Linear quadratic optimal control for discrete descriptor systems

The present paper deals with the investigation of the linear quadratic optimal control problem for the discrete-time descriptor systems Ex(k+1) = AX(k)+Bu(k), where E is in general a singular matrix and the system structure is in general noncausal. The problem is considered in its general form, havi...

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Bibliographic Details
Published in:	Journal of optimization theory and applications Vol. 61; no. 2; pp. 221 - 245
Main Authors:	MANTAS, G. P, KRIKELIS, N. J
Format:	Journal Article
Language:	English
Published:	New York, NY Springer 01-05-1989
Subjects:	Applied sciences Computer science; control theory; systems Control theory. Systems Exact sciences and technology Optimal control Singular control Descriptor system LQ control Optimal control Discrete system Regulator Riccati equation Optimization
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Summary:	The present paper deals with the investigation of the linear quadratic optimal control problem for the discrete-time descriptor systems Ex(k+1) = AX(k)+Bu(k), where E is in general a singular matrix and the system structure is in general noncausal. The problem is considered in its general form, having singular cost matrices and cross-weighting term in the cost functional. The key idea for the solution approach is the use of the Weierstrass theorem for regular pencils, combined with a suitable permutation transformation, to form a base for the image of E. The optimization problem is solved by forcing causality to the Hamiltonian equations, which are produced by considering the entire N-stage process as a large system of linear equations. The feedback gain matrix is obtained as a manifold which is generated by the intersection of two other manifolds. (Author)
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0022-3239 1573-2878
DOI:	10.1007/BF00962798