Advanced Search
Article Contents
Article Contents

SISO H-Optimal synthesis with initially specified structure of control law

  • * Corresponding author: Evgeny I. Veremey

    * Corresponding author: Evgeny I. Veremey 
This article was written based on a study partially supported by the Russian Foundation for Basic Research (RFBR), research project No. 14-07-00083a.
Abstract / Introduction Full Text(HTML) Figure(2) Related Papers Cited by
  • The paper is devoted to particular cases of H-optimization problems for LTI systems with scalar control and external disturbance. The essence of these problems is to find an output feedback optimal controller having initially given structure to attenuate disturbances action with respect to controlled variable and control. An admissible set of controllers can be additionally restricted by the requirement to assign given poles spectrum of the closed-loop system. Specific features of the posed problems are considered and three simple numerical methods of synthesis are proposed to design correspondent H-optimal controllers. To show the simplicity and effectiveness of the proposed approach and the benefits of developed methods, illustrative examples are enclosed to the paper.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


    \begin{equation} \\ \end{equation}
  • 加载中
  • Figure 1.  Fragment of the surface $J=J(h_{0}, h_{1} )$

    Figure 2.  The crossed sections of the surface $J=J(h_{0}, h_{1} )$ for the fixed value of the parameter $h_1$

  • [1] B. Anderson and J. Moore, Optimal Control: Linear Quadratic Methods, Prentice-Hall, New Jersey, 1989.
    [2] S. Bhattacharyya, A. Datta and L. Keel, Linear Control Theory: Structure, Robustness and Optimization, CRC Press, Taylor & Francis Group, Boca Raton, FL, 2009. doi: 10.1201/9781420019612.
    [3] Ya. M. Bokova and E. I. Veremei, Numerical aspects of spectral method of $H_∞$ -optimal synthesis, Journal of Automat. and Inform. Sciences, 28 (1996), 1-12. 
    [4] S. Boyd, S. L. El. Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, 1994. doi: 10.1137/1.9781611970777.
    [5] B. M. ChenA. SaberiP. Sanutti and Ya. Shamash, Construction and parameterization of all static and dynamic $H_2$ -optimal state feedback solutions, optimal fixed modes, and fixed decoupling zeros, IEEE Trans. Automat. Contr., 38 (1993), 248-261.  doi: 10.1109/9.250513.
    [6] J. C. Doyle, B. A. Francis and A. R. Tanenbaum, Feedback Control Theory, Mac Millan, New York, 1992.
    [7] H. E. Musch and M. Steiner, Tuning advanced PID controllers via direct $H_∞$-norm minimization, Proc. of European Control Conference, Brussel, Belgium, 1-4 July, (1997), 179. doi: 10.1016/j.ejcon.2015.04.008.
    [8] A. Saberi, P. Sannuti and B. M. Chen, $H_2$ -Optimal Control, Prentice-Hall, New Jersey, 1995.
    [9] G. S. WangB. Liang and G. R. Duan, $H_2$ -optimal control with regional pole assignment via state feedback, International Journal of Control, Automation, and Systems, 4 (2006), 653-659. 
    [10] E. I. Veremey, Algorithms for solving a class of problems of $H_∞$ -optimization of control systems, Journal of Comput. and Syst. Sci. Int., 50 (2011), 403-412.  doi: 10.1134/S1064230711010187.
    [11] E. I. Veremey, Efficient spectral approach to SISO problems of $H_2$ -optimal synthesis, Appl. Math. Sciences, 9 (2015), 3897-3909. 
    [12] E. I. Veremey, M. V. Sotnikova, V. V. Eremeev and M. V. Korovkin, Modal parametric optimization of control laws with special structure, Proc. of 14th Intern. Conf. on Control, Automation and Systems, Oct. 22-25, KINTEX, Gyeonggi-do, Korea, (2014), 1278–1283.
  • 加载中



Article Metrics

HTML views(1467) PDF downloads(181) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint