Paper Info
Title
Adaptive pseudospectral methods for solving constrained linear and nonlinear time-delay optimal control problems
Abstract
In this paper, we first develop an adaptive shifted Legendre–Gauss (ShLG) pseudospectral method for solving constrained linear time-delay optimal control problems. The delays in the problems are on the state and/or on the control input. By dividing the domain of the problem into a uniform mesh based on the delay terms, the constrained linear time-delay optimal control problem is reduced to a quadratic programming problem. Next, we extend the application of the adaptive ShLG pseudospectral method to nonlinear problems through quasilinearization. Using this scheme, the constrained nonlinear time-delay optimal control problem is replaced with a sequence of constrained linear-quadratic sub-problems whose solutions converge to the solution of the original nonlinear problem. The method is called the iterative-adaptive ShLG pseudospectral method. One of the most important advantages of the proposed method lies in the case with which nonsmooth optimal controls can be computed when inequality constraints and terminal constraints on the state vector are imposed. Moreover, a comparison is made with optimal solutions obtained analytically and/or other numerical methods in the literature to demonstrate the applicability and accuracy of the proposed methods.
Year
DOI
Venue
2014
10.1016/j.jfranklin.2013.09.027
Journal of the Franklin Institute
Field
DocType
Volume
Chebyshev pseudospectral method,Mathematical optimization,State vector,Nonlinear system,Optimal control,Control theory,Gauss pseudospectral method,Pseudospectral optimal control,Legendre pseudospectral method,Quadratic programming,Mathematics
Journal
351
Issue
ISSN
Citations 
2
0016-0032
3
PageRank 
References 
Authors
0.45
16
2
Name
Order
Citations
PageRank
Mohammad Maleki1173.53
Ishak Hashim27516.70