Robust reference tracking and transient response shaping of a class of nonlinear systems

References

• Aleksandrov, A., Hu, G., & Zhabko, A. P. (2014). Delay-independent stability conditions for some classes of nonlinear systems. IEEE Transactions on Automatic Control, 59(8), 2209–2214. doi: 10.1109/TAC.2014.2299012
   Web of Science ®Google Scholar
• Antidifferentiation. (2002). In Practical analysis in one variable (pp. 301–314). New York, NY: Springer New York.
   Google Scholar
• Boyd, S. P., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory (Vol. 15). Philadelphia: SIAM.
   Google Scholar
• Cao, C., & Hovakimyan, N. (2008). Design and analysis of a novel L1 adaptive control architecture with guaranteed transient performance. IEEE Transactions on Automatic Control, 53(2), 586–591. doi: 10.1109/TAC.2007.914282
   Web of Science ®Google Scholar
• Chen, W., Jiao, L., Li, J., & Li, R. (2009). Adaptive NN backstepping output-feedback control for stochastic nonlinear strict-feedback systems with time-varying delays. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 40(3), 939–950. doi: 10.1109/TSMCB.2009.2033808
   PubMed Web of Science ®Google Scholar
• Dashkovskiy, S., & Naujok, L. (2010). Lyapunov–Razumikhin and Lyapunov–Krasovskii theorems for interconnected ISS time-delay systems. In Proceedings of the 19th international symposium on mathematical theory of networks and systems (MTNS10) (pp. 1179–1184).
   Google Scholar
• Dashkovskiy, S., Rüffer, B. S., & Wirth, F. R. (2007). An ISS small gain theorem for general networks. Mathematics of Control, Signals, and Systems, 19(2), 93–122. doi: 10.1007/s00498-007-0014-8
   Web of Science ®Google Scholar
• Dashkovskiy, S. N., Rüffer, B. S., & Wirth, F. R. (2010). Small gain theorems for large scale systems and construction of ISS Lyapunov functions. SIAM Journal on Control and Optimization, 48(6), 4089–4118. doi: 10.1137/090746483
   Web of Science ®Google Scholar
• Datta, A., & Ioannou, P. A. (1994). Performance analysis and improvement in model reference adaptive control. IEEE Transactions on Automatic Control, 39(12), 2370–2387. doi: 10.1109/9.362856
   Web of Science ®Google Scholar
• Deng, H., Krstic, M., & Williams, R. J. (2001). Stabilization of stochastic nonlinear systems driven by noise of unknown covariance. IEEE Transactions on Automatic Control, 46(8), 1237–1253. doi: 10.1109/9.940927
   Web of Science ®Google Scholar
• Ekramian, M., Sheikholeslam, F., Hosseinnia, S., & Yazdanpanah, M. J. (2013). Adaptive state observer for Lipschitz nonlinear systems. Systems and Control Letters, 62(4), 319–323. doi: 10.1016/j.sysconle.2013.01.002
   Web of Science ®Google Scholar
• Eriksson, K., Estep, D., & Johnson, C. (2013). Applied mathematics: Body and soul: Calculus in several dimensions. Berlin: Springer Science & Business Media.
   Google Scholar
• Fridman, E., Dambrine, M., & Yeganefar, N. (2008). On input-to-state stability of systems with time-delay: A matrix inequalities approach. Automatica, 44(9), 2364–2369. doi: 10.1016/j.automatica.2008.01.012
   Web of Science ®Google Scholar
• Gibson, T. E., Annaswamy, A. M., & Lavretsky, E. (2013). Adaptive systems with closed-loop reference-models, Part I: Transient performance. In 2013 American control conference (pp. 3376–3383).
   Google Scholar
• Hassan, L., Zemouche, A., & Boutayeb, M (2014, June). A new observer-based controller design method for a class of time-varying delay systems with Lipschitz nonlinearities. In American control conference (ACC), 2014 (pp. 4163–4168).
   Google Scholar
• Ho, D. W. C., & Niu, Y. (2007). Robust fuzzy design for nonlinear uncertain stochastic systems via sliding-mode control. IEEE Transactions on Fuzzy Systems, 15(3), 350–358. doi: 10.1109/TFUZZ.2006.880006
   Web of Science ®Google Scholar
• Hou, M., Fu, F., & Duan, G. (2013). Global stabilization of switched stochastic nonlinear systems in strict-feedback form under arbitrary switchings. Automatica, 49(8), 2571–2575. doi: 10.1016/j.automatica.2013.04.031
   Web of Science ®Google Scholar
• Ibrir, S., & Diopt, S. (2008). Novel LMI conditions for observer-based stabilization of Lipschitzian nonlinear systems and uncertain linear systems in discrete-time. Applied Mathematics and Computation, 206(2), 579–588. doi: 10.1016/j.amc.2008.05.150
   Web of Science ®Google Scholar
• Jiang, Z. -P., Teel, A. R., & Praly, L. (1994). Small-gain theorem for ISS systems and applications. Mathematics of Control, Signals, and Systems, 7(2), 95–120. doi: 10.1007/BF01211469
   Web of Science ®Google Scholar
• Khalil, H., & Grizzle, J. (1996). Nonlinear systems (Vol. 3). New Jersey: Prentice Hall.
