Linear Quadratic Optimal Control Via Fourier-Based State Parameterization

[+] Author and Article Information
V. Yen

Department of Mechanical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan, 80424

M. Nagurka

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213

J. Dyn. Sys., Meas., Control 113(2), 206-215 (Jun 01, 1991) (10 pages) doi:10.1115/1.2896367 History: Received July 01, 1989; Revised June 01, 1990; Online March 17, 2008


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.

Copyright © 1991 by The American Society of Mechanical Engineers
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