» Download Article

Authors
Branislav Rehák

Digital Object Identifier (DOI)
10.3182/20060830-2-SF-4903.00009

Page Numbers:
47-52

Index Terms
decomposition,decentralized control,linear matrix inequalities

Abstract
The problem of design of a controller for a large-scale system is studied. The design objective is to achieve behavior comparable with the standard controller that is LQ optimal. On the other hand the amount of interconnections between subsystems should be kept as small as possible. This is guaranteed by solving of an optimization problem where the number of interconnections is minimized while the difference in the values of the cost functional for the standard and decentralized controller is a constraint. To find the value of the cost of the decentralized control in presence of interconnections one can use linear matrix inequalities.

References

[1] Bertsekas, D. (1995) Nonlinear Programming.
    Athena Scientific, Belmont.
[2] Boyd, S., L. El Ghaoui, E. Feron and V. Balakrishnan
     (1994) Linear Matrix Inequalities in System
     and Control Theory. SIAM studies in applied
     mathematics, Philadelphia.
[3] Cepák, M., Rehák, B., Havlena, V. (2003) Decentralized
     Control Design via the Dynamical
    Compensation Method. In: MATLAB 2003.
    Praha: VŠCHT, s. 89-93. (in Czech)
[4] Jamshidi, M. (1997) Large Scale Systems: Modeling,
     Control and Fuzzy Logic. New Jersey,
    Prentice Hall.
[5] Kailath, T. (1980) Linear Systems. Prentice Hall,
    Englewood Cliffs.
[6] Larin, V. (2003) About the inverse problem of
    optimal control, Appl. Comput. Math. No. 2,
    pp. 90-97.
[7] Rehák, B. (2003) Design of the Hierarchical Controller
     Using Femlab. In: The 22nd IASTED
    International Conference on Modelling Identification
     and Control. Calgary: IASTED, pp.
    543-547.
[8] Singh, M. (1981) Decentralised Control. Amsterdam,
     North-Holland.
[9] Singh, M. G. and A. Titli (1986) Systems: Decomposition,
     Optimization and Control, Mashinostrojenye,
     Moscow. (in Russian)
[10] Stipanovic, D. M., G. Inalhan, R. Teo and C.
     J. Tomlin (2004) Decentralized Overlapping
     Control of a Formation of Unmanned Aerial
     Vehicles. Automatica No. 40, pp. 1285-1296.
[11] Trave, Titli, Tarras (1989) Decomposition, Fixed
     Modes and Structure Constraints. Berlin,
     Springer.
[12] Tsurkov, V. (2000) Hierarchical Optimization and
     Mathematical Physics. Dordrecht, Kluwer.
[13] Tsurkov, V. (2001) Large-scale Optimization -
     Problems and Methods Dordrecht, Kluwer.