Stabilization of nonlinear time-varying systems via receding-horizon control

A new stabilizing nonlinear Receding-Horizon (RH) control scheme for nonlinear time-varying systems is proposed which is based on a Finite-Horizon (FH) 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. Robustness properties in the face of gain, additive and general perturbations are established.