Sensitivity-Based Warmstarting for Nonlinear Model Predictive Control With Polyhedral State and Control Constraints

Model predictive control (MPC) is of increasing interest in applications for constrained control of multivariate systems. However, one of the major obstacles to its broader use is the computation time and effort required to solve a possibly nonconvex optimal control problem (OCP) online. This article introduces a sensitivity-based warmstarting strategy for systems with nonlinear dynamics and polyhedral constraints with the goal of reducing the computational footprint of MPC controllers. It predicts changes in the solution of the parameterized OCP as the parameter varies by calculating the semiderivative of the solution mapping. The main novelty of this article is that the polyhedrality of the constraints allows us to avoid imposing any constraint qualification conditions or strict complementarity assumptions. A numerical study featuring MPC applied to unmanned aerial vehicles illustrates the proposed approach.