Primal–dual adaptive dynamic programming for finite-horizon optimal control of nonlinear systems with isoperimetric constraints

In this paper, a novel primal–dual adaptive dynamic programming (PDADP) method is developed to solve finite-horizon optimal control problems (OCPs) with isoperimetric constraints for continuous-time nonlinear systems. The OCP with isoperimetric constraints is approximated by a series of linear quadr...

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Bibliographic Details
Published inAutomatica (Oxford) Vol. 173; p. 112029
Main Authors Wei, Qinglai, Li, Tao, Zhang, Jie, Wang, Fei-Yue
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.03.2025
Subjects
Adaptive dynamic programming
Isoperimetric constraints
Nonlinear systems
Optimal control
Isoperimetric constraints
Adaptive dynamic programming
Nonlinear systems
Optimal control
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ISSN0005-1098
DOI10.1016/j.automatica.2024.112029

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Summary:In this paper, a novel primal–dual adaptive dynamic programming (PDADP) method is developed to solve finite-horizon optimal control problems (OCPs) with isoperimetric constraints for continuous-time nonlinear systems. The OCP with isoperimetric constraints is approximated by a series of linear quadratic time-varying OCPs with isoperimetric quadratic constraints, which are solved by the primal–dual (PD) method. The convergence of the PDADP method is proven. Furthermore, the optimality of the solution is analyzed by deriving the necessary optimality conditions via Pontryagin’s principle and proving that the limiting values of the iterations satisfy the necessary optimality conditions. Finally, simulation experiments are provided to show the effectiveness of the present PDADP method.
ISSN:0005-1098
DOI:10.1016/j.automatica.2024.112029