devised to steer the infeasible state asymptotically to the feasible state space without violating the hard constraint. Consequently, global robustness is guaranteed by introducing a minimum robust positively invariant set by means of the tube-based technique, despite the coexistence of external disturbance and training error. Finally, the performance of the presently proposed control law is evaluated through three groups of numerical examples.