Explicit feasible initialization for nonlinear MPC with guaranteed stability

We present a method for the computation of control invariant (c.i.) sets and a simple suboptimal explicit controller for a large class of constrained nonlinear discrete time systems. The explicit controller provides, for any point in the c.i. set, a finite sequence of input values that drive the system to the origin. These input sequences may serve as feasible initializations for the nonlinear program (NLP) associated to nonlinear model predictive control (NMPC). The proposed method is a straightforward extension of an existing method for the computation of c.i. sets, which we augment by a mechanism to record feasible control actions. In contrast to existing explicit NMPC approaches, the explicit control law is calculated without solving the underlying NLP. The method is computationally expensive, but most of the computational effort can be moved offline, and the evaluation of the resulting explicit controller is quite fast.