Multi-Phase Optimal Control Problems for Efficient Nonlinear Model Predictive Control with acados

TL;DR

This paper presents a new multi-phase optimal control interface for acados, enabling efficient formulation and solution of nonlinear model predictive control problems with flexible approximations, improving computational efficiency and control performance.

Contribution

The work introduces a novel multi-phase OCP interface for acados that simplifies formulation and enhances efficiency for NMPC, incorporating advanced control parametrizations and multi-fidelity models.

Findings

Multi-phase formulations enable efficient NMPC with reduced computation time.

The new interface supports advanced control parametrizations like piecewise polynomials.

Numerical experiments show improved trade-offs between control performance and computational effort.

Abstract

Computationally efficient nonlinear model predictive control relies on elaborate discrete-time optimal control problem (OCP) formulations trading off accuracy with respect to the continuous-time problem and associated computational burden. Such formulations, however, are in general not easy to implement within specialized software frameworks tailored to numerical optimal control. This paper introduces a new multi-phase OCP interface for the open-source software acados allowing to conveniently formulate such problems and generate fast solvers that can be used for nonlinear model predictive control (NMPC). While multi-phase OCP (MOCP) formulations occur naturally in many applications, this work focuses on MOCP formulations that can be used to efficiently approximate standard continuous-time OCPs in the context of NMPC. To this end, the paper discusses advanced control parametrizations, such as closed-loop costing and piecewise polynomials with varying degree, as well as partial tightening and formulations that leverage models of different fidelity. An introductory example is presented to showcase the usability of the new interface. Finally, three numerical experiments demonstrate that NMPC controllers based on multi-phase formulations can efficiently trade-off computation time and control performance.