Method for solving bang-bang and singular optimal control problems using adaptive Radau collocation
| Autor: | Elisha R. Pager, Anil V. Rao |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
0209 industrial biotechnology
Computational Mathematics 020901 industrial engineering & automation Control and Optimization Optimization and Control (math.OC) Applied Mathematics FOS: Mathematics 010103 numerical & computational mathematics 02 engineering and technology 0101 mathematics Mathematics - Optimization and Control 01 natural sciences |
| Zdroj: | Computational Optimization and Applications. 81:857-887 |
| ISSN: | 1573-2894 0926-6003 |
| DOI: | 10.1007/s10589-022-00350-6 |
| Popis: | A method is developed for solving bang-bang and singular optimal control problems using adaptive Legendre-Gauss-Radau (LGR) collocation. The method is divided into several parts. First, a structure detection method is developed that identifies switch times in the control and analyzes the corresponding switching function for segments where the solution is either bang-bang or singular. Second, after the structure has been detected, the domain is decomposed into multiple domains such that the multiple-domain formulation includes additional decision variables that represent the switch times in the optimal control. In domains classified as bang-bang, the control is set to either its upper or lower limit. In domains identified as singular, the objective function is augmented with a regularization term to avoid the singular arc. An iterative procedure is then developed for singular domains to obtain a control that lies in close proximity to the singular control. The method is demonstrated on four examples, three of which have either a bang-bang and/or singular optimal control while the fourth has a smooth and nonsingular optimal control. The results demonstrate that the method of this paper provides accurate solutions to problems whose solutions are either bang-bang or singular when compared against previously developed mesh refinement methods that are not tailored for solving nonsmooth and/or singular optimal control problems, and produces results that are equivalent to those obtained using previously developed mesh refinement methods for optimal control problems whose solutions are smooth. 37 pages, 6 figures, 5 tables To Appear in Computational Optimization and Applications |
| Databáze: | OpenAIRE |
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