A nonlinear model predictive control algorithm with proven robustness and resolvability

A robustly stabilizing MPC (model predictive control) algorithm with guaranteed resolvability is developed for uncertain nonlinear systems. With resolvability, initial feasibility of the finite-horizon optimal control problem implies future feasibility in a receding-horizon framework. The control consists of two components; (i) feedforward; and (ii) feedback. Feedforward control and the associated nominal trajectory are obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line, based on a bound on the model uncertainty. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives and derivatives in polytopes. An illustrative numerical example is also provided