Using Homotopy Method to Solve Bang–Bang Optimal Control Problems

Zhijie Gao () and Hexi Baoyin ()
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Zhijie Gao: Tsinghua University
Hexi Baoyin: Tsinghua University

A chapter in Optimization, Simulation, and Control, 2013, pp 243-256 from Springer

Abstract: 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.

Keywords: Homotopy method; Maximum principle; Bang–bang control (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-5131-0_15

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DOI: 10.1007/978-1-4614-5131-0_15

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