Optimal Feedback Control Laws by Legendre Pseudospectral Approximations
Loading...
Authors
Yan, Hui, NRC Research Fellow
Ross, I. Michael
Fahroo, Fariba
Subjects
Advisors
Date of Issue
2001-06-25
Date
June 25-27, 2001
Publisher
IEEE
Language
Abstract
We develop state feedback control laws for linear time-varying systems with quadratic cost criteria by an indirect Legendre pseudospectral method. This method approximates the linear two-point boundary value problem to a system of algebraic equations by way of a differentiation matrix. The algebraic system is solved to generate discrete linear transformations between the states and controls at the Legendre-Gauss-Lobatto points. Since these linear transformations involve simple matrix operations, they can be computed rapidly and efficiently. Two methods are proposed: one that circumvents solving the differential Riccati equation by a discrete solution of the boundary value problem, and another that generates a predictor feedback law without the use of transition matrices. Thus our methods obviate the need for solving the time-intensive backward integration of the matrix Riccati differential equation or inverting ill-conditioned transition matrices. A numerical example illustrates the techniques and demonstrates the accuracy and efficiency of these controllers.
Type
Conference Paper
Description
The article of record as published may be located at http://dx.doi.org/10.1109/ACC.2001.946110
Proceedings of the American Control Conference ; Arlington, VA June 25-27, 2001, pp. 2388-2393.
Proceedings of the American Control Conference ; Arlington, VA June 25-27, 2001, pp. 2388-2393.
Series/Report No
Organization
Identifiers
NPS Report Number
Sponsors
Funding
Format
Citation
Distribution Statement
Approved for public release; distribution is unlimited.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.