Optimal Control of Parametrically Excited Linear Delay Differential Systems via Chebyshev Polynomials

Venkatesh Deshmukh, Haitao Ma, Eric Butcher

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

Use of Chebyshev polynomials in solving finite horizon optimal control problems associated with general linear time varying systems with constant delay is well known in the literature. The technique is modified in the present manuscript for the finite horizon control of dynamical systems with time periodic coefficients and constant delay. The governing differential equations of motion are converted into an algebraic recursive relationship in terms of the Chebyshev coefficients of the system matrices, delayed and present state vectors, and the input vector. Three different approaches are considered. First approach computes the Chebyshev coefficients of the control vector by minimizing a quadratic cost function over a finite horizon or a finite sequence of time intervals. Then two convergence conditions are presented to improve the performance of the optimized trajectories in terms of the oscillations of controlled states. The second approach computes the Chebyshev coefficients of the control vector by maximizing a quadratic decay rate of L2 norm of Chebyshev coefficients of the state subject to a linear matching and quadratic convergence condition. The control vector in each interval is computed by formulating a nonlinear optimization program. The third approach computes the Chebyshev coefficients of the control vector by maximizing a linear decay rate of L norm of Chebyshev coefficients of the state subject to a linear matching and linear convergence condition. The proposed techniques are illustrated by designing regulation controllers for a delayed Mathieu equation over a finite control horizon.

Original languageEnglish (US)
Title of host publicationProceedings of the American Control Conference
Pages1524-1529
Number of pages6
Volume2
StatePublished - 2003
Externally publishedYes
Event2003 American Control Conference - Denver, CO, United States
Duration: Jun 4 2003Jun 6 2003

Other

Other2003 American Control Conference
CountryUnited States
CityDenver, CO
Period6/4/036/6/03

Fingerprint

Polynomials
Time varying systems
Cost functions
Equations of motion
Dynamical systems
Differential equations
Trajectories
Controllers

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Deshmukh, V., Ma, H., & Butcher, E. (2003). Optimal Control of Parametrically Excited Linear Delay Differential Systems via Chebyshev Polynomials. In Proceedings of the American Control Conference (Vol. 2, pp. 1524-1529)

Optimal Control of Parametrically Excited Linear Delay Differential Systems via Chebyshev Polynomials. / Deshmukh, Venkatesh; Ma, Haitao; Butcher, Eric.

Proceedings of the American Control Conference. Vol. 2 2003. p. 1524-1529.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Deshmukh, V, Ma, H & Butcher, E 2003, Optimal Control of Parametrically Excited Linear Delay Differential Systems via Chebyshev Polynomials. in Proceedings of the American Control Conference. vol. 2, pp. 1524-1529, 2003 American Control Conference, Denver, CO, United States, 6/4/03.
Deshmukh V, Ma H, Butcher E. Optimal Control of Parametrically Excited Linear Delay Differential Systems via Chebyshev Polynomials. In Proceedings of the American Control Conference. Vol. 2. 2003. p. 1524-1529
Deshmukh, Venkatesh ; Ma, Haitao ; Butcher, Eric. / Optimal Control of Parametrically Excited Linear Delay Differential Systems via Chebyshev Polynomials. Proceedings of the American Control Conference. Vol. 2 2003. pp. 1524-1529
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