Previous |  Up |  Next

Article

Keywords:
disturbance decoupling; optimal performance; $\ell _1$ optimal control
Summary:
In this paper we present an input-output point of view for the problem of closed loop norm minimization of stable plants when a decentralized structure and a disturbance decoupling property are imposed on the controller. We show that this problem is convex and present approaches to its solution in the optimal $\ell _1$ sense in the nontrivial case which is when the block off- diagonal terms of the plant have more columns than rows.
References:
[1] Boyd S. P., Barratt C. H.: Linear Controller Design: Limits of Performance. Prentice Hall, Englewood Cliffs, N. J. 1991 Zbl 0748.93003
[2] Conway J. B.: A Course in Functional Analysis. Springer–Verlag, New York 1990 MR 1070713 | Zbl 0706.46003
[3] Cuhna N. O. Da, Polak E.: Constrained minimization under vector valued criteria in finite dimensional spaces. J. Math. Anal. Appl. 19 (1967), 103–124 DOI 10.1016/0022-247X(67)90025-X | MR 0216346
[4] Francis B. A.: A Course in ${H}_\infty $ Control Theory. (Lecture Notes in Control and Information Sciences 88.) Springer–Verlag, New York 1987 MR 0932459
[5] Dahleh M. A., Diaz-Bobillo I. J.: Control of Uncertain Systems: A Linear Programming Approach. Prentice Hall, Englewood Cliffs, N. J. 1995 Zbl 0838.93007
[6] Gundes A. N., Desoer C. A.: Algebraic Theory of Linear Feedback Systems with Full and Decentralized Compensators. Springer–Verlag, Heidelberg 1990 MR 1055359
[7] Goodwin G. C., Seron M. M., Salgado M. E.: ${\mathcal {H}}_2$ design of decentralized controllers. In: Proc. American Control Conference, San Diego 1999
[8] Khammash M.: Solution of the $\ell _1$ optimal control problem without zero interpolation. In: Proc. Control Decision Conference, Kobe 1996; IEEE Trans. Automat. Control, to appear
[9] Kučera V.: Discrete Linear Control. Wiley, Chichester 1979 MR 0573447 | Zbl 0762.93060
[10] Linnemann A., Wang Q.: Block decoupling with stability by unity output feedback-solution and performance limitations. Automatica 29 (1993), 735–744 DOI 10.1016/0005-1098(93)90067-4 | MR 1217792 | Zbl 0771.93072
[11] Salapaka M. V., Khammash M., Dahleh M.: Solution of MIMO ${\mathcal {H}}_2/\ell _1$ problem without zero interpolation. In: Proc. Control Decision Conference, San Diego 1997
[12] Ünyelioģlu K. A., Özgüner U.: ${\mathcal {H}}_\infty $ sensitivity minimization using decentralized feedback: 2-input 2-output systems. Systems Control Lett. (1994), 99–109 MR 1261849
[13] Qi X., Khammash M. H., Salapaka M. V.: Optimal controller synthesis with multiple objectives. In: Proc. 2001 American Control Conference, Arlington 2001, pp. 2730–2735
[14] Qi X., Khammash M. H., Salapaka M. V.: A Matlab package for multiobjective control synthesis. In: IEEE Conference on Decision and Control 2001, to appear
[15] Quek C. K., Loh A. P.: Robust decoupling of discrete systems using $\ell _1$ optimization. IEEE Trans. Automat. Control 42 (1997), 549–553 DOI 10.1109/9.566667 | MR 1442592
[16] Woude J. W. van der: Almost noninteracting control by measurement feedback. Systems Control Lett. 9 (1987), 7–16 DOI 10.1016/0167-6911(87)90003-X | MR 0894721
[17] Youla D. C., Jabr H. A., Bongiorno J. J.: Modern Wiener-Hopf design of optimal controllers. Part 2: The multivariable case. IEEE Trans. Automat. Control AC-21 (1976), 319–338 DOI 10.1109/TAC.1976.1101223 | MR 0446637 | Zbl 0339.93035
Partner of
EuDML logo