×

Variance-constrained dissipative observer-based control for a class of nonlinear stochastic systems with degraded measurements. (English) Zbl 1214.93104

Summary: This paper is concerned with the variance-constrained dissipative control problem for a class of stochastic nonlinear systems with multiple degraded measurements, where the degraded probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over a given interval. The purpose of the problem is to design an observer-based controller such that, for all possible degraded measurements, the closed-loop system is exponentially mean-square stable and strictly dissipative, while the individual steady-state variance is not more than the pre-specified upper bound constraints. A general framework is established so that the required exponential mean-square stability, dissipativity as well as the variance constraints can be easily enforced. A sufficient condition is given for the solvability of the addressed multiobjective control problem, and the desired observer and controller gains are characterized in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programming method. Finally, a numerical example is presented to show the effectiveness and applicability of the proposed algorithm.

MSC:

93E03 Stochastic systems in control theory (general)
93B35 Sensitivity (robustness)
93C10 Nonlinear systems in control theory
90C22 Semidefinite programming
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Chang, K.; Wang, W., Robust covariance control for perturbed stochastic multivariable system via variable structure control, Systems Control Lett., 37, 323-328 (1999) · Zbl 0948.93008
[2] Dong, X., Robust strictly dissipative control for discrete singular systems, IET Control Theory Appl., 1, 4, 1060-1067 (2007)
[3] He, X.; Wang, Z.; Ji, Y. D.; Zhou, D., Fault detection for discrete-time systems in a networked environment, Internat. J. Systems Sci., 41, 8, 937-945 (2010) · Zbl 1213.93123
[4] Hill, D.; Moylan, P., The stability of nonlinear dissipative systems, IEEE Trans. Automat. Control, 708-711 (1976) · Zbl 0339.93014
[5] Hotz, A.; Skelton, R. E., A covariance control theory, Internat. J. Control, 46, 1, 13-32 (1987) · Zbl 0626.93080
[6] Hung, Y.; Yang, F., Robust \(H_\infty\) filtering with error variance constraints for uncertain discrete time-varying systems with uncertainty, Automatica, 39, 7, 1185-1194 (2003) · Zbl 1022.93046
[7] Liang, J.; Wang, Z.; Li, P., Robust synchronisation of delayed neural networks with both linear and non-linear couplings, Internat. J. Systems Sci., 40, 9, 973-984 (2009) · Zbl 1291.93012
[8] Li, Z.; Wang, J.; Shao, H., Delay-dependent dissipative control for linear time-delay systems, J. Franklin Inst., 339, 529-542 (2002) · Zbl 1048.93050
[9] Ma, L.; Wang, Z.; Hu, J.; Bo, Y.; Guo, Z., Robust variance-constrained filtering for a class of nonlinear stochastic systems with missing measurements, Signal Process., 90, 6, 2060-2071 (2010) · Zbl 1197.94088
[10] M. Oliveira, J. Geromel, Numerical comparison output feedback design methods, in: Proceedings of American Control Conference, Albuquerque, NM, 1997, pp. 72-76.; M. Oliveira, J. Geromel, Numerical comparison output feedback design methods, in: Proceedings of American Control Conference, Albuquerque, NM, 1997, pp. 72-76.
[11] Subramanian, A.; Sayed, A., Multiobjective filter design for uncertain stochastic time-delay systems, IEEE Trans. Automat. Control, 49, 1, 149-154 (2004) · Zbl 1365.93513
[12] Tan, Z.; Soh, Y.; Xie, L., Dissipative control for linear discrete-time systems, Automatica, 35, 1557-1564 (1999) · Zbl 0949.93068
[13] Tarn, T.; Rasis, Y., Observers for nonlinear stochastic systems, IEEE Trans. Automat. Control, 21, 6, 441-447 (1976) · Zbl 0332.93075
[14] Wang, Z.; Yang, F.; Ho, D. W.C.; Liu, X., Robust variance-constrained \(H_\infty\) control for stochastic systems with multiplicative noises, J. Math. Anal. Appl., 328, 487-502 (2007) · Zbl 1117.93068
[15] Wang, Z.; Ho, D. W.C.; Liu, X., Robust filtering under randomly varying sensor delay with variance constraints, IEEE Trans. Circuits Syst. II: Express Briefs, 51, 6, 320-326 (2004)
[16] Wang, Z.; Ho, D. W.C.; Liu, X., Variance-constrained filtering for uncertain stochastic systems with missing measurements, IEEE Trans. Automat. Control, 48, 7, 560-567 (2003)
[17] Wang, Z.; Gao, H., Dynamics analysis of gene regulatory networks, Internat. J. Systems Sci., 41, 1, 1-4 (2010) · Zbl 1298.00190
[18] Wang, Z.; Gao, H., Analysis and synchronization of complex networks, Internat. J. Systems Sci., 40, 9, 905-907 (2009) · Zbl 1298.00189
[19] Wei, G.; Wang, Z.; Shu, H., Robust filtering with stochastic nonlinearities and multiple missing measurements, Automatica, 45, 836-841 (2009) · Zbl 1168.93407
[20] Willems, J., Dissipative dynamical systems, part 1: general theory; part 2: linear systems with quadratic supply rate, Arch. Ration. Mech. Anal., 45, 321-393 (1972)
[21] Xie, S.; Xie, L.; Souza, C., Robust dissipative control for linear systems with dissipative uncertainty, Internat. J. Control, 70, 169-191 (1998) · Zbl 0930.93068
[22] Yang, F.; Wang, Z.; Ho, D. W.C.; Liu, X., Robust \(H_2\) filtering for a class of systems with stochastic nonlinearities, IEEE Trans. Circuits Syst. II: Express Briefs, 53, 3, 235-239 (2006)
[23] Yang, F.; Wang, Z.; Ho, D. W.C.; Gani, M., Robust \(H_\infty\) control with missing measurements and time delays, IEEE Trans. Automat. Control, 52, 9, 1666-1672 (2007) · Zbl 1366.93166
[24] K. Yasuda, S. Kherat, R. Skelton, E. Yaz, Covariance control and robustness of bilinear systems, in: Proc. IEEE Conf. Decision Contr., Honolulu, Hawaii, 1990, pp. 1421-1425.; K. Yasuda, S. Kherat, R. Skelton, E. Yaz, Covariance control and robustness of bilinear systems, in: Proc. IEEE Conf. Decision Contr., Honolulu, Hawaii, 1990, pp. 1421-1425.
[25] Yaz, Y.; Yaz, E., On LMI formulations of some problems arising in nonlinear stochastic system analysis, IEEE Trans. Automat. Control, 44, 4, 813-816 (1999) · Zbl 0957.93088
[26] Zhao, Y.; Gao, H.; Lam, J.; Du, B., Stability and stabilization of delayed T-S fuzzy systems: a delay partitioning approach, IEEE Trans. Fuzzy Syst., 17, 4, 750-762 (2009)
[27] Zhao, Y.; Lam, J.; Gao, H., Fault detection for fuzzy systems with intermittent measurement, IEEE Trans. Fuzzy Syst., 17, 2, 398-410 (2009)
[28] Zhao, Y.; Zhang, C.; Gao, H., A new approach to guaranteed cost control of T-S fuzzy dynamic systems with interval parameter uncertainties, IEEE Trans. Syst. Man Cybernet., Part B, 39, 6, 1516-1527 (2009)
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.