Constrained receding horizon controls for nonlinear time-delay systems

This paper proposes a constrained receding horizon control (RHC) for a nonlinear time-delay system with input and state delays. The control law is obtained by minimizing a receding horizon cost function with weighting functions of inputs and states on the end portion of the horizon. For stability, a general condition on the weighting functions is presented and its feasibility is illustrated via a certain type of nonlinear time-delay systems. In order to deal with input and state constraints, an invariant set is obtained, where the trajectories of the inputs and the states satisfy given constraints and stay forever under some conditions. It is shown in a numerical example that the proposed RHC guarantees the closed-loop stability for nonlinear time-delay systems while meeting the constraints.