Explicit multiobjective model predictive control for nonlinear systems with symmetries

TL;DR

This paper extends explicit model predictive control to nonlinear systems with multiple conflicting objectives by building a Pareto optimal solution library offline, exploiting symmetries, and interpolating solutions online for fast decision-making.

Contribution

It introduces a novel approach combining multiobjective MPC, symmetry exploitation, and solution interpolation for nonlinear systems.

Findings

Library of Pareto optimal solutions created offline

Symmetry exploitation reduces offline computational effort

Method verified on autonomous driving examples

Abstract

Model predictive control is a prominent approach to construct a feedback control loop for dynamical systems. Due to real-time constraints, the major challenge in MPC is to solve model-based optimal control problems in a very short amount of time. For linear-quadratic problems, Bemporad et al.~have proposed an explicit formulation where the underlying optimization problems are solved a priori in an offline phase. In this article, we present an extension of this concept in two significant ways. We consider nonlinear problems and -- more importantly -- problems with multiple conflicting objective functions. In the offline phase, we build a library of Pareto optimal solutions from which we then obtain a valid compromise solution in the online phase according to a decision maker's preference. Since the standard multi-parametric programming approach is no longer valid in this situation, we instead use interpolation between different entries of the library. To reduce the number of problems that have to be solved in the offline phase, we exploit symmetries in the dynamical system and the corresponding multiobjective optimal control problem. The results are verified using two different examples from autonomous driving.