Efficient Zero-Order NMPC with Feasibility and Stability Guarantees

This paper discusses systems theoretic and computational aspects of a feasible, but suboptimal, nonlinear model predictive control scheme based on fixed sensitivities of the functions representing the constraints and cost of the underlying nonlinear programs. In particular, it will be shown how, by freezing the sensitivities computed at the desired steady state of the system, an efficient, structure-exploiting scheme is obtained that can considerably speed up the computations required for both construction and solution of the quadratic subproblems. Moreover, the local stability properties of the converged solution are analysed using results on pseudoexpansions of generalized equations present in the literature. The effectiveness of the proposed scheme is demonstrated on a non-trivial benchmark where large speedups can be achieved.