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The linear-quadratic optimal regulator for descriptor systems: Discrete- time case. (English) Zbl 0612.93045

This paper presents an analysis of linear-quadratic optimal regulators for discrete time-invariant descriptor systems. The analysis is done following an orthogonal coordinate change that puts the descriptor system into semi-explicit form. Both finite and infinite time problems are considered.
Reviewer: S.Campbell

MSC:

93C55 Discrete-time control/observation systems
49J99 Existence theories in calculus of variations and optimal control
93C05 Linear systems in control theory
34A99 General theory for ordinary differential equations
39A12 Discrete version of topics in analysis
93C35 Multivariable systems, multidimensional control systems

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[1] Arnold, W. F.; Laub, A. J., Generalized eigenproblem algorithms and software for algebraic Riccati equations, (Proc. IEEE, 72 (1984)), 1746-1754
[2] Bender, D. J., Descriptor systems and geometric control theory, (Ph.D. dissertation (1985), University of California at Santa Barbara, Department of Electrical and Computer Engineering)
[3] Bender, D. J.; Laub, A. J., The linear-quadratic regulator problem for descriptor systems, IEEE Trans. Aut. Control (1987), (submitted) · Zbl 0624.93030
[4] Campbell, S. L., (Singular Systems of Differential Equations, Vol. 40 (1980), Pitman: Pitman San Francisco), Research Notes in Math. · Zbl 0419.34007
[5] Cobb, D. J., Descriptor variable systems and optimal state regulation, IEEE Trans. Aut. Control, AC-28, 601-611 (1983) · Zbl 0522.93036
[6] Cobb, D. J., Controllability, observability and duality in singular systems, IEEE Trans. Aut. Control, AC-29, 1076-1084 (1984)
[7] Emami-Naeini, A.; Franklin, G. F., Deadbeat control and tracking of discrete-time systems, IEEE Trans. Aut. Control, AC-27, 176-181 (1982) · Zbl 0469.93057
[8] Gaalman, G. J., Comments on ‘A nonrecursive algebraic solution for the discrete Riccati equation’, IEEE Trans. Aut. Control, AC-25, 610-612 (1980)
[9] Kailath, T., (Linear Systems (1980), Prentice-Hall: Prentice-Hall Englewood Cliffs, New Jersey) · Zbl 0458.93025
[10] Klema, V. C.; Laub, A. J., The singular value decomposition: its computation and some applicances, IEEE Trans. Aut. Control, AC-25, 164-176 (1980) · Zbl 0433.93018
[11] Kwakernaak, H.; Sivan, R., (Linear Optimal Control Systems (1972), Wiley-Interscience: Wiley-Interscience New York) · Zbl 0276.93001
[12] Larson, R. E.; Luenberger, D. G.; Stengel, D. N., Optimization of large-scale deterministic systems using descriptor variable theory and spatial dynamic programming, (SCI Report No. TM 5168-9 (1978), Systems Control, Inc: Systems Control, Inc Palo Alto, California)
[13] Laub, A. J., Filtering for generalized state space models, (Proc. Parallel Algorithms Signal Process., Part X (1981), University of Southern California: University of Southern California Los Angeles), October 9
[14] Laub, A. J., Schur techniques in invariant imbedding methods for solving two-point boundary value problems, (Proc. 21st IEEE Conf. Dec. Control. Proc. 21st IEEE Conf. Dec. Control, Orlando, Florida (1982)), 56-61
[15] Leontief, W., The dynamic inverse, (Carter, A. P.; Bródy, A., Contributions to Input-Output Analysis (1970), North-Holland: North-Holland Amsterdam) · Zbl 0118.14803
[16] Lewis, F. L.; Ozcaldiran, K., Reachability and controlliability for descriptor systems, (Proc. 27th Midwest Symp. Circ. Syst.. Proc. 27th Midwest Symp. Circ. Syst., Morgantown, West Virginia (1984)) · Zbl 0689.93004
[17] Luenberger, D. G.; Arbel, A., Singular dynamic Leontief systems, Econometrica, 45, 991-995 (1977) · Zbl 0368.90029
[18] Paige, C., Covariance matrix representation in linear filtering, Contemp. Math. (AMS), 47, 309-321 (1985) · Zbl 0571.93062
[19] Pappas, T.; Laub, A. J.; Sandell, N. R., On the numerical solution of the discrete-time algebraic Riccati equation, IEEE Trans. Aut. Control, AC-25, 631-641 (1980) · Zbl 0456.49010
[20] Payne, H. J.; Silverman, L. M., On the discrete-time algebraic Riccati equation, IEEE Trans. Aut. Control, AC-18, 226-234 (1973) · Zbl 0297.93036
[21] Sage, A. P., (Optimum Systems Control (1968), Prentice-Hall: Prentice-Hall Englewood Cliffs, New Jersey)
[22] Silverman, L. M., Discrete Riccati equations: alternative algorithms, asymptotic properties, and system theory interpretations, (Leondes, C., Advances in Control Systems, Vol. 12 (1976), Academic Press: Academic Press New York) · Zbl 0362.49014
[23] Van Dooren, P., A generalized eigenvalue approach for solving Riccati equations, SIAM J. Sci. Stat. Comp., 2, 121-135 (1981) · Zbl 0463.65024
[24] Walker, R. A.; Emami-Naeini, A.; Van Dooren, P., A generalized algorithm for solving the algebraic Riccati equation, (Proc. 21st IEEE Conf. Dec. Control (1982)), 68-72
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