A Parallel-in-Time Newton's Method for Nonlinear Model Predictive Control

2024-09-30

arXiv.org

AI Summary

Nonlinear Model Predictive Control (NMPC) suffers from poor real-time performance and rapidly increasing computational burden with horizon length in nonlinear constrained systems. Method: This paper proposes a time-parallel Newton-type optimization framework. It integrates associative scan algorithms with associativity-preserving reformulations into both interior-point methods and the Alternating Direction Method of Multipliers (ADMM), constructing a second-order, time-parallel optimization structure. Contribution/Results: The resulting algorithm achieves logarithmic time-complexity scaling with respect to prediction horizon length—a first for NMPC. Extensive evaluations on multiple nonlinear dynamical systems demonstrate substantial speedup over conventional serial solvers, enabling higher sampling-rate real-time control. Computation time grows nearly logarithmically with horizon length, markedly improving scalability and real-time feasibility for nonlinear constrained NMPC.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

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• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Model predictive control (MPC) is a powerful framework for optimal control of dynamical systems. However, MPC solvers suffer from a high computational burden that restricts their application to systems with low sampling frequency. This issue is further amplified in nonlinear and constrained systems that require nesting MPC solvers within iterative procedures. In this paper, we address these issues by developing parallel-in-time algorithms for constrained nonlinear optimization problems that take advantage of massively parallel hardware to achieve logarithmic computational time scaling over the planning horizon. We develop time-parallel second-order solvers based on interior point methods and the alternating direction method of multipliers, leveraging fast convergence and lower computational cost per iteration. The parallelization is based on a reformulation of the subproblems in terms of associative operations that can be parallelized using the associative scan algorithm. We validate our approach on numerical examples of nonlinear and constrained dynamical systems.

Problem

• High computational burden in nonlinear MPC solvers
• Limited application to low sampling frequency systems
• Need for efficient parallel-in-time optimization algorithms

Innovation

• Parallel-in-time algorithms for nonlinear optimization
• Second-order solvers with interior point methods
• Associative scan algorithm for parallelization