×

Static output feedback stabilization of interconnected systems. (English) Zbl 1250.93102

Summary: This paper is concerned with the celebrated Static Output Feedback control Problem (SOFP) subject to linear constraints on control input \(K\), e.g. bounds on control magnitude, zeros in some elements of \(K\), etc. These constraints typically arise in the control of resource-limited systems interconnected to each other, where the local control for each system makes use of its own and neighboring systems’ outputs only, and its magnitude is bounded. This control problem can be approached by a Spectral-Norm Minimization (\(q\)-SNM) technique, whose preliminary version was previously introduced with little mathematical justification but shown to be promising for the regular SOFP without control constraints. This paper mathematically justifies \(q\)-SNM by showing its explicit relationship with spectral radius, and extends \(q\)-SNM to accommodate various linear control constraints. This paper also discusses the practical application of \(q\)-SNM to vehicle formation control, which demonstrates the merit of \(q\)-SNM.

MSC:

93D15 Stabilization of systems by feedback
93C15 Control/observation systems governed by ordinary differential equations
93B60 Eigenvalue problems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bakule, L., Decentralized control: an overview, Annual Reviews, 32, 87-98 (2008)
[2] Menon, P. P.; Edwards, C., Decentralised static output feedback stabilisation and synchronisation of networks, Automatica, 45, 2910-2916 (2009) · Zbl 1192.93101
[3] Massioni, P.; Verhaegen, M., Distributed control for identical dynamically coupled systems: a decomposition approach, IEEE Transactions on Automatic Control, 54, 1, 124-135 (2009) · Zbl 1367.93217
[4] Siljak, D. D., Decentralized Control of Complex Systems (1991), Academic Press: Academic Press Cambridge · Zbl 0382.93003
[5] D’Andrea, R.; Dullerud, G. E., Distributed control design for spatially interconnected systems, IEEE Transactions on Automatic Control, 48, 9, 1478-1495 (2003) · Zbl 1364.93206
[6] Langbort, C.; Chandra, R. S.; D’Andrea, R., Distributed control design for systems interconnected over an arbitrary graph, IEEE Transactions on Automatic Control, 49, 9, 1502-1519 (2004) · Zbl 1365.93141
[7] S. Darbha, S. Pargaonkar, S.P. Bhattacharya, A linear programming approach to the synthesis of fixed structure controllers, in: Proc. American Control Conf., 2004, pp. 3942-3949.; S. Darbha, S. Pargaonkar, S.P. Bhattacharya, A linear programming approach to the synthesis of fixed structure controllers, in: Proc. American Control Conf., 2004, pp. 3942-3949.
[8] Zecevic, A. I.; Siljak, D. D., Control design with arbitrary information structure constraints, Automatica, 44, 2642-2647 (2008) · Zbl 1155.93347
[9] Kim, Y.; Gu, D.-W.; Postlethwaite, I., Spectral radius minimization for optimal average consensus and output feedback stabilization, Automatica, 45, 6, 1379-1386 (2009) · Zbl 1166.93018
[10] Overton, M. L.; Womersley, R. S., On mininizing the spectral radius of a nonsymmetric matrix function-optimality conditions and duality theory, SIAM Journal on Matrix Analysis and Applications, 9, 1, 474-498 (1988) · Zbl 0684.65062
[11] Burke, J.; Lewis, A.; Overton, M., Two numerical methods for optimizing matrix stability, Linear Algebra and its Applications, 351-352, 117-145 (2002) · Zbl 1005.65041
[12] W. Yan, Static output feedback stabilization, in: Proc. IEEE Region 10 Conf., 2006.; W. Yan, Static output feedback stabilization, in: Proc. IEEE Region 10 Conf., 2006.
[13] S. Gumussoy, D. Henrion, M. Millstone, M.L. Overton, Multiobjective robust control with HIFOO 2.0, in: Proc. IFAC Symposium on Robust Control Design, Haifa, Israel, 2009.; S. Gumussoy, D. Henrion, M. Millstone, M.L. Overton, Multiobjective robust control with HIFOO 2.0, in: Proc. IFAC Symposium on Robust Control Design, Haifa, Israel, 2009.
[14] Lafferrire, G.; Williams, A.; Caughman, J.; Veerman, J. J.P., Decentralized control of vehicle formations, Systems & Control Letters, 54, 899-910 (2005) · Zbl 1129.93303
[15] Qiu, J.; Feng, G.; Gao, H., Approaches to robust \(H_\infty\) static output feedback control of discrete-time piecewise-affine systems with norm-bounded uncertainties, International Journal of Robust and Nonlinear Control, 21, 7, 790-814 (2011) · Zbl 1222.93066
[16] Sturm, J. F., Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones, Optimization Methods and Software, 11-12, 625-653 (1999) · Zbl 0973.90526
[17] J. Lofberg, YALMIP: a toolbox for modeling and optimization in MATLAB, in: Proc. CACSD Conf., 2004.; J. Lofberg, YALMIP: a toolbox for modeling and optimization in MATLAB, in: Proc. CACSD Conf., 2004.
[18] Kim, Y., Bisection algorithm of increasing algebraic connectivity by adding an edge, IEEE Transactions on Automatic Control, 55, 1, 170-174 (2010) · Zbl 1368.05146
[19] D. Peaucelle, D. Henrion, Y. Labit, K. Taitz, Users guide for SEDUMI INTERFACE 1.04, LAAS—CNRS, 2002.; D. Peaucelle, D. Henrion, Y. Labit, K. Taitz, Users guide for SEDUMI INTERFACE 1.04, LAAS—CNRS, 2002.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.