Chaos synchronization based on unknown input proportional multiple-integral fuzzy observer. (English) Zbl 1421.93082

Summary: This paper presents an unknown input proportional multiple-integral observer (PIO) for synchronization of chaotic systems based on Takagi-Sugeno (TS) fuzzy chaotic models subject to unmeasurable decision variables and unknown input. In a secure communication configuration, this unknown input is regarded as a message encoded in the chaotic system and recovered by the proposed PIO. Both states and outputs of the fuzzy chaotic models are subject to polynomial unknown input with \(k\)th derivative zero. Using Lyapunov stability theory, sufficient design conditions for synchronization are proposed. The PIO gains matrices are obtained by resolving linear matrix inequalities (LMIs) constraints. Simulation results show through two TS fuzzy chaotic models the validity of the proposed method.


93C42 Fuzzy control/observation systems
34H10 Chaos control for problems involving ordinary differential equations
34D06 Synchronization of solutions to ordinary differential equations
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C15 Control/observation systems governed by ordinary differential equations
Full Text: DOI


[1] Jiang, G.; Chen, G.; Tang, W. K., Stabilizing unstable equilibria of chaotic systems from a state observer approach, IEEE Transactions on Circuits and Systems II, 51, 6, 281-288, (2004)
[2] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Physical Review Letters, 64, 8, 821-824, (1990) · Zbl 0938.37019
[3] Carroll, T. L.; Pecora, L. M., Synchronizing chaotic circuits, IEEE Transactions on Circuits and Systems, 38, 4, 453-456, (1991)
[4] Lorenz, E. N., Deterministic nonperiodic flow, Journal of the Atmospheric Sciences, 20, 2, 130-141, (1963) · Zbl 1417.37129
[5] Yang, J.; Hu, G.; Xiao, J., Chaos synchronization in coupled chaotic oscillators with multiple positive lyapunov exponents, Physical Review Letters, 80, 3, 496-499, (1998)
[6] Boccaletti, S.; Grebogi, C.; Lai, Y.-C.; Mancini, H.; Maza, D., The control of chaos: theory and applications, Physics Reports, 329, 3, 103-197, (2000)
[7] Boccaletti, S.; Kurths, J.; Osipov, G.; Valladares, D. L.; Zhou, C. S., The synchronization of chaotic systems, Physics Reports, 366, 1-2, 1-101, (2002) · Zbl 0995.37022
[8] Shahverdiev, E. M., Synchronization in systems with multiple time delays, Physical Review E, 70, 6, (2004)
[9] Xu, J.; Min, L.; Chen, G., A chaotic communication scheme based on generalized synchronization and hash functions, Chinese Physics Letters, 21, 8, 1445-1448, (2004)
[10] Haefner, J. W., Modeling Biological Systems: Principles and Applications, (2005), New York, NY, USA: Springer, New York, NY, USA · Zbl 1204.92002
[11] Shen, B.; Wang, Z.; Liu, X., Bounded \(H_\infty\) synchronization and state estimation for discrete time-varying stochastic complex networks over a finite horizon, IEEE Transactions on Neural Networks, 22, 1, 145-157, (2011)
[12] Liu, Y.; Wang, Z.; Liang, J.; Liu, X., Synchronization of coupled neutral-type neural networks with jumping-mode-dependent discrete and unbounded distributed delays, IEEE Transactions on Cybernetics, 43, 1, 102-114, (2013)
[13] Shen, B.; Wang, Z.; Liu, X., Sampled-data synchronization control of dynamical networks with stochastic sampling, IEEE Transactions on Automatic Control, 57, 10, 2644-2650, (2012) · Zbl 1369.93047
[14] Ding, D.; Wang, Z.; Dong, H.; Shu, H., Distributed \(H_\infty\) state estimation with stochastic parameters and nonlinearities through sensor networks: the finite-horizon case, Automatica, 48, 8, 1575-1585, (2012) · Zbl 1267.93167
[15] Shen, B.; Wang, Z.; Hung, Y. S.; Chesi, G., Distributed \(H_\infty\) filtering for polynomial nonlinear stochastic systems in sensor networks, IEEE Transactions on Industrial Electronics, 58, 5, 1971-1979, (2011)
[16] Dong, H.; Wang, Z.; Gao, H., Distributed filtering for a class of time-varying systems over sensor networks with quantization errors and successive packet dropouts, IEEE Transactions on Signal Processing, 60, 6, 3164-3173, (2012) · Zbl 1391.93232
[17] Dong, H.; Wang, Z.; Lam, J.; Gao, H., Fuzzy-model-based robust fault detection with stochastic mixed time delays and successive packet dropouts, IEEE Transactions on Systems, Man, and Cybernetics B, 42, 2, 365-376, (2012)
[18] Wanga, B.; Wang, J.; Zhong, S. M., Impulsive synchronization control for chaotic systems, Procedia Engineering, 15, 2721-2726, (2011)
[19] Tao, C.; Yang, C.; Luo, Y.; Xiong, H.; Hu, F., Speed feedback control of chaotic system, Chaos, Solitons and Fractals, 23, 1, 259-263, (2005) · Zbl 1091.93518
