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Admissible controls and controllable sets for a linear time-varying ordinary differential equation

  • * Corresponding author: Yashan Xu

    * Corresponding author: Yashan Xu

The first author is supported by the National Natural Science Foundation under grants 11771344 and 11371285; the second author is supported by the National Natural Science Foundation under grants 11471080 and 11631004

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  • In this paper, for a time optimal control problem governed by a linear time-varying ordinary differential equation, we give a description to check whether the set of admissible controls is nonempty or not by finite times.

    Mathematics Subject Classification: Primary: 49J15, 93C15; Secondary: 93B05.


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  •   M. E. Achhab , F. M. Callier  and  V. Wertz , Admissible controls and attainable states for a class of nonlinear systems with general constraints, Internat. J. Robust Nonlinear Control, 4 (1994) , 267-288.  doi: 10.1002/rnc.4590040204.
      S. A. A$\breve{{\rm{i}}}$sagaliev and M. K. Ospanova, Existence of admissible controls for ordinary differential equations with fixed end-points of trajectories in the presence of phase and integral constraints, (Russian) Vestn. Minist. Obraz. Nauki Nats. Akad. Nauk Resp. Kaz., (2003), 16-26.
      V. Barbu, Optimal Control of Variational Inequalities, Research Notes in Mathematics, 100, Pitman, Boston, MA, 1984.
      R. Conti, Teoria del Controllo e del Controllo Ottimo, UTET, Torino, Italy, 1974.
      A. L. Dontchev , On the admissible controls of constrained linear systems, C. R. Acad. Bulgare Sci., 42 (1989) , 33-36. 
      H. Hermes , On the closure and convexity of attainable sets in finite and infinite dimensions, SIAM J. Control, 5 (1967) , 409-417.  doi: 10.1137/0305025.
      J. B. Hiriart-Urruty and C. Lemaréchal, Fundamentals of Convex Analysis, Springer-Verlag, Berlin, 2001. doi: 10.1007/978-3-642-56468-0.
      V. A. Komarov, Estimates for the accessibility set and the construction of admissible controls for linear systems, (Russian) Dokl. Akad. Nauk SSSR, 268 (1983), 537-541.
      S. R. Musaev, A certain sufficient condition for the existence of admissible controls for a multimensional optimal control problem, (Russian) Akad. Nauk $Azerba\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over i} d\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over z} an$, SSR Dokl., 32 (1976), 3-7.
      S. R. Musaev and T. M. Èfendiev, Construction of scalar admissible controls by the Picard-Rakovshchik method, (Russian) Questions of Mathematical Cybernetics and Applied Mathematics, "Èlm", Baku, 1980,134-145.
      L. D. Pustyl'nikov, On a method for finding admissible controls in a linear system with phase constraints, (Russian) Differentsial'nye Uravneniya, 17 (1981), 2176-2184, 2300.
      E. O. Roxin, The attainable set in control systems, in Mathematical Theory Of Control (Bombay, 1990), 307-319, Lecture Notes in Pure and Appl. Math., 142, Dekker, New York, 1993.
      W. E. Schmitendorf  and  B. R. Barmish , Null controllability of linear systems with constrained controls, SIAM J. Control and Optim., 18 (1980) , 327-345.  doi: 10.1137/0318025.
      G. Wang , The existence of time optimal control of semilinear parabolic equations, Systems Control Lett., 53 (2004) , 171-175.  doi: 10.1016/j.sysconle.2004.04.002.
      G. Wang , Y. Xu  and  Y. Zhang , Attainable subspaces and the bang-bang property of time optimal controls for heat equations, SIAM J. Control Optim., 53 (2015) , 592-621.  doi: 10.1137/140966022.
      L. Wang  and  Q. Yan , Bang-bang property of time optimal null controls for some semilinear heat equation, SIAM J. Control Optim., 54 (2016) , 2949-2964.  doi: 10.1137/140997452.
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