OPTIMAL CONTROL STRATEGY IN THE PROBLEM OF GUARANTEED OPTIMIZATION OF A LINEAR SYSTEM WITH DISTURBANCES
Abstract
This article deals with the problem of optimal control of a linear dynamical object subject to unknown bounded disturbances with the control requiring to robustly steer an object to a given target set while minimizing a total impulse of a multidimensional sampled-data input. We define an optimal control strategy, which takes into account one future state of an object, and propose an efficient numerical method to construct it. The optimal strategy performance is compared to an optimal open-loop worst-case input, and some estimates for cost improvement are provided.
About the Author
Natalia M. Dmitruk
Belarusian State University, Minsk
Belarus
Belarus
Ph. D. (Physics and Mathematics), Associate professor
4, Nezavisimosti Ave., 220030
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. doi.org/10.1109/tac.1968.1098788
2. Kurzhanski A. B. Control and observation under uncertainty conditions. Moscow, Nauka Publ., 1977. 392 p. (in Russian).
3. Krasovskii N. N. Control of a dynamical system. Moscow, Nauka Publ., 1985. 520 p. (in Russian).
4. Scokaert P. O. M., Mayne D. Q. Min-max feedback model predictive control for constrained linear systems. IEEE Transactions on Automatic Control, 1998, vol. 43, no. 8, pp. 1136–1142. doi.org/10.1109/tac.1968.1098788
5. Kostyukova O. I., Kurdina M. A. Worst-case control policies with intermediate correct moments. Trudy Instituta Matematiki = Proceedings of the Institute of Mathematics, 2006, vol. 14, no. 1, pp. 82–93 (in Russian).
6. 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. doi.org/10.1016/j.automatica.2005.08.023
7. Bemporad A., Borrelli F., Morari M. Model predictive control based on linear programming the explicit solution. IEEE Transactions on Automatic Control, 2002, vol. 47, no. 12, pp. 1974–1985. doi.org/10.1109/tac.2002.805688
8. Gabasov R., Kirillova F. M., Kostina E. A. Subtended Feedback with Respect to State for Optimization of Uncertain Control Systems. I. Single Loop. Automation and Remote Control, 1996, vol. 57, no. 7, pp. 1008–1015.
9. Gabasov R., Kirillova F. M., Kostina E. A. Closed-Loop State Feedback for Optimization of Uncertain Control Systems. II. Multiply Closed Feedback. Automation and Remote Control, 1996, vol. 57, no. 8, pp. 1137–1145.
10. 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.
11. 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. doi.org/10.1007/s10107-005-0682-4
12. Kostina E., Kostyukova O. Worst-case control policies for (terminal) linear–quadratic control problems under disturbances. International Journal of Robust and Nonlinear Control, 2009, vol. 19, no. 17, pp. 1940–1958. doi.org/10.1002/rnc.1417
13. Jones C., Kerrigan E. C., Maciejowski J. Equality set projection: A new algorithm for the projection of polytopes in halfspace representation. Technical Report CUED/F-INFENG/TR. 463. Department of Engineering, University of Cambridge, 2004. Available at: https://infoscience.epfl.ch/record/169768/files/resp_mar_04_15.pdf
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