Adaptive pseudospectral methods for solving constrained linear and nonlinear time-delay optimal control problems

Mohammad Maleki, Ishak Hashim

Research output: Contribution to journalArticle

17 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)811-839
Number of pages29
JournalJournal of the Franklin Institute
Volume351
Issue number2
DOIs
Publication statusPublished - Feb 2014

Fingerprint

Pseudospectral Method
Adaptive Method
Optimal Control Problem
Time Delay
Time delay
Legendre
Gauss
Nonlinear Problem
Linear Time
Quasilinearization
Inequality Constraints
Quadratic Programming
Quadratic programming
Optimal Control
Optimal Solution
Numerical Methods
Mesh
Numerical methods
Converge
Term

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Networks and Communications
  • Applied Mathematics
  • Signal Processing

Cite this

Adaptive pseudospectral methods for solving constrained linear and nonlinear time-delay optimal control problems. / Maleki, Mohammad; Hashim, Ishak.

In: Journal of the Franklin Institute, Vol. 351, No. 2, 02.2014, p. 811-839.

Research output: Contribution to journalArticle

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