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Tytuł artykułu

Optimal control for bilinear systems with delay on control

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The quadratic optimal control for bilinear distributed systems with delays in the control is considered. A semigroup model which involves no explicit delays in control is introduced. In the case of continuous delay, the control operator is bounded and the classical results can be applied. The case of general delays can be considered as a distributed system with boundary control. With the aid of a family of approximating systems, it is shown that the optimal control is obtained as a limit of sequence which is solution of classical control problems.
Słowa kluczowe
Rocznik
Strony
23--55
Opis fizyczny
Bibliogr 23 poz., rys., wzory
Twórcy
autor
  • LTS, Université de Perpignan, Perpignan-France
  • LERMA, Ecole Mohamadia d’Ingénieurs, Rabat-Maroc
autor
  • Faculté des Sciences Ben M'sik, Casablanca, Maroc
autor
  • Faculté des Sciences Ben M'sik, Casablanca, Maroc
Bibliografia
  • [1] D.H. Chyung and E.B. Lee: Linear optimal control problems with time delays. SIAM J. Control, 4 (1966), 548-575.
  • [2] R.F. Curtain and A.J. Pritchard: Infinite dimensional linear systems theory. Lectures Notes in Control and Information Sciences, 1978.
  • [3] M.C. Delfour: Linear hereditary differential systems and their control. Optimal control and its Applications, Part II, B.J. Kirby, (Ed), Springer-Verlag, New York, 1974, 92-154.
  • [4] M.C. Delfour: The linear quadratic optimal control problem for hereditary differential systems: theory and numerical solution. Applied Mathematics and Optimization, 3 (1977), 101-162.
  • [5] M.C. Delfour: Status of the state space theory of linear hereditary differential systems with delays in state and control variables. Analysis and Optimization of Systems, A. Bensoussan and J.L. Lion, (Eds), Springer-Verlag, New York, (1980), 83-96.
  • [6] M.C. Delfour: The linear-quadratic optimal control problem with delays in state and control variables: A state space approach. SIAM. J. Cont. and Optim., 24 (1986), 835-883.
  • [7] M.C. Delfour: The linear-quadratic optimal control theory for systems with delays in state and control variables. Control sciences and technology for the progress of society, Vol I, H. Akaski, (Ed), Pergamon Press, Oxford, New York, (1981), 361- 366.
  • [8] M.C. Delfour: The product space approach in the state space theory of linear time-invariant differential systems with delays in state and control variables. Mathematical Control Theory, Banach Center Publications, PWN, Warsaw, 14 (1983), 147-169.
  • [9] M.C. Delfour: The linear-quadratic optimal control problem for hereditary differential systems: theory and numerical solution. Applied Mathematics and Optimization, 3 (1977), 101-162.
  • [10] M.C. Delfour and J. Karrakchou: State space theory of linear time invariant systems with delays in state, control and observation variable. J. Mathematical Analysis and Applications, 25 (1987) part I, 361-399, part II, 400-450.
  • [11] N. El Alami: Analyse et commande optimale des systémes bilinéaires distribués: Application aux procedes energétiques. Thése d’état, Perpignan-France, 1986.
  • [12] A. Ichikawa: Generation of a semigroup on some product space with applications to evolution equation with delays. Control Theory Center, University of Warwick, Coventry, UK, Report 52, 1977.
  • [13] A. Ichikawa: Optimal (quadratic) control and filtering for evolution equations with delay in control and observation. Control Theory Center, University of Warwick, Coventry, UK, Report 53, 1977.
  • [14] A. Ichikawa: Quadratic control of evolution equations with delays in control. SIAM, Journal Cont., 20(5), (1982), 645-668.
  • [15] J. Karrakchou: Analyse et commande des systèmes différentiels fonctionnels de type héréditaire. Thèse de doctorat, Université de Montréal, 1984.
  • [16] J. Karrakchou and A. Namir: A new approach for a linear quadratic optimalcontrol problem of distributed systems with delays in the control. IMA.
  • [17] J. Karrakchou and M. Rachik: On approximation of the quadratic control problem for a class of distributed systems. Proc. 17th IFIP Conf. on System Modelling and Optimization, Prague, (1995), 625-628.
  • [18] H.N. Koivo and E.B. Lee: Controller synthesis for linear systems with retarded state and control variables and quadratic cost. Automatica, 8 (1972), 203-208.
  • [19] A.J. Pritchard and D. Salomon: The linear quadratic optimal control problem for infinite dimensional systems with unbounded input and ouput operators. MRC, University of Wisconsin, Madison TSR 2624, 1984.
  • [20] M. Rachik: Problèmes de contrôle stochastique pour les systèmes distribués avec retard sur la commande et sur l’observation. Thèse 3eme cycle, Faculté des Sciences de Rabat, Maroc, 1987.
  • [21] M. Rachik: Quelques éléments sur l’analyse et le contrôle des systèmes distribués. Thèse de Doctorat d’état, Rabat, Maroc, 1995.
  • [22] R.B. Vinter And R.H. Kwong: The infinite time quadratic control problem for linear systems with state and control delays. An evolution equation approach. SIAM J. Cont. and Opt., 19(1), (1981).
  • [23] J. Zabczyk: A semi group approach to boundary controls. Proc. 2nd IFAC Conf. on Distributed Parameter Systems, Warwick, UK, (1977).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BSW9-0007-1337
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