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Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints

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Abstract

A parametric variational principle and the corresponding numerical algorithm are proposed to solve a linear-quadratic (LQ) optimal control problem with control inequality constraints. Based on the parametric variational principle, this control problem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is effective for LQ optimal control problems with control inequality constraints.

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116024, Liaoning Province, P. R. China

    Hai-jun Peng  (彭海军), Qiang Gao  (高 强), Hong-wu Zhang  (张洪武) & Wan-xie Zhong  (种万勰)

  2. State Key Laboratory of Structural Analysis for Industrial Equipment, School of Aeronautics and Astronautics, Dalian University of Technology, Dalian, 116024, Liaoning Province, P. R. China

    Zhi-gang Wu  (吴志刚)

Authors
  1. Hai-jun Peng  (彭海军)
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  2. Qiang Gao  (高 强)
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  3. Hong-wu Zhang  (张洪武)
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  4. Zhi-gang Wu  (吴志刚)
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  5. Wan-xie Zhong  (种万勰)
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Corresponding author

Correspondence to Qiang Gao  (高 强).

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11102031 and 11272076), the Fundamental Research Funds for Central Universities (No.DUT13LK25), the Key Laboratory Fund of Liaoning Province (No. L2013015), the China Postdoctoral Science Foundation (No. 2014M550155), and the State Key Laboratory of Mechanics and Control of Mechanical Structures (Nanjing University of Aeronautics and Astronautics) (No.MCMS-0114G02)

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Peng, Hj., Gao, Q., Zhang, Hw. et al. Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints. Appl. Math. Mech.-Engl. Ed. 35, 1079–1098 (2014). https://doi.org/10.1007/s10483-014-1858-6

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  • DOI: https://doi.org/10.1007/s10483-014-1858-6

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