# Sensitivity-based Warmstarting for Nonlinear Model Predictive Control with Polyhedral State and Control Constraints

## TL;DR

This paper presents a sensitivity-based warmstarting method for nonlinear MPC with polyhedral constraints, significantly reducing computation time by predicting solution changes without strict assumptions, demonstrated on UAV control.

## Contribution

It introduces a novel warmstarting strategy leveraging semiderivatives for nonlinear MPC with polyhedral constraints, avoiding constraint qualification assumptions.

## Key findings

- Reduces MPC computation time significantly.
- Applicable to systems with nonlinear dynamics and polyhedral constraints.
- Validated on unmanned aerial vehicle control scenarios.

## 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 mapping. The main novelty of the paper 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.