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Special Spectral Approach to Solutions of SISO LTI H-Optimization Problems

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Abstract

The paper is devoted to H-optimization problems for linear time invariant (LTI) systems with scalar control, external disturbance and measurement noise. All these problems can be numerically solved with the help of the well-known universal approaches based on Riccati equations, linear matrix inequalities (LMI) or maximum entropy technique. Nevertheless, in our opinion there exists a possibility to increase the computational efficiency of synthesis using a special spectral approach to the above mentioned problems in frequency domain. Some relevant details are discussed and efficient numerical algorithms are proposed for the practical implementation of spectral approach. One of its virtues is a possibility to present optimal solutions in a specific form, which is convenient for investigation.

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References

  1. M. J. Grimble. Robust Industrial Control Systems: Opti-mal Design Approach for Polynomial Systems, New Jersey, USA: John Wiley & Sons, 2006.

    Book  Google Scholar 

  2. S. P. Bhattacharyya, A. Datta, L. H. Keel. Linear Control Theory: Structure, Robustness and Optimization, Boca Raton, USA: CRC Press, Taylor & Francis Group, 2009.

    MATH  Google Scholar 

  3. D. Liberzon. Calculus of Variations and Optimal Control Theory: A Concise Introduction, Princeton, USA: Princeton University Press, 2012.

    MATH  Google Scholar 

  4. D. W. Gu, P. H. Petkov, M. M. Konstantinov. Robust Control Design with Matlab, London, UK: Springer, 2013.

    Book  MATH  Google Scholar 

  5. A. Domahidi. Methods and Tools for Embedded Optimization and Control, Ph. D. dissertation, Swiss Federal Institute of Technology Zurich, Zurich, Switzerland, 2013.

    Google Scholar 

  6. W. Yu, S. Thenozhi. Active Structural Control with Stable Fuzzy PID Techniques, Switzerland: Springer, 2016.

    Book  MATH  Google Scholar 

  7. Y. F. Zhu, F. W. Yang. Simultaneous H 2/H ∞ stabilization for chemical reaction systems based on orthogonal complement space. International Journal of Automation and Computing, vol. 13, no. 1, pp. 19–30, 2016. DOI: 10.1007/s11633-015-0907-9.

    Article  Google Scholar 

  8. H. A. Ismail, M. S. Packianather, R. I. Grosvenor. Multi-objective invasive weed optimization of the LQR controller. International Journal of Automation and Computing, vol. 14, no. 3, pp. 321–329, 2017. DOI: 10.1007/s11633-017-1061-3.

    Article  Google Scholar 

  9. F. A. Aliev, V. B. Larin. Parametrization of sets of stabilizing controllers in mechanical systems. International Applied Mechanics, vol. 44, no. 6, pp. 599–618, 2008. DOI: 10.1007/s10778-008-0085-3.

    Article  MathSciNet  Google Scholar 

  10. V. Kuçera. Polynomial control: Past, present, and future. International Journal of Robust and Nonlinear Control, vol. 17, no. 8, pp. 682–705, 2007. DOI: 10.1002/rnc.1127.

    Article  MathSciNet  MATH  Google Scholar 

  11. J. C. Doyle, B. A. Francis, A. R. Tannenbaum. Feedback Control Theory, New York, USA: Maxwell MacMillan Internat, 1992.

    Google Scholar 

  12. S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory, Philadelphia, USA: SIAM, 1994.

    Book  MATH  Google Scholar 

  13. G. J. Balas, J. C. Doyle, K. Glover, A. Packard, R. Smith. μ-Analysis and Synthesis TOOLBOX: Users Guide, Natick, USA: The MathWorks Inc., 1998.

    Google Scholar 

  14. H. Kwakernaak. H 2-optimization-theory and applications to robust control design. Annual Reviews in Control, vol. 26, no. 1, pp. 45–56, 2002. DOI: 10.1016/S1367-5788(02)80010-4.

    Article  Google Scholar 

  15. E. I. Veremey. Algorithms for solving a class of problems of H ∞-optimization of control systems. Journal of Computer and Systems Sciences International, vol. 50, no. 3, pp. 403–412, 2011. DOI: 10.1134/S1064230711010187.

    Article  MathSciNet  MATH  Google Scholar 

  16. E. I. Veremey. Efficient spectral approach to SISO problems of H 2-optimal synthesis. Applied Mathematical Sciences, vol. 9, no. 79, pp. 3897–3909, 2015. DOI: 10.12988/ams.2015.54335.

    Article  Google Scholar 

  17. E. I. Veremey. H 2-optimal synthesis problem with nonunique solution. Applied Mathematical Sciences, vol. 10, no. 38, pp. 1891–1905, 2016. DOI: 10.12988/ ams.2016.63120.

    Article  Google Scholar 

  18. E. Veremey, M. Sotnikova. Spectral approach to H ∞-optimal SISO synthesis problem. WSEAS Transactions on Systems and Control, vol. 9, pp. 415–424, 2014.

    Google Scholar 

  19. E. I. Veremey. H ∞-approach to wave disturbance filtering for marine autopilots. In Proceedings of the 9th IFAC Conference on Maneuvering and Control of Marine Craft, IFAC, Arenzano, Italy, pp. 410–415, 2012.

    Google Scholar 

  20. E. I. Veremey. Dynamical correction of control laws for marine ships accurate steering. Journal of Marine Science and Application, vol. 13, no. 2, pp. 127–133, 2014. DOI: 10.1007/s11804-014-1250-1.

    Article  Google Scholar 

  21. E. I. Veremey. Optimization of filtering correctors for autopilot control laws with special structures. Optimal Control Applications and Methods, vol. 37, no. 2, pp. 323–339, 2016. DOI: 10.1002/oca.2170.

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

This work was supported by the Russian Foundation for Basic Research (RFBR), that controlled by the Government of Russian Federation (No. 17-07-00361).

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Authors and Affiliations

  1. Faculty of Applied Mathematics and Control Processes, Saint-Petersburg State University, Saint-Petersburg, 198504, Russia

    Evgeny I. Veremey

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  1. Evgeny I. Veremey
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Correspondence to Evgeny I. Veremey.

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Recommended by Associate Editor Min Wu

Evgeny I. Veremey received the Ph. D. and D. Sc. degrees in control science and engineering from Applied Mathematics and Control Processes Faculty, Saint Petersburg State University, Russia in 1980 and 1995, respectively. Since 2002, he is a professor of Saint Petersburg State University, head of the Computer Applications and Systems Department, Saint Petersburg State University, Russia. Since 2004, he has been the full member of International Public Association “Academy of Navigation and Motion Control”.

His research interests include control theory and its applications to marine and power systems.

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Veremey, E.I. Special Spectral Approach to Solutions of SISO LTI H-Optimization Problems. Int. J. Autom. Comput. 16, 112–128 (2019). https://doi.org/10.1007/s11633-017-1110-y

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  • DOI: https://doi.org/10.1007/s11633-017-1110-y

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