Linear Quadratic Optimal Control Via Fourier-Based State Parameterization

Document Type

Article

Language

eng

Publication Date

6-1991

Publisher

American Society of Mechanical Engineers

Source Publication

Journal of Dynamic Systems, Measurement, and Control

Source ISSN

0022-0434

Abstract

A method for determining the optimal control of unconstrained and linearly constrained linear dynamic systems with quadratic performance indices is presented. The method is based on a modified Fourier series approximation of each state variable that converts the linear quadratic (LQ) problem into a mathematical programming problem. In particular, it is shown that an unconstrained LQ problem can be cast as an unconstrained quadratic programming problem where the necessary condition of optimality is derived as a system of linear algebraic equations. Furthermore, it is shown that a linearly constrained LQ problem can be converted into a general quadratic programming problem. Simulation studies for constrained LQ systems, including a bang-bang control problem, demonstrate that the approach is accurate. The results also indicate that in solving high order unconstrained LQ problems the approach is computationally more efficient and robust than standard methods.

Comments

Journal of Dynamic Systems, Measurement, and Control, Vol. 113, No. 2 (June 1991): 206-215. DOI.

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