An efficient bounded-variable nonlinear least-squares algorithm for embedded MPC

TL;DR

This paper introduces a memory-efficient, adaptable active-set algorithm for solving linear and nonlinear MPC problems in real-time embedded systems, eliminating the need for problem re-construction at runtime.

Contribution

It proposes a unified, bounded-variable active-set method that handles various MPC types without re-deriving problem matrices, improving efficiency and adaptability.

Findings

The algorithm reduces memory and computational requirements for embedded MPC.

It effectively handles linear, nonlinear, and adaptive MPC variants.

Numerical results confirm its suitability for real-time applications.

Abstract

This paper presents a new approach to solve linear and nonlinear model predictive control (MPC) problems that requires small memory footprint and throughput and is particularly suitable when the model and/or controller parameters change at runtime. Typically MPC requires two phases: 1) construct an optimization problem based on the given MPC parameters (prediction model, tuning weights, prediction horizon, and constraints), which results in a quadratic or nonlinear programming problem, and then 2) call an optimization algorithm to solve the resulting problem. In the proposed approach the problem construction step is systematically eliminated, as in the optimization algorithm problem matrices are expressed in terms of abstract functions of the MPC parameters. We present a unifying algorithmic framework based on active-set methods with bounded variables that can cope with linear, nonlinear, and adaptive MPC variants based on a broad class of prediction models and a sum-of-squares cost function. The theoretical and numerical results demonstrate the potential, applicability, and efficiency of the proposed framework for practical real-time embedded MPC.