Fourier-Based Optimal Control of Nonlinear Dynamic Systems

[+] Author and Article Information
M. L. Nagurka

Department of Mechanical Engineering and The Robotics Institute, Carnegie-Mellon University, Pittsburgh, PA 15213

V. Yen

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

J. Dyn. Sys., Meas., Control 112(1), 17-26 (Mar 01, 1990) (10 pages) doi:10.1115/1.2894133 History: Received December 02, 1987; Revised September 09, 1988; Online March 17, 2008


A method for generating near optimal trajectories of linear and nonlinear dynamic systems, represented by deterministic, lumped-parameter models, is proposed. The method is based on a Fourier series approximation of each generalized coordinate that converts the optimal control problem into an algebraic nonlinear programming problem. Due to its inverse dynamic nature, the method avoids many of the numerical difficulties typically encountered in solving standard optimal control problems. Furthermore, the method is easy to implement, capable of handling various types of constraints, and quite effective for solving non-bang-bang type control problems. The results of computer simulation studies compare favorably to optimal solutions obtained by closed-form analyses and/or by other numerical schemes.

Copyright © 1990 by The American Society of Mechanical Engineers
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