An adaptive regulation problem and its application

J. Rinzel. A formal classification of bursting mechanisms in excitable systems, in mathematical topics in population biology, morphogenesis and neurosciences. Lecture Notes in Biomathematics, Springer, Kyoto, Japan, vol. 71, pp. 267–281, 1987. C. D. Johnson. Accomodation of external disturbances in linear regulator and servomechanism problems. IEEE Transactions on Automatic Control, vol. 16, no. 6, pp. 635–644, 1971. D. A. Francis, W. M.Wonham. The internal model principle for linear multivariable regulators. Applied Mathematics & Optimization, vol. 2, no. 2, pp. 170–194, 1975. E. J. Davison. The robust control of a servomechanism problem for linear time-invariant multivariable systems. IEEE Transactions on Automatic Control, vol. 21, no. 1, pp. 25–34, 1976. C. A. Desoer, C. A. Lin. Tracking and disturbance rejection of MIMO nonlinear systems with PI controller. IEEE Transactions on Automatic Control, vol. 30, no. 9, pp. 861–867, 1985. M. D. D. Benedetto. Synthesis of an internal model for nonlinear output regulation. International Journal of Control, vol. 45, no. 3, pp. 1023–1034, 1987. J. Huang, W. J. Rugh. On a nonlinear multivariable servomechanism problem. Automatica, vol. 26, no. 6, pp. 963–972, 1990. J. Huang, C. F. Lin. On a robust nonlinear servomechanism problem. IEEE Transactions on Automatic Control, vol. 39, no. 7, pp. 1510–1513, 1994. J. Huang. Asymptotic tracking and disturbance rejection in uncertain nonlinear systems. IEEE Transactions on Automatic Control, vol. 40, no. 6, pp. 1118–1122, 1995. D. Mishra, A. Yadav, P. K. Kalra. Chaotic behavior in neural networks and FitzHugh-Nagumo neuronal model. In Proceedings of the 11th International Conference, on Neural Information Processing, Springer, Calcutta, India, pp. 868–873, 2004. D. Mishra, A. Yadav, S. Ray, P. K. Kalra. Nonlinear dynamical analysis on coupled modified FitzHugh-Nagumo neuron model. In Proceedings of the 2nd International Symposium on Neural Networks, Chongqing, China, pp. 95–101, 2005. D. Mishra, A. Yadav, S. Ray, P. K. Kalra. Controlling synchronization of modified FitzHugh-Nagumo neurons under external electrical stimulation. NeuroQuantology, vol. 4, no. 1, pp. 50–67, 2006. J. Wang, T. Zhang, B. Deng. Synchronization of FitzHugh- Nagumo neurons in external electrical stimulation via nonlinear control. Chaos, Solitons & Fractals, vol. 31, no. 1, pp. 30–38, 2007. Y. Q. Che, J. Wang, S. S. Zhou, B. Deng. Robust synchronization control of coupled chaotic neurons under external electrical stimulation. Chaos, Solitons & Fractals, vol. 40, no. 3, pp. 1333–1342, 2009. W. Lin, C. Q. Qian. Adaptive control of nonlinearly parameterized systems: The smooth feedback case. IEEE Transactions on Automatic Control, vol. 47, no. 8, pp. 1249–1266, 2002. A. Serrani, A. Isidori. Global robust output regulation for a class of nonlinear systems. Systems & Control Letters, vol. 39, no. 2, pp. 133–139, 2000. J. Huang. Nonlinear Output Regulation: Theory and Application, Philadelphia, USA: SIAM, pp. 69–83, 2004. J. Huang, Z. Chen. A general framework for tackling the output regulation problem. IEEE Transactions on Automatic Control, vol. 49, no. 12, pp. 2203–2218, 2004. Z. Xi, Z. Ding. Global decentralised output regulation for a class of large-scale nonlinear systems with nonlinear exosystem. IET Control Theory & Applications, vol. 1, no. 5, pp. 1504–1511, 2007. R. Marino, P. Tomei. Nonlinear Control Design: Geometric, Adaptive and Robust, Englewood Cliffs, New York, USA: Prentice Hall, pp. 157–283, 1994. A. Isidori. Nonlinear Control Systems, 3rd ed., New York, USA: Springer-Verlag, pp. 159–386, 1995. A. Isidori, C. I. Byrnes. Output regulation of nonlinear systems. IEEE Transactions on Automatic Control, vol. 35, no. 2, pp. 131–140, 1990. C. I. Byrnes, F. D. Priscoli, A. Isidori. Structurally stable output regulation of nonlinear systems. Automatica, vol. 33, no. 3, pp. 369–385, 1997. Z. T. Ding. Global output regulation of uncertain nonlinear systems with exogenous signals. Automatica, vol. 37, no. 1, pp. 113–119, 2001. Q. Gong, W. Lin. A note on global output regulation of nonlinear system in the output feedback form. IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 1049–1054, 2003. Z. Chen, J. Huang. Global robust output regulation for output feedback systems. IEEE Transactions on Automatic Control, vol. 50, no. 1, pp. 117–121, 2005. Z. Y. Chen, J. Huang. Robust output regulation with nonlinear exosystems. Automatica, vol. 41, no. 8, pp. 1447–1454, 2005. Z. T. Ding. Output regulation of uncertain nonlinear systems with nonlinear exosystems. IEEE Transactions on Automatic Control, vol. 51, no. 3, pp. 498–503, 2006. Z. R. Xi, Z. T. Ding. Global adaptive output regulation of a class of nonlinear systems with nonlinear exosystems. Automatica, vol. 43, no. 1 pp. 143–149, 2007. Y. Jiang, S. T. Liu, R. L. Wang. Rejection of nonharmonic disturbances for a class of uncertain nonlinear systems with nonlinear exosystems. Science China Information Sciences, vol. 56, no. 3, pp. 1–12, 2013. Y. Jiang, S. T. Liu. Rejection of nonharmonic disturbances in a class of nonlinear systems with nonlinear exosystems. Asian Journal of Control, vol. 13, no. 6, pp. 858–867, 2011.