Paper Info
Title
Modified Radau Collocation Method For Solving Optimal Control Problems With Nonsmooth Solutions Part I: Lavrentiev Phenomenon And The Search Space
Abstract
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
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. Eide101.01
William W. Hager21603214.67
Anil V. Rao334129.35