On linear-quadratic optimal control problems for time-varying descriptor systems

SIAM Journal on Control and Optimization

Volumn 42, Issue 6, 2004, Pages 2062-2077

  Kurina, Galina A ^a   März, Roswitha ^b  

^a VORONEZH STATE UNIVERSITY OF FORESTRY AND TECHNOLOGIES NAMED AFTER G F MOROZOV   (Russian Federation)

^b HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Abstract implicit differential equation; Linear quadratic control problem; Variable coefficient descriptor system

Indexed keywords

APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; FUNCTIONS; HAMILTONIANS; MATRIX ALGEBRA; PROBLEM SOLVING; TIME VARYING CONTROL SYSTEMS;

ABSTRACT IMPLICIT DIFFERENTIAL EQUATION; LINEAR-QUADRATIC CONTROL PROBLEMS; VARIABLE DESCRIPTOR SYSTEM;

OPTIMAL CONTROL SYSTEMS;

EID: 6944221508     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012900380991     Document Type: Review

References (12)

1. F. L. LEWIS, A survey of linear singular systems, Circuits Systems Signal Process., 5 (1986), pp. 3-36.
2. G. A. KURINA, Singular perturbations of control problems with state equation unresolved with respect to derivative. A survey, Izv, Ross. Akad. Nauk Tekhn. Kibernet., 4 (1992), pp. 20-48 (in Russian).
3. L. V. KANTOROVICH AND G. P. AKILOV, Funkcional'nyj analiz, Nauka, Moscow, 1984 (in Russian).
4. D. J. BENDER AND A. J. LAUB, The linear-quadratic optimal regulator for descriptor systems, IEEE Trans. Automat. Control, 32 (1987), pp. 672-688.
5. G. A. KURINA, To theory of linear-quadratic control problems unresolved with respect to derivative, in Funkcional'nye prostranstva i uravnenija matematicheskoi fiziki. Sbornik statei. Voronezh, izdatel'stvo VGU, 1988, pp. 25-32. See also the unpublished paper VINITI 755-B86 (1986) (in Russian).
6. G. A. KURINA, On linear-quadratic control problems for descriptor systems, in Proceedings of the International Conference "Dynamical Systems: Stability, Control, Optimization" (DSSCO'98), Minsk, Belarus, 1998, pp. 170-172 (in Russian).
7. K. BALLA AND R. MÄRZ, Linear differential algebraic equations of index 1 and their adjoint equations, Results Math., 37 (2000), pp. 13-35.
8. n with application to iterative methods, J. Math. Anal. Appl., 18 (1967), pp. 417-439.
9. P. KUNKEL AND V. MEHRMANN, The linear quadratic optimal control problem for linear descriptor systems with variable coefficients, Math. Control Signals Systems, 10 (1997), pp. 247-264.
10. V. MEHRMANN, The autonomous linear quadratic control problem, Lecture Notes in Control and Inform. Sci. 163, Springer-Verlag, Berlin, 1991.
11. R. MÄRZ, Differential algebraic systems anew, Appl. Numer. Math., 42 (2002), pp. 315-335.
12. G. A. KURINA, Feed-back control for time-varying descriptor systems, Systems Sci., 26 (2000), pp. 47-59.