Abstract
In this paper, an adaptive output feedback control algorithm based on the dynamic surface control (DSC) is proposed for a class of uncertain chaotic systems. Because the system states are assumed to be unavailable, an observer is designed to estimate those unavailable states. The main advantage of this algorithm can overcome the problem of “explosion of complexity” inherent in the backstepping design. Thus, the proposed control approach is simpler than the traditional backstepping control for the uncertain chaotic systems. The stability analysis shows that the system is stable in the sense that all signals in the closed-loop system are uniformly ultimately bounded (UUB) and the system output can track the reference signal to a bounded compact set. Finally, an example is provided to illustrate the effectiveness of the proposed control system.
Similar content being viewed by others
References
Chen, G.R., Yu, X.H.: On time-delayed feedback control of chaotic systems. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 46(6), 767–772 (1999)
Nijmeijer, H., Mareels, I.M.Y.: An observer looks at synchronization. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 44(10), 882–890 (1997)
Solak, E.: Partial identification of Lorenz system and its application to key space reduction of chaotic cryptosystems. IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. 51(10), 557–560 (2004)
Hua, C.C., Guan, X.P.: Synchronization of chaotic systems based on PI observer design. Phys. Lett. A 334(5–6), 382–389 (2005)
Celikovsky, S., Chen, G.R.: Secure synchronization of a class of chaotic systems from a nonlinear observer approach. IEEE Trans. Autom. Control 50(1), 76–82 (2005)
Loría, A., Panteley, E., Zavala-Río, A.: Adaptive observers with persistency of excitation for synchronization of chaotic systems. IEEE Trans. Circuits Syst. I, Regul. Pap. 56(12), 2703–2716 (2009)
Yu, S.M., Lü, J.H., Chen, G.R., Yu, X.H.: Design and implementation of grid multiwing butterfly chaotic attractors from a piecewise Lorenz system. IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. 57(10), 803–807 (2010)
Chen, M., Chen, W.H.: Robust adaptive neural network synchronization controller design for a class of time delay uncertain chaotic systems. Chaos Solitons Fractals 41(5), 2716–2724 (2009)
Lu, J.Q., Cao, J.D., Ho, D.W.C.: Adaptive stabilization and synchronization for chaotic Lur’e systems with time-varying delay. IEEE Trans. Circuits Syst. I, Regul. Pap. 55(5), 1347–1356 (2008)
Loría, A., Zavala-Río, A.: Adaptive tracking control of chaotic systems with applications to synchronization. IEEE Trans. Circuits Syst. I, Regul. Pap. 54(9), 2019–2029 (2007)
Hua, C.C., Guan, X.P., Shi, P.: Adaptive feedback control for a class of chaotic systems. Chaos Solitons Fractals 23(3), 757–765 (2005)
Hua, C.C., Guan, X.P., Li, X.L., Shi, P.: Adaptive observer-based control for a class of chaotic systems. Chaos Solitons Fractals 22(1), 103–110 (2004)
Ge, S.S., Wang, C.: Adaptive control of uncertain Chua’s circuits. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 47(9), 1397–1404 (2000)
Ge, S.S., Wang, C., Lee, T.H.: Adaptive backstepping control of a class of chaotic systems. Int. J. Bifurc. Chaos Appl. Sci. Eng. 10(5), 1149–1156 (2000)
Wang, C., Ge, S.S.: Adaptive backstepping control of uncertain Lorenz system. Int. J. Bifurc. Chaos Appl. Sci. Eng. 11(4), 1115–1119 (2001)
Zhou, J., Er, M.J.: Adaptive output control of a class of uncertain chaotic systems. Syst. Control Lett. 56(6), 452–460 (2007)
