Solving Linear Quadratic Optimal Control Problems by Chebyshev-Based State Parameterization

Authors

Mark L. Nagurka, Marquette UniversityFollow
S. Wang, Carnegie Mellon University
V. Yen, National Sun Yat-Sen UniversityFollow

Document Type

Article

Language

eng

Publication Date

6-26-1991

Publisher

Institute of Electrical and Electronic Engineers (IEEE)

Source Publication

1991 American Control Conference

Source ISSN

0879425652

Abstract

A Chebyshev-based state representation method is developed for solving optimal control problems involving unconstrained linear time-invariant dynamic systems with quadratic performance indices. In this method, each state variable is represented by the superposition of a finite-term shifted Chebyshev series and a third order polynomial. In contrast to solving a two-point boundary-value problem, here the necessary condition of optimality is a system of linear algebraic equations which can be solved by a method such as Gaussian elimination. The results of simulation studies demonstrate that the proposed method offers computational advantages relative to a previous Chebyshev method and to a standard state transition method.

Comments

Published as a part of 1991 American Control Conference (June 26-28, 1991), DOI.

Mark L. Nagurka was affiliated with Carnegie Mellon University at the time of publication.

Recommended Citation

Nagurka, Mark L.; Wang, S.; and Yen, V., "Solving Linear Quadratic Optimal Control Problems by Chebyshev-Based State Parameterization" (1991). Mechanical Engineering Faculty Research and Publications. 183.
https://epublications.marquette.edu/mechengin_fac/183