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| Computational symplectic numerical methods for optimal control |
| Received:September 11, 2023 Revised:October 17, 2023 |
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| DOI：10.7511/jslx20230911003 |
| KeyWord:nonlinear optimal control Hamiltonian systems symplectic methods ODE DAE |
| Author | Institution |
| 彭海军 |
大连理工大学 工业装备结构分析优化与CAE软件全国重点实验室 工程力学系 大连 |
| 王磊 |
大连理工大学 数学科学学院, 大连 |
| 王昕炜 |
大连理工大学 工业装备结构分析优化与CAE软件全国重点实验室 工程力学系 大连 |
| 吴志刚 |
中山大学 航空航天学院, 深圳 |
| 易雪玲 |
大连理工大学 数学科学学院, 大连 |
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| Abstract: |
| This review focuses on symplectic numerical methods for different types of nonlinear optimal control problems (OCP).It covers:OCPs where dynamic systems are described by ordinary differential equations (ODE) with unconstrained, inequality constraints and time delays, OCPs where dynamic systems are described by differential algebraic equations (DAE) with unconstrained, inequality constraints and switching systems, together with the closed-loop optimal control problems.Symplectic algorithms can be constructed in both the direct and indirect frameworks.In indirect methods, OCPs are transformed into nonlinear equations by generating functions and the variational principle.In direct methods, dynamic systems are discretized in a symplectic manner, then the OCPs are transformed into nonlinear programming (NLP) problems.For closed-loop OCPs, symplectic model predictive control, rolling horizon estimation, and instantaneous optimal control algorithms are introduced.The results reveal that symplectic algorithms have high precision and efficiency, which find applications in aeronautical and aerospace engineering, robotics and other fields. |
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