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Using Homotopy Method to Solve Bang–Bang Optimal Control Problems

In: Optimization, Simulation, and Control

Author

Listed:
  • Zhijie Gao

    (Tsinghua University)

  • Hexi Baoyin

    (Tsinghua University)

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.

Suggested Citation

  • Zhijie Gao & Hexi Baoyin, 2013. "Using Homotopy Method to Solve Bang–Bang Optimal Control Problems," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & E. N. Pistikopoulos (ed.), Optimization, Simulation, and Control, edition 127, pages 243-256, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-5131-0_15
    DOI: 10.1007/978-1-4614-5131-0_15
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