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Distributed control of nonstationary LPV systems over arbitrary graphs. (English) Zbl 1375.93048
Summary: This paper deals with the \(\ell_2\)-induced norm control of discrete-time, Non-Stationary Linear Parameter-Varying (NSLPV) subsystems, represented in a Linear Fractional Transformation (LFT) framework and interconnected over arbitrary directed graphs. Communication between the subsystems is subjected to a one-step time-delay. NSLPV models have state-space matrix-valued functions with explicit dependence on time-varying terms that are known a-priori, as well as parameters that are not known a-priori but are available for measurement at each discrete time-step. The sought controller has the same interconnection and LFT structures as the plant. Convex analysis and synthesis results are derived using a parameter-independent Lyapunov function. These conditions are infinite dimensional in general, but become finite-dimensional in the case of eventually time-periodic subsystems interconnected over finite graphs. The method is applied to an illustrative example.

MSC:
93B50 Synthesis problems
93A14 Decentralized systems
93C55 Discrete-time control/observation systems
93C05 Linear systems in control theory
93D30 Lyapunov and storage functions
Software:
SDPT3; YALMIP
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References:
[1] Farhood, M.; Dullerud, G. E., Model reduction of nonstationary LPV systems, IEEE Trans. Automat. Control, 52, 2, 181-196, (2007) · Zbl 1366.93089
[2] Farhood, M.; Dullerud, G. E., Control of nonstationary LPV systems, Automatica, 44, 8, 2108-2119, (2008) · Zbl 1283.93082
[3] DAndrea, R.; Dullerud, G. E., Distributed control design for spatially interconnected systems, IEEE Trans. Automat. Control, 48, 9, 1478-1495, (2003) · Zbl 1364.93206
[4] Wu, F., Distributed control for interconnected linear parameter-dependent systems, IEE Proc., Control Theory Appl., 150, 5, 518-527, (2003)
[5] Q. Liu, C. Hoffmann, H. Werner, Distributed control of parameter-varying spatially interconnected systems using parameter-dependent Lyapunov functions, in: Proceedings of the American Control Conference, 2013,pp. 3278-3283.
[6] C. Hoffmann, A. Eichler, H. Werner, Control of heterogeneous groups of LPV systems interconnected through directed and switching topologies, in: Proc. American Control Conference, 2014, pp. 5156-5161.
[7] M. Farhood, Distributed control of LPV systems over arbitrary graphs: a parameter-dependent Lyapunov approach, in: Proceedings of the American Control Conference, 2015, pp. 1525-1530.
[8] Chughtai, S.; Werner, H., Simply structured controllers for parameter varying distributed systems, Smart Mater. Struct., 20, (2011)
[9] van Horssen, E. P.; Weiland, S., Synthesis of distributed robust H-infinity controllers for interconnected discrete time systems, IEEE Trans. Control Netw. Syst., 3, 3, 286-295, (2016) · Zbl 1370.93166
[10] Farhood, M.; Di, Z.; Dullerud, G. E., Distributed control of linear time-varying systems interconnected over arbitrary graphs, Internat. J. Robust Nonlinear Control, 25, 2, 179-206, (2015) · Zbl 1305.93131
[11] Gahinet, P.; Apkarian, P., A linear matrix inequality approach to \(H_\infty\) control, Internat. J. Robust Nonlinear Control, 4, 4, 421-448, (1994) · Zbl 0808.93024
[12] Packard, A., Gain scheduling via linear fractional transformations, Systems Control Lett., 22, 2, 79-92, (1994) · Zbl 0792.93043
[13] Dullerud, G. E.; Lall, S., A new approach for analysis and synthesis of time-varying systems, IEEE Trans. Automat. Control, 44, 8, 1486-1497, (1999) · Zbl 1136.93321
[14] D. Abou Jaoude, M. Farhood, Balanced truncation of spatially distributed nonstationary LPV systems, in: Proceedings of the American Control Conference, 2017, pp. 3470-3475. · Zbl 1375.93048
[15] Dullerud, G. E.; DAndrea, R., Distributed control of heterogeneous systems, IEEE Trans. Automat. Control, 49, 12, 2113-2128, (2004) · Zbl 1365.93317
[16] Beck, C., Coprime factors reduction methods for linear parameter varying and uncertain systems, Systems Control Lett., 55, 3, 199-213, (2006) · Zbl 1129.93352
[17] A.M. Gonzalez, H. Werner, LPV formation control of non-holonomic multi-agent systems, in: The International Federation of Automatic Control \(19\)th World Congress, 2014, pp. 1997-2002.
[18] Apkarian, P., On the discretization of LMI-synthesized linear parameter-varying controllers, Automatica, 33, 4, 655-661, (1997) · Zbl 0879.93016
[19] Lawton, J. R.T.; Beard, R. W.; Young, B. J., A decentralized approach to formation maneuvers, IEEE Trans. Robot. Autom., 19, 6, 933-941, (2003)
[20] Farhood, M.; Dullerud, G. E., Duality and eventually periodic systems, Internat. J. Robust Nonlinear Control, 15, 13, 575-599, (2005) · Zbl 1100.93019
[21] J. Lofberg, YALMIP: A toolbox for modeling and optimization in Matlab,in: Proceedings of the CACSD Conference, Taipei, Taiwan, 2004,pp. 284-289.
[22] Toh, K. C.; Todd, M. J.; Tutuncu, R. H., SDPT3 — a Matlab software packagefor semidefinite programming, Optim. Methods Softw., 11, 545-581, (1999) · Zbl 0997.90060
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