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A closed-loop strategy in an optimal guaranteed control problem for a linear system

https://doi.org/10.29235/1561-8323-2020-64-5-519-525

Abstract

This paper deals with an optimal control problem for a linear discrete system subject to unknown bounded disturbances with the control goal being to steer the system with guarantees to a given target set while minimizing a given cost function. We define an optimal control strategy with one correction time instant, meaning taking into account information about one future state of the object, and propose an efficient numerical method for constructing it.

About the Authors

Dz. A. Kastsiukevich
Belarusian State University
Belarus

Kastsiukevich Dzmitry A. - Master (Physics and Mathematics), Postgraduate student, Belarusian State University.
4, Nezavisimosti Ave., 220030, Minsk.



N. M. Dmitruk
Belarusian State University
Belarus

Dmitruk Natalia M. - Ph. D. (Physics and Mathematics), Associate рrofessor, Belarusian State University.
4, Nezavisimosti Ave., 220030, Minsk.



References

1. Witsenhausen H. A minimax control problem for sampled linear systems. IEEE Transactions on Automatic Control, 1968, vol. 13, no. 1, pp. 5-21. https://doi.org/10.1109/tac.1968.1098788

2. Kurzhanski A. B. Control and observation under uncertainty conditions. Moscow, 1977. 392 p. (in Russian).

3. Krasovskii N. N. Control of a dynamical system. Moscow, 1985. 518 p. (in Russian).

4. Rawlings J. B., Mayne D. Q. Model Predictive Control: Theory and Design. Madison, 2009. 576 p.

5. Goulart P. J., Kerrigan E. C., Maciejowski J. M. Optimization over state feedback policies for robust control with constraints. Automatica, 2006, vol. 42, no. 4, pp. 523-533. https://doi.org/10.1016/j.automatica.2005.08.023

6. Bemporad A., Borrelli F., Morari M. Min-max control of constrained uncertain discrete-time linear systems. IEEE Transactions on Automatic Control, 2003, vol. 48, no. 9, pp. 1600-1606. https://doi.org/10.1109/tac.2003.816984

7. Balashevich N. V., Gabasov R., Kirillova F. M. The construction of optimal feedback from mathematical models with uncertainty. Computational Mathematics and Mathematical Physics, 2004, vol. 44, no. 2, pp. 247-267 (in Russian).

8. Kostyukova O., Kostina E. Robust optimal feedback for terminal linear-quadratic control problems under disturbances. Mathematical programming, 2006, vol. 107, no. 1-2, pp. 131-153. https://doi.org/10.1007/s10107-005-0682-4

9. Dmitruk N. M. Optimal strategy with one closing instant for a linear optimal guaranteed control problem. Computational Mathematics and Mathematical Physics, 2018, vol. 58, no. 5, pp. 642-658. https://doi.org/10.1134/s096554251805007x

10. Boyd S., Vandenberghe L. Convex Optimization. Cambridge, 2004. https://doi.org/10.1017/cbo9780511804441

11. Gal T. Postoptimal analyses, parametric programming and related topics. Berlin, 1994. https://doi.org/10.1515/9783110871203

12. Herceg M., Kvasnica M., Jones C. N., Morari M. Multi-Parametric Toolbox 3.0. European Control Conference, Zurich, Switzerland, July 17-19, 2013. Zurich, 2013, pp. 502-510. https://doi.org/10.23919/ecc.2013.6669862


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ISSN 1561-8323 (Print)
ISSN 2524-2431 (Online)