REGULATORS OF FINITE STABILIZATION FOR HYBRID LINEAR CONTINUOUS-DISCRETE SYSTEMS

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Resumo

For hybrid linear autonomous continuous-discrete systems, methods for designing two types of regulators that provide finite stabilization are proposed. The implementation of one of them, a regulators for finite stabilization by state, is based on knowledge of the values of the control system solution at discrete moments of time, multiples of the quantization step. For this purpose, an observer has been built that makes it possible to obtain the necessary solution values based on the observed output signal in real time and with zero error. The second type of regulator — the regulator of finite stabilization by output — uses the observed output signal as feedback, and its design is a modification of the finite state stabilization regulator by state by including the above observer in its circuit.

Sobre autores

V. Khartovskii

Yanka Kupala State University of Grodno

Email: hartows@mail.ru
Belarus

Bibliografia

  1. Vasil’yev, S.N. and Malikov, A.I., On some results on the stability of switchable and hybrid systems, in Aktual’nyye problemy mekhaniki sploshnoy sredy. K 20-letiyu IMM KazNTS RAN, Kazan: Foliant, 2011. vol. 1, pp. 23–81.
  2. Gurman, V.I., Models and optimality conditions for hybrid controlled systems, J. Comput. Syst. Sci. Int., 2004, vol. 43, no. 4, pp. 560–565.
  3. Cassandras, C.G. Optimal control of a class of hybrid systems / C.G. Cassandras, D.L. Pepyne, Y. Wardi // IEEE Trans. Automat. Control. — 2001. — V. 46, № 3. — P. 398-415.
  4. Savkin, A.V. Hybrid Dynamical Systems: Controller and Sensor Switching Problems / A.V. Savkin, R.J. Evans. — Boston : Birkhauser, 2002. — 153 p.
  5. Bortakovsky, A.S. and Uryupin, I.V., Optimization of switchable systems’ trajectories, J. Comput. Syst. Sci. Int., 2021, vol. 60, no. 5, pp. 701–718.
  6. Bortakovskiy, A.S., Optimizatsiya pereklyuchayushchikh sistem (Optimization of Switching Systems), Moscow: Izd-vo MAI, 2016.
  7. Maksimov, V.P., Continuous-discrete dynamic models, Ufa Math. J., 2021, vol. 13, no. 3, pp. 95–103.
  8. Baturin, V.A., Goncharova E.V., and Maltugueva, N.S., Iterative methods for solution of problems of optimal control of logic-dynamic systems, J. Comput. Syst. Sci. Int., 2010, vol. 49, no. 5, pp. 731–739.
  9. Gabasov, R., Kirillova, F.M., and Paulianok, N.S., Optimal control of some hybrid systems, J. Comput. Syst. Sci. Int., 2010, no. 49, pp. 872–882.
  10. Agranovich, G. Observer for discrete-continuous LTI systems with continuous-time measurements / G. Agranovich // Funct. Differ. Equat. — 2011. — № 18 (1). — P. 3-12.
  11. Branicky, M. A unified framework for hybrid control: model and optimal control theory / M. Branicky, V. Borkar, S. Mitter // IEEE Trans. Automat. Control. — 1998. — V. 43, № 1. — P. 31-45.
  12. De la Sen, M. On the controller synthesis for linear hybrid systems / M. De la Sen // IMA J. Math. Control and Information. — 2001. — № 18 (4). — P. 503-529.
  13. Marchenko, V.M., Hybrid discrete-continuous systems. Controllability and reachability, Differ. Equat., 2013, vol. 49, no. 1, pp. 112–125.
  14. Marchenko, V.M., Observability of hybrid discrete-continuous systems, Differ. Equat., 2013, vol. 49, no. 11, pp. 1389–1404.
  15. Metel’skii, A.V. and Khartovskii, V.E., Synthesis of damping controllers for the solution of completely regular differential-algebraic delay systems, Differ. Equat., 2017, vol. 53, no. 4, pp. 539–550.
  16. Khartovskii, V.E., Controlling the spectrum of linear completely regular differential-algebraic systems with delay, J. Comput. Syst. Sci. Int., 2020, vol. 59, no. 1, pp. 19–38.
  17. Khartovskii, V.E., Designing asymptotic observers for linear completely regular differential algebraic systems with delay, Izv. In-ta Matematiki i Informatiki Udmurtsk. Gos. Un-ta, 2022, vol. 60, pp. 114–136.
  18. Fomichev, V.V., Sufficient conditions for the stabilization of linear dynamical systems differential equations, Differ. Equat., 2015, vol. 51, no. 11, pp. 1512–1518.
  19. Khartovskii, V.E., Spectral reduction of linear systems of the neutral type, Differ. Equat., 2017, vol. 53, no. 3, pp. 366–381.
  20. Metel’skii, A.V., Separation of identifiable and controllable component of the state of a dynamic system with delay, Differ. Equat., 1992, vol. 28, no. 6, pp. 972–984.

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