NDLI: Optimal feedback control laws by Legendre pseudospectral approximations

Content Provider	IEEE Xplore Digital Library
Author	Hui Yan Fahroo, F. Ross, I.M.
Copyright Year	2001
Description	Author affiliation: INRC Res., Naval Postgraduate Sch., Monterey, CA, USA (Hui Yan)
Abstract	We develop state feedback control laws for linear time-varying systems with quadratic cost criteria by an indirect Legendre pseudo-spectral 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 the other 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.
Sponsorship	American Autom. Control Council
Starting Page	2388
Ending Page	2393
File Size	494951
Page Count	6
File Format	PDF
ISBN	0780364953
ISSN	07431619
DOI	10.1109/ACC.2001.946110
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2001-06-25
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Feedback control Riccati equations Control systems Boundary value problems Differential algebraic equations State feedback Linear feedback control systems Time varying systems Costs Linear approximation
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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