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Numerical Method with High Real-time Property Based on Shortest Path Algorithm for Optimal Control

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  • Control Theory and Applications
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Abstract

A numerical method consisting of an off-line part and an on-line part for optimal control problems is proposed in this paper. In the off-line part, the state space is discretized into a Cartesian grid structure and then define a graph over all grid points by connecting two points if the Euclidean norm between them is closer than a positive number called adjacent radius, the minimum cost between them is estimated using difference method and stored in a matrix. After that the matrix is updated by a shortest path algorithm and a matrix holding the information of the shortest paths between any two grid points is generated. In the on-line part, the optimal control vector at each time step can be generated by reading data from the matrix according to the current state and target state and doing some simple calculations. Since there is no need to do a lot of calculation in the on-line part, this method can satisfy the real-time requirements in some engineering control problems. We prove that the solution of the proposed method converge to the analytical solution when the adjacent radius and the grid size tend to zero and the grid size tend is a higher order infinitesimal of the adjacent radius. At the end of this paper, some numerical examples are taken to illustrate the effectiveness of the proposed method.

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Authors and Affiliations

  1. Key laboratory of Fundamental Science for National Defense-Advanced Design Technology of Flight Vehicle and the State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China

    Wei Liao, Xiaohui Wei & Hao Sun

  2. College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210001, China

    Jizhou Lai

Authors
  1. Wei Liao
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  2. Xiaohui Wei
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  3. Jizhou Lai
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  4. Hao Sun
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Corresponding author

Correspondence to Xiaohui Wei.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors gratefully acknowledge support from National Defense Outstanding Youth Science Foundation (Grant No. 2018-JCJQ-ZQ-053), A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions and Central University Basic Scientific Research Operating Expenses Special Fund Project Support (Grant No. NF2018001). Also, the authors would like to thank the anonymous reviewers, associate editor, and editor for their valuable and constructive comments and suggestions. In the on-line part, the optimal control vector can be generated by reading data from the path matrix and doing some simple calculations.

Wei Liao was born in 1991. He received his bachelor degree in flight vehicle design and engineering from Nanchang Hangkong University, Nanchang, China, in 2012. And received his master degree in flight vehicle design from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2016. He is currently working towards his doctoral degree in flight vehicle design at Nanjing University of Aeronautics and Astronautics. His research interests include optimal control, reachability analysis and artificial intelligence.

Xiaohui Wei was born in 1978. He received his bachelor degree and doctoral degree in flight vehicle design from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2000 and 2006, respectively. He is now a professor at College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics. His research interests include nonlinear dynamics and engineering reliability.

Jizhou Lai was born in 1977. He received his bachelor degree and doctoral degree in navigation, guidance and control from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 1999 and 2005, respectively. He is now a professor at College of Automation Engineering, Nanjing University of Aeronautics and Astronautics. His research interests include navigation guidance and control and artificial intelligence.

Hao Sun was born in 1996. He received his bachelor degree in flight vehicle design and engineering from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2019. He is currently working towards his master degree in flight vehicle design at Nanjing University of Aeronautics and Astronautics. His research interests include adaptive and nonlinear control.

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Liao, W., Wei, X., Lai, J. et al. Numerical Method with High Real-time Property Based on Shortest Path Algorithm for Optimal Control. Int. J. Control Autom. Syst. 19, 2038–2046 (2021). https://doi.org/10.1007/s12555-020-0196-0

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  • DOI: https://doi.org/10.1007/s12555-020-0196-0

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