Title | ||
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Modified Radau Collocation Method For Solving Optimal Control Problems With Nonsmooth Solutions Part I: Lavrentiev Phenomenon And The Search Space |
Abstract | ||
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A new method is developed for solving optimal control problems whose solutions contain a nonsmooth optimal control. The method developed in this paper employs a modified form of the Legendre-Gauss-Radau (LGR) orthogonal direct collocation method in which an additional variable and two additional constraints are included at the end of a mesh interval. The additional variable is the switch time where a discontinuity occurs. The two additional constraints are a collocation condition on each differential equation that is a function of control along with a control constraint at the endpoint of the mesh interval that defines the location of the nonsmoothness. These additional constraints modify the search space of the NLP in a manner such that an accurate approximation to the location of the nonsmoothness is obtained. An example with a nonsmooth solution is used throughout the paper to illustrate the improvement of the method over the standard Legendre-Gauss-Radau collocation method. |
Year | DOI | Venue |
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2018 | 10.1109/CDC.2018.8619830 | 2018 IEEE CONFERENCE ON DECISION AND CONTROL (CDC) |
Field | DocType | ISSN |
Differential equation,Mathematical optimization,Optimal control,Computer science,Discontinuity (linguistics),Collocation method,Collocation | Conference | 0743-1546 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 |
Name | Order | Citations | PageRank |
---|---|---|---|
Joseph D. Eide | 1 | 0 | 1.01 |
William W. Hager | 2 | 1603 | 214.67 |
Anil V. Rao | 3 | 341 | 29.35 |