   Google Scholar
• Khasminskii, R. (2011). Stochastic stability of differential equations (Vol. 66). Berlin: Springer Science & Business Media.
   Google Scholar
• Kheloufi, H., Zemouche, A., Bedouhene, F., & Boutayeb, M. (2013). On LMI conditions to design observer-based controllers for linear systems with parameter uncertainties. Automatica, 49(12), 3700–3704. doi: 10.1016/j.automatica.2013.09.046
   Web of Science ®Google Scholar
• Kreyszig, E. (2009). Advanced engineering mathematics. Hoboken: Wiley .
   Google Scholar
• Langill, A. W. (1964). Transient response analysis of a nonlinear sampled-data control system. IEEE Transactions on Aerospace, 2, 2597–604. doi: 10.1109/TA.1964.4319643
   Web of Science ®Google Scholar
• Li, P., & Yang, G. H (2008, June). Adaptive fuzzy control of unknown nonlinear systems with actuator failures for robust output tracking. In American control conference, 2008 (pp. 4898–4903).
   Google Scholar
• Liberzon, D. (2003). Switching in systems and control. Basel: Springer Science & Business Media.
   Google Scholar
• Liu, P. L. (2009). Robust exponential stability for uncertain time-varying delay systems with delay dependence. Journal of the Franklin Institute, 346(10), 958–968. doi: 10.1016/j.jfranklin.2009.04.005
   Web of Science ®Google Scholar
• Liu, Y., Niu, B., Chu, F., & Liu, Y. (2016). Adaptive fuzzy output-feedback tracking control for a class of switched stochastic nonlinear time-delay systems. Circuits, Systems, and Signal Processing, 35(8), 2762–2788. doi: 10.1007/s00034-015-0174-6
   Web of Science ®Google Scholar
• Mao, X. (2007). Stochastic differential equations and applications. Cambridge: Elsevier.
   Google Scholar
• Marquez, H. J. (2003). Nonlinear control systems: Analysis and design (Vol. 1). Hoboken, NJ: Wiley-Interscience.
   Google Scholar
• Na, J., Herrmann, G., & Zhang, K. (2016). Improving transient performance of adaptive control via a modified reference model and novel adaptation. International Journal of Robust and Nonlinear Control, 27(8), 1351–1372. doi: 10.1002/rnc.3636
   Web of Science ®Google Scholar
• Niu, B., Ahn, C. K., Li, H., & Liu, M. (2018). Adaptive control for stochastic switched nonlower triangular nonlinear systems and its application to a one-link manipulator. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48(10), 1701–1714. doi: 10.1109/TSMC.2017.2685638
   Web of Science ®Google Scholar
• Niu, Y., Ho, D. W. C., & Lam, J. (2005). Robust integral sliding mode control for uncertain stochastic systems with time-varying delay. Automatica, 41(5), 873–880. doi: 10.1016/j.automatica.2004.11.035
   Web of Science ®Google Scholar
• Niu, B., Karimi, H. R., Wang, H., & Liu, Y. (2016). Adaptive output-feedback controller design for switched nonlinear stochastic systems with a modified average dwell-time method. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47(7), 1371–1382. doi: 10.1109/TSMC.2016.2597305
   Web of Science ®Google Scholar
• Niu, B., Wang, D., Li, H., Xie, X., Alotaibi, N. D., & Alsaadi, F. E. (2019). A novel neural-network-based adaptive control scheme for output-constrained stochastic switched nonlinear systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49, 418–432. doi: 10.1109/TSMC.2017.2777472
   Web of Science ®Google Scholar
• Pagilla, P., & Zhu, Y (2004, June). Controller and observer design for Lipschitz nonlinear systems. In American control conference, 2004. Proceedings of the 2004 (Vol. 3, pp. 2379–2384).
   Google Scholar
• Phanomchoeng, G., & Rajamani, R (2010, June). Observer design for Lipschitz nonlinear systems using Riccati equations. In American control conference (ACC), 2010 (pp. 6060–6065).
   Google Scholar
• Povy, L. (1971). Transient response of a class of nonlinear sampled-data control systems. Electronics Letters, 7(11), 307–309. doi: 10.1049/el:19710212
   Web of Science ®Google Scholar
• Rajamani, R. (1998, March). Observers for Lipschitz nonlinear systems. IEEE Transactions on Automatic Control, 43(3), 397–401. doi: 10.1109/9.661604
   Web of Science ®Google Scholar
• Rehan, M., Hong, K. S., & Ge, S. S. (2011). Stabilization and tracking control for a class of nonlinear systems. Nonlinear Analysis: Real World Applications, 12(3), 1786–1796. doi: 10.1016/j.nonrwa.2010.11.011
   Web of Science ®Google Scholar
• Slotine, J. J., & Li, W. (1991). Applied nonlinear control (Vol. 60). Englewood Cliffs, NJ: Prentice-Hall.
