Stabilizing receding-horizon control of nonlinear time-varying systems

A receding horizon control scheme for nonlinear time-varying systems is proposed which is based on a finite-horizon optimization problem with a terminal state penalty. The penalty is equal to the cost that would be incurred over an infinite horizon by applying a (locally stabilizing) linear control law to the nonlinear system. Assuming only stabilizability of the linearized system around the desired equilibrium, the new scheme ensures exponential stability of the equilibrium. As the length of the optimization horizon goes from zero to infinity, the domain of attraction moves from the basin of attraction of the linear controller toward the basin of attraction of the infinite-horizon nonlinear controller. Stability robustness in the face of system perturbations is also established.