Similar articles

Abstract: This paper investigates the H_∞; trajectory tracking control for a class of nonlinear systems with time-varying delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. A unified model consisting of a linear delayed dynamic system and a bounded static nonlinear operator is introduced, which covers most of the nonlinear systems with bounded nonlinear terms, such as the one-link robotic manipulator, chaotic systems, complex networks, the continuous stirred tank reactor (CSTR), and the standard genetic regulatory network (SGRN). First, the definition of the tracking control is given. Second, the H_∞; performance analysis of the closed-loop system including this unified model, reference model, and state feedback controller is presented. Then criteria on the tracking controller design are derived in terms of LMIs such that the output of the closed-loop system tracks the given reference signal in the H_∞; sense. The reference model adopted here is modified to be more flexible. A scaling factor is introduced to deal with the disturbance such that the control precision is improved. Finally, a CSTR system is provided to demonstrate the effectiveness of the established control laws.

This paper investigates the H infinity trajectory tracking control for a class of nonlinear systems with time-varying delays by Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique.

一类时变时滞非线性系统的H_∞参考跟踪控制设计

[1]Ahn, C.K., 2013. Takagi-Sugeno fuzzy receding horizon H_∞ chaotic synchronization and its application to the Lorenz system. Nonl. Anal. Hybr. Syst., 9(1):1-8.

[2]Boyd, S., Ghaoui, L., Feron, E., et al., 1994. Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia, USA.

[3]Cao, Y.Y., Frank, P.M., 2000. Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach. IEEE Trans. Fuzzy Syst., 8(2):200-211.

[4]Chen, Y., Zheng, W., 2015. L₂-L_∞ filtering for stochastic Markovian jump delay systems with nonlinear perturbations. Signal Process., 109:154-164.

[5]Chen, Y., Xue, A., Ge, M., et al., 2007. On exponential stability for systems with state delays. J. Zhejiang Univ.-Sci. A, 8(8):1296-1303.

[6]Feng, J., Tang, Z., Zhao, Y., et al., 2013. Cluster synchronisation of non-linearly coupled Lur’e networks with identical and non-identical nodes and an asymmetrical coupling matrix. IET Contr. Theory Appl., 7(18):2117-2127.

[7]Guan, X., Chen, C., 2003. Adaptive fuzzy control for chaotic systems with H_∞ tracking performance. Fuzzy Sets Syst., 139(1):81-93.

[8]Hsiao, F., 2013. Robust H_∞ fuzzy control of dithered chaotic systems. Neurocomputing, 99:509-520.

[9]Jin, X., Yang, G., Li, P., 2012. Robust adaptive tracking control of distributed delay systems with actuator and communication failures. Asian J. Contr., 14(5):1282-1298.

[10]Lee, T., Park, J., Kwon, O., et al., 2013. Stochastic sampled-data control for state estimation of time-varying delayed neural networks. Neur. Netw., 46:99-108.

[11]Li, L., Wang, W., 2012. Fuzzy modeling and H_∞ control for general 2D nonlinear systems. Fuzzy Sets Syst., 207:1-26.

[12]Liu, M., Zhang, S., Fan, Z., et al., 2013. Exponential H_∞ synchronization and state estimation for chaotic systems via a unified model. IEEE Trans. Neur. Netw. Learn. Syst., 24(7):1124-1126.

[13]Liu, M., Zhang, S., Chen, H., et al., 2014. H_∞ output tracking control of discrete-time nonlinear systems via standard neural network models. IEEE Trans. Neur. Netw. Learn. Syst., 25(10):1928-1935.

[14]Liu, P., Chiang, T., 2012. H_∞ output tracking fuzzy control for nonlinear systems with time-varying delays. Appl. Soft Comput., 12(9):2963-2972.

[15]Nodland, D., Zargarzadeh, H., Jagannathan, S., 2013. Neural network-based optimal adaptive output feedback control of a helicopter UAV. IEEE Trans. Neur. Netw. Learn. Syst., 24(7):1061-1073.

[16]Park, P., Co, J., Jeong, C., 2011. Reciprocally convex approach to stability of systems with time-varying delays. Automatica, 47(1):235-238.

[17]Peng, C., Han, Q., Yue, D., et al., 2011. Sampled-data robust H_∞ control for T-S fuzzy systems with time delay and uncertainties. Fuzzy Sets Syst., 179(1):20-23.

[18]Suykens, J., Vandewalle, J., de Moor, B., 1996. Artificial Neural Networks for Modelling and Control of Non-linear Systems.Springer, London.

[19]Yang, C., 2013. One input control of exponential synchronization for a four-dimensional chaotic system. Appl. Math. Comput., 219(10):5152-5161.

[20]Yang, X., Liu, D., Huang, Y., 2013. Neural-network-based online optimal control for uncertain non-linear continuous-time systems with control constraints. IET Contr. Theory Appl., 7(17):2037-2047.

[21]Yang, Y., Wu, J., Zheng, W., 2012. Trajectory tracking for an autonomous airship using fuzzy adaptive sliding mode control. J. Zhejiang Univ.-Sci. C (Comput. & Electron.), 13(7):534-543.

[22]Yao, C., Zhao, Q., Yu, J., 2011. Complete synchronization induced by disorder in coupled chaoticlattices. Phys. Lett. A, 377(5):370-377.

[23]Zhang, D., Yu, L., 2010. H_∞ output tracking control for neutral systems with time-varying delay and nonlinear perturbations. Commun. Nonl. Sci. Numer. Simul., 15(11):3284-3292.

[24]Zhang, G., Shen, Y., Wang, L., 2013. Global anti-synchronization of a class of chaotic memristive neural networks with time-varying delays. Neur. Netw., 46:1-8.

[25]Zhang, H., Shi, Y., Liu, M., 2013a. H_∞ step tracking control for networked discrete-time nonlinear systems with integral and predictive actions. IEEE Trans. Ind. Inform., 9(1):337-345.

[26]Zhang, H., Shi, Y., Xu, M., et al., 2013b. Observer-based tracking controller design for networked predictive control systems with uncertain Markov delays. Proc. 36th American Control Conf., p.5682-5687.

[27]Zhu, B., Zhang, Q., Chang, C., 2014. Delay-dependent dissipative control for a class of nonlinear system via Takagi-Sugeno fuzzy descriptor model with time delay. IET Contr. Theory Appl., 8(7):451-461.