A Chebyshev-Based State Representation for Linear Quadratic Optimal Control

[+] Author and Article Information
M. L. Nagurka, S.-K. Wang

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

J. Dyn. Sys., Meas., Control 115(1), 1-6 (Mar 01, 1993) (6 pages) doi:10.1115/1.2897400 History: Received November 01, 1991; Revised April 01, 1992; Online March 17, 2008


A computationally attractive method for determining the optimal control of unconstrained linear dynamic systems with quadratic performance indices is presented. In the proposed method, the difference between each state variable and its initial condition is represented by a finite-term shifted Chebyshev series. The representation leads to a system of linear algebraic equations as the necessary condition of optimality. Simulation studies demonstrate computational advantages relative to a standard Riccati-based method, a transition matrix method, and a previous Fourier-based method.

Copyright © 1993 by The American Society of Mechanical Engineers
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