Computational symplectic numerical methods for optimal control
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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