[20] Yu, Y., Adaptive synchronization of a unified chaotic system, Chaos, Solitons and Fractals, 36, 2, 329-333, (2008) · Zbl 1141.93361
[21] Li, C.; Liao, X.; Wong, K.-W., Lag synchronization of hyperchaos with application to secure communications, Chaos, Solitons and Fractals, 23, 1, 183-193, (2005) · Zbl 1068.94004
[22] Tavazoei, M. S.; Haeri, M., Determination of active sliding mode controller parameters in synchronizing different chaotic systems, Chaos, Solitons and Fractals, 32, 2, 583-591, (2007)
[23] Barajas-Ramírez, J. G.; Chen, G.; Shieh, L. S., Fuzzy chaos synchronization via sampled driving signals, International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 14, 8, 2721-2733, (2004) · Zbl 1129.93430
[24] Liao, T.; Tsai, S., Adaptive synchronization of chaotic systems and its application to secure communications, Chaos, solitons and fractals, 11, 9, 1387-1396, (2000) · Zbl 0967.93059
[25] Cheng, C.-J., Robust synchronization of uncertain unified chaotic systems subject to noise and its application to secure communication, Applied Mathematics and Computation, 219, 5, 2698-2712, (2012) · Zbl 1308.94065
[26] Yang, T., Secure communication via chaotic parameter modulation, IEEE Transactions on Circuits and Systems I, 43, 9, 817-819, (1996)
[27] Dedieu, H.; Kennedy, M. P.; Hasler, M., Chaos shift keying: modulation and demodulation of a chaotic carrier using self-synchronizing Chua’s circuits, IEEE Transactions on Circuits and Systems II, 40, 10, 634-642, (1993)
[28] Cuomo, K. M.; Oppenheim, A. V.; Strogatz, S. H., Synchronization of Lorenz-based chaotic circuits with applications to communications, IEEE Transactions on Circuits and Systems II, 40, 10, 626-633, (1993)
[29] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on Systems, Man and Cybernetics, 15, 1, 116-132, (1985) · Zbl 0576.93021
[30] Lian, K.; Chiang, T.; Chiu, C.; Liu, P., Synthesis of fuzzy model-based designs to synchronization and secure communications for chaotic systems, IEEE Transactions on Systems, Man, and Cybernetics B, 31, 1, 66-83, (2001)
[31] Kim, J.-H.; Park, C.-W.; Kim, E.; Park, M., Adaptive synchronization of T-S fuzzy chaotic systems with unknown parameters, Chaos, Solitons and Fractals, 24, 5, 1353-1361, (2005) · Zbl 1092.37512
[32] Hyun, C.-H.; Park, C.-W.; Kim, J.-H.; Park, M., Synchronization and secure communication of chaotic systems via robust adaptive high-gain fuzzy observer, Chaos, Solitons and Fractals, 40, 5, 2200-2209, (2009) · Zbl 1198.94152
[33] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory. Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, (1994), Philadelphia, Pa, USA: Society for Industrial and Applied Mathematics, Philadelphia, Pa, USA · Zbl 0816.93004
[34] Tanaka, K.; Wang, H. O., Fuzzy Control System Design and Analysis. A Linear Matrix Inequality Approach, (2001), New York, NY, USA: John Wiley & Sons, New York, NY, USA
[35] Chadli, M.; Karimi, H. R., Robust observer design for unknown inputs Takagi-Sugeno models, IEEE Transactions on Fuzzy Systems, 21, 1, 158-164, (2013)
[36] Dimassi, H.; Loria, A.; Belghith, S., A new secured transmission scheme based on chaotic synchronization via smooth adaptive unknown-input observers, Communications in Nonlinear Science and Numerical Simulation, 17, 9, 3727-3739, (2012) · Zbl 1258.94010
[37] Chen, M.; Min, W., Unknown input observer based chaotic secure communication, Physics Letters A, 372, 10, 1595-1600, (2008) · Zbl 1217.94094
[38] Chadli, M.; Zlinka, I., Unknown input observer design for fuzzy systems with application to chaotic system reconstruction, Computers and Mathematics with Applications, 66, 2, 147-154, (2013) · Zbl 1343.93052
[39] Chadli, M.; Akhenak, A.; Ragot, J.; Maquin, D., State and unknown input estimation for discrete time multiple model, Journal of the Franklin Institute, 346, 6, 593-610, (2009) · Zbl 1169.93361
[40] Youssef, T.; Chadli, M.; Karimi, H. R.; Zelmat, M., Design of unknown inputs proportional integral observers for TS fuzzy models, Neurocomputing Journal, 210, 163, 174, (2013) · Zbl 1272.93034
[41] Meng, X.; Yu, Y.; Wen, G.; Chen, R., Chaos synchronization of unified chaotic system using fuzzy logic controller, Proceedings of the IEEE International Conference on Fuzzy Systems (FUZZ ’08)
[42] Tanaka, K.; Ikeda, T.; Wang, H. O., A unified approach to controlling chaos via an LMI-based fuzzy control system design, IEEE Transactions on Circuits and Systems I, 45, 10, 1021-1040, (1998) · Zbl 0951.93046
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.