NDLI: The linear-quadratic optimal regulator for descriptor systems

Content Provider	IEEE Xplore Digital Library
Author	Bender, D.J. Laub, A.J.
Copyright Year	1985
Description	Author affiliation: University of California, Santa Barbara, CA (Bender, D.J.; Laub, A.J.)
Abstract	In this paper we investigate the linear-quadratic optimal regulator problem for the continuous-time descriptor system Ex = Ax + Bu where E is, in general, a singular matrix. The infinite-horizon version of this problem was previously solved by Cobb [5] by a quite different approach. We solve a somewhat more general finite-horizon problem by applying Hamiltonian minimization to derive the optimal trajectory of the vector consisting of the concatenated descriptor, codescriptor, and control vectors. From this trajectory the optimal feedback gain relating the control and descriptor variable can be computed. By transforming to a coordinate system which can be computed by performing a singular value decomposition of E, we derive a Riccati differential equation whose solution gives the optimal cost. The steady-state optimal feedback gain can be computed by solving an eigenvalue eigenvector problem formulated from the untransformed system parameters. In general there does not exist a unique optimal feedback gain but a linear variety whose dimension is equal to the number of inputs times the rank deficiency of E. A more complete version of this paper has been submitted for publication [3].
Starting Page	957
Ending Page	962
File Size	588656
Page Count	6
File Format	PDF
DOI	10.1109/CDC.1985.268642
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1985-12-11
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Regulators Feedback Optimal control Concatenated codes Singular value decomposition Riccati equations Differential equations Cost function Steady-state Eigenvalues and eigenfunctions
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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