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Using Homotopy Method to Solve Bang–Bang Optimal Control Problems

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Optimization, Simulation, and Control

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 76))

Abstract

According to the Pontryagin maximum principle, some optimal control problem can result in a bang-bang control law. In despite of what method is used in the optimization procedure for the bang-bang control, fixing switching points of the bang-bang control is very intractable. In this chapter, the smoothing technique presented by Bertrand et al. for solving bang-bang optimal control problems is introduced, but its convergence is quite slow. To overcome this flaw, based upon a method termed homotopy method, this chapter presents an integration switching method which can converge very fast. Finally, two numerical examples are solved illustrating the interest of our method, and the simulation results are provided to demonstrate the effectiveness of our method.

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Acknowledgments

The authors are supported by the National Natural Science Foundation of China (Grants No: 60625304, 60621062).

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Authors and Affiliations

  1. Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, China

    Zhijie Gao

  2. Department of Aerospace Engineering, Tsinghua University, Beijing, 100084, China

    Hexi Baoyin

Authors
  1. Zhijie Gao
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  2. Hexi Baoyin
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Corresponding author

Correspondence to Hexi Baoyin .

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Editors and Affiliations

  1. , Institute of Mathematics, National University of Mongolia, University Street 1, Ulaanbaatar, 210646, Erdenet, Mongolia

    Altannar Chinchuluun

  2. , Department of Industrial & Systems Engin, University of Florida, Weil Hall 401, Gainesville, 32611, Florida, USA

    Panos M. Pardalos

  3. The School of Economic Studies, Dept.of Mathematics & Computer Science, National University of Mongolia, Ulaanbaatar, 210646, Mongolia

    Rentsen Enkhbat

  4. , Centre for Process Systems Engineering, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom

    E. N. Pistikopoulos

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Gao, Z., Baoyin, H. (2013). Using Homotopy Method to Solve Bang–Bang Optimal Control Problems. In: Chinchuluun, A., Pardalos, P., Enkhbat, R., Pistikopoulos, E. (eds) Optimization, Simulation, and Control. Springer Optimization and Its Applications, vol 76. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5131-0_15

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