CONTROLLABILITY OF AN ENSEMBLE OF LINEAR SYSTEMS BY A DESCRIPTOR DYNAMIC REGULATOR
UDC 517.977
Key words: ensemble of systems, controllability, interval analysis, descriptor linear system, dynamic regulator.
For citation: Krakhotko V. V., Goryachkin V. V., Ignatenko V. V., Razmyslovich G. P. Controllability of an ensemble of linear systems by a descriptor dynamic regulator. Proseedings of BSTU, issue 3, Physics and Mathematics. Informatics, 2022, no. 2 (260), pp. 5–9 (In Russian). DOI: https://doi.org/10.52065/2520-6141-2022-260-2-5-9.
Abstract
The controllability problems of dynamic systems are important from the point of view of applications. This is especially true for dynamical systems with interval uncertainties. For the control of such systems, it is important to have control actions that are easy to implement practically. Such an implementation can be carried out with the help of descriptor dynamic regulators. The article attempts to transfer the known results to more complex dynamic control systems such as systems with interval parameters.
A linear dynamic control system with interval coefficients is considered. The problem of transferring a beam of system trajectories from the initial state to the minimal neighborhood of a polyhedral set in finite time using a descriptor controller is posed. A constructive method of approximate solution of the problem is proposed, which comes to solving a special linear programming problem. If the minimal neighborhood coincides with the polyhedral set itself, then the control found is guaranteed to solve the problem in the exact formulation.
References
- Gaishun I. V., Goryachkin V. V., Krakhotko V. V. Control of an ensemble of linear discrete twoparameter systems. Vesti NAN Belarusi [Vesti National Academy of Sciences of Belarus], 2018, no. 1, pp. 20–23 (In Russian).
- Krakhotko V. V., Goryachkin V. V., Ignatenko V. V., Razmyslovich G. P. Management of an ensemble of linear systems with a delay in control in the class of succulent-constant functions. Trudу BGTU [Proceedings of BSTU], issue 3, Physics and Mathematics. Informatics, 2021, no. 1, pp. 5–8 (In Russian).
- Ignatenko V. V. The Controllability of dynamical systems with a controller. Vestnik BGU [Bulletin of the Belarusian State University], series 1, Physics, Mathematics, Mechanics, 1976, no. 2, pp. 56–58 (In Russian).
- Krakhotko V. V., Ignatenko V. V., Razmyslovich G. P. On controllability of linear systems by descriptor regulator. Trudu BGTU Proceedings of BSTU], issue 3, Physics and Mathematics. Informatics, 2017, no. 1, pp. 5–7 (In Russian).
- Campbell S. L., Meyer C. D., Rose, N. J. Applications of the Drazin inverse to Linear systems of Differential equations with Singular constant Coefficients. SIAM J. Appl. Math., 1976, vol. 31, no. 3, pp. 411–425.
- Kalmykov S. A., Shokin Yu. I., Yuldashev Z. H. Metody interval’nogo analisa [Methods of interval analysis]. Novosibirsk, Nauka Publ., 1986. 224 p. (In Russian).
- Alefeld G., Herzberger Yu. Vvedenie v interval’nyye vichisleniya [Introduction to interval calculations]. Moscow, Mir Publ., 1987. 360 p. (In Russian).
- Ashchepkov L. T. External estimates and stepwise controllability of interval linear systems. Avtomatika i telemekhanika [Automation and telemechanics], 2008, no. 4, pp. 51–58 (In Russian).
- Ashchepkov L. T., Davydov D. V. Universal’nyye resheniya interval’nikh zadach optimizatsii i upravleniya [Universal solutions of interval optimization and control problems]. Moscow, Nauka Publ., 2006. 151 p. (In Russian).