Swaroop, D., Hedrick, J.K., Yip, P.P., Gerdes, J.C.: Dynamic surface control for a class of nonlinear systems. IEEE Trans. Autom. Control 45(10), 1893–1899 (2000)
Yip, P.P., Hedrick, J.K.: Adaptive dynamic surface control: a simplified algorithm for adaptive backstepping control of nonlinear systems. Int. J. Control 71(5), 959–979 (1998)
Wang, D., Huang, J.: Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form. IEEE Trans. Neural Netw. 16(1), 195–202 (2005)
Yoo, S.J., Park, J.B., Choi, Y.H.: Adaptive dynamic surface control for stabilization of parametric strict-feedback nonlinear systems with unknown time delays. IEEE Trans. Autom. Control 52(12), 2360–2365 (2007)
Yoo, S.J., Park, J.B., Choi, Y.H.: Decentralized adaptive stabilization of interconnected nonlinear systems with unknown non-symmetric dead-zone inputs. Automatica 45(2), 436–443 (2009)
Krishnamurthy, P., Khorrami, F., Jiang, Z.P.: Global output feedback tracking for nonlinear systems in generalized output-feedback canonical form. IEEE Trans. Autom. Control 47(5), 814–819 (2002)
Liu, Y.J., Wang, W., Tong, S.C., Liu, Y.S.: Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters. IEEE Trans. Syst. Man Cybern., Part A, Syst. Hum. 40(1), 170–184 (2010)
Liu, Y.J., Wang, W.: Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems. Inf. Sci. 177(18), 3901–3917 (2007)
Liu, Y.J., Tong, S.C., Wang, W.: Adaptive fuzzy output tracking control for a class of uncertain nonlinear systems. Fuzzy Sets Syst. 160(19), 2727–2754 (2009)
Liu, Y.J., Tong, S.C., Li, T.S.: Observer-based adaptive fuzzy tracking control for a class of uncertain nonlinear MIMO systems. Fuzzy Sets Syst. 164(1), 25–44 (2011)
Liu, Y.J., Zheng, Y.Q.: Adaptive robust fuzzy control for a class of uncertain chaotic systems. Nonlinear Dyn. 57(3), 431–439 (2009)
Liu, Y.J., Tong, S.C., Wang, W., Li, Y.M.: Observer-based direct adaptive fuzzy control of uncertain nonlinear systems and its applications. Int. J. Control. Autom. Syst. 7(4), 681–690 (2009)
Wang, X.Y., Wang, X.J., Zhao, J.F., Zhang, Z.F.: Chaotic encryption algorithm based on alternant of stream cipher and block cipher. Nonlinear Dyn. 63(4), 587–597 (2011)
Wang, X.Y., Sun, P.: Multi-switching synchronization of chaotic system with adaptive controllers and unknown parameters. Nonlinear Dyn., 63(4), 599–609 (2011)
Wang, X.Y., Yang, L., Liu, R.: A chaotic image encryption algorithm based on perception model. Nonlinear Dyn. 62(3), 615–621 (2010)
Wang, X.Y., Wang, M.J.: Projective synchronization of nonlinear-coupled spatiotemporal chaotic systems. Nonlinear Dyn. 62(3), 567–571 (2010)
Wang, R., Liu, Y.J., Tong, S.C.: Decentralized control of uncertain nonlinear stochastic systems based on DSC. Nonlinear Dyn. 64(4), 305–314 (2011)
Liu, Y.J., Chen, C.L.P., Wen, G.X., Tong, S.C.: Adaptive neural output feedback tracking control for a class of uncertain discrete-time nonlinear systems. IEEE Trans. Neural Netw. 22(7), 1162–1167 (2011)
Liu, Y.J., Tong, S.C., Wang, D., Li, T.S., Wang, D., Chen, C.L.P.: Adaptive neural output feedback controller design with reduced-order observer for a class of uncertain nonlinear SISO systems. IEEE Trans. Neural Netw. 22(8), 1328–1334 (2011)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, DJ. Adaptive output feedback control of uncertain nonlinear chaotic systems based on dynamic surface control technique. Nonlinear Dyn 68, 235–243 (2012). https://doi.org/10.1007/s11071-011-0222-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-011-0222-0