A Parallel-in-Time Newton's Method for Nonlinear Model Predictive Control
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912268984254464 |
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| author | Iacob, Casian Abdulsamad, Hany Särkkä, Simo |
| author_facet | Iacob, Casian Abdulsamad, Hany Särkkä, Simo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20027 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Parallel-in-Time Newton's Method for Nonlinear Model Predictive Control Iacob, Casian Abdulsamad, Hany Särkkä, Simo Optimization and Control Robotics Systems and Control 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. |
| title | A Parallel-in-Time Newton's Method for Nonlinear Model Predictive Control |
| topic | Optimization and Control Robotics Systems and Control |
| url | https://arxiv.org/abs/2409.20027 |