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

Abstract

Model predictive control (MPC) is of increasing interest in applications for constrained control of multivariable systems. However, one of the major obstacles to its broader use is the computation time and effort required to solve a possibly non-convex optimal control problem (OCP) online. This paper 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. We apply the theory of variational inequalities over polyhedral convex sets, thus avoiding restrictive conditions regarding the activity status of the constraints. A numerical study featuring MPC applied to unmanned aerial vehicles illustrates the proposed approach.