   Google Scholar
• Slotine, J. J., & Sastry, S. S. (1983). Tracking control of non-linear systems using sliding surfaces, with application to robot manipulators. International Journal of Control, 38(2), 465–492. doi: 10.1080/00207178308933088
   Web of Science ®Google Scholar
• Sokolov, V. F. (2003). Adaptive suboptimal tracking for a first-order object under Lipschitz uncertainty. Automation and Remote Control, 64(3), 457–467. doi: 10.1023/A:1023269709937
   Web of Science ®Google Scholar
• Sontag, E. D. (2008). Input to state stability: Basic concepts and results. In Nonlinear and optimal control theory (pp. 163–220). Springer.
   Google Scholar
• Sui, S., Li, Y., & Tong, S. (2016). Observer-based adaptive fuzzy control for switched stochastic nonlinear systems with partial tracking errors constrained. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 46(12), 1605–1617. doi: 10.1109/TSMC.2016.2523904
   Web of Science ®Google Scholar
• Swaroop, D., Hedrick, J. K., Yip, P. P., & Gerdes, J. C. (2000). Dynamic surface control for a class of nonlinear systems. IEEE Transactions on Automatic Control, 45(10), 1893–1899. doi: 10.1109/TAC.2000.880994
   Web of Science ®Google Scholar
• Teel, A. R. (1998, July). Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem. IEEE Transactions on Automatic Control, 43(7), 960–964. doi: 10.1109/9.701099
   Web of Science ®Google Scholar
• Tiwari, S., Wang, Y., & Jiang, Z. P. (2009). A nonlinear small-gain theorem for large-scale time delay systems. In Proceedings of the 48th IEEE Conference on Decision and control, 2009 held jointly with the 2009 28th Chinese control conference. CDC/CCC 2009 (pp. 7204–7209).
   Google Scholar
• Wang, H., Chen, B., Liu, X., Liu, K., & Lin, C. (2013). Robust adaptive fuzzy tracking control for pure-feedback stochastic nonlinear systems with input constraints. IEEE Transactions on Cybernetics, 43(6), 2093–2104. doi: 10.1109/TCYB.2013.2240296
   PubMed Web of Science ®Google Scholar
• Yang, J., Na, J., & Gao, G. (2017). Robust adaptive control with a modified controller for transient response improvement. In 2017 9th international conference on modelling, identification and control (ICMIC) (pp. 929–934).
   Google Scholar
• Yucelen, T., & Haddad, W. M. (2013). Low-frequency learning and fast adaptation in model reference adaptive control. IEEE Transactions on Automatic Control, 58(4), 1080–1085. doi: 10.1109/TAC.2012.2218667
   Web of Science ®Google Scholar
• Zang, Z., & Bitmead, R. R. (1990). Transient bounds for adaptive control systems. In 29th IEEE conference on decision and control (Vol. 5, pp. 2724–2729).
   Google Scholar
• Zemouche, A., & Boutayeb, M. (2013). On LMI conditions to design observers for Lipschitz nonlinear systems. Automatica, 49(2), 585–591. doi: 10.1016/j.automatica.2012.11.029
   Web of Science ®Google Scholar
• Zhang, T., & Ge, S. S. (2009, March). Adaptive neural network tracking control of MIMO nonlinear systems with unknown dead zones and control directions. IEEE Transactions on Neural Networks, 20(3), 483–497. doi: 10.1109/TNN.2008.2010349
   PubMed Web of Science ®Google Scholar
• Zhang, H., & Xia, Y. (2018). Adaptive tracking control for a class of stochastic switched systems. International Journal of Control, 91(2), 253–265. doi: 10.1080/00207179.2016.1278270
   Web of Science ®Google Scholar
• Zhang, T., & Xia, X. (2015). Adaptive output feedback tracking control of stochastic nonlinear systems with dynamic uncertainties. International Journal of Robust and Nonlinear Control, 25(9), 1282–1300. doi: 10.1002/rnc.3139
   Web of Science ®Google Scholar
• Zhao, P., Feng, W., & Kang, Y. (2012). Stochastic input-to-state stability of switched stochastic nonlinear systems. Automatica, 48(10), 2569–2576. doi: 10.1016/j.automatica.2012.06.058
   Web of Science ®Google Scholar
• Zhou, Q., Wu, C., & Shi, P. (2017). Observer-based adaptive fuzzy tracking control of nonlinear systems with time delay and input saturation. Fuzzy Sets and Systems, 316, 49–68. doi: 10.1016/j.fss.2016.11.002
   Web of Science ®Google Scholar