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An iterative framework to solve nonlinear optimal control with proportional delay using successive convexification and symplectic multi-interval pseudospectral scheme

Author

Listed:
  • Wang, Xinwei
  • Liu, Jie
  • Peng, Haijun
  • Zhao, Xudong

Abstract

In this paper, we propose an iterative framework to solve optimal control for nonlinear proportional state-delay systems. The successive convexification technique is first implemented to convert the original nonlinear problem into a sequence of linear-quadratic problems. And a symplectic pseudospectral method, where the multi-interval pseudospectral scheme is applied with a proportional mesh, to solve the transformed problems is then developed based on the first-order necessary conditions. Each linear-quadratic problem is finally transformed into a system of linear algebraic equations with a sparse coefficient matrix. Due to the benefit of the successive convexification technique and the multi-interval pseudospectral method, initial guess on costate variables is avoided and converged solutions can be obtained with an exponential convergent rate. The proposed iterative framework is validated by four examples with distinct features, highlighting its numerical precision and efficiency. And either exponential or linear convergence property can be exhibited by tuning the approximation degree or the mesh number.

Suggested Citation

  • Wang, Xinwei & Liu, Jie & Peng, Haijun & Zhao, Xudong, 2022. "An iterative framework to solve nonlinear optimal control with proportional delay using successive convexification and symplectic multi-interval pseudospectral scheme," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    • Handle: RePEc:eee:apmaco:v:435:y:2022:i:c:s0096300322005227
    DOI: 10.1016/j.amc.2022.127448
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    References listed on IDEAS

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    1. Marzban, H.R. & Razzaghi, M., 2004. "Solution of time-varying delay systems by hybrid functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(6), pages 597-607.
    2. Tan, Guoqiang & Wang, Zhanshan & Li, Cong, 2020. "H∞ performance state estimation of delayed static neural networks based on an improved proportional-integral estimator," Applied Mathematics and Computation, Elsevier, vol. 370(C).
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