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Spectral method for constrained linear–quadratic optimal control

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  • Jaddu, Hussein

Abstract

A computational method based on Chebyshev spectral method is presented to solve the linear–quadratic optimal control problem subject to terminal state equality constraints and state-control inequality constraints. The method approximates each of the system state variables and each of the control variables by a finite Chebyshev series of unknown parameters. The method converts the optimal control problem into a quadratic programming problem which can be solved more easily than the original problem. This paper gives explicit results that simplify the implementation of the method. To show the numerical behavior of the proposed method, the simulation results of an example are presented.

Suggested Citation

  • Jaddu, Hussein, 2002. "Spectral method for constrained linear–quadratic optimal control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(2), pages 159-169.
    • Handle: RePEc:eee:matcom:v:58:y:2002:i:2:p:159-169
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    Cited by:

    1. Chen, Xin & Yuan, Yue & Yuan, Dongmei & Ge, Xiao, 2024. "Optimal control for both forward and backward discrete-time systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 298-314.
    2. Ho, Wen-Hsien & Chou, Jyh-Horng, 2005. "Shifted-Chebyshev series solutions of Takagi–Sugeno fuzzy-model-based dynamic equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(4), pages 309-316.
    3. Jianwei Zhou & Danping Yang, 2015. "Legendre–Galerkin spectral methods for optimal control problems with integral constraint for state in one dimension," Computational Optimization and Applications, Springer, vol. 61(1), pages 135-158, May.

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