## New results on robust output regulation of nonlinear systems with a nonlinear exosystem.(English)Zbl 1274.93076

Summary: The global robust output regulation problem for nonlinear plants subject to nonlinear exosystems has been a challenging problem and has not been well addressed. The main difficulty lies in finding a suitable internal model. The existing internal model for handling the nonlinear exosystem is not zero input globally asymptotically stable, and can only guarantee a local solution for the output regulation problem. In this paper, we first propose a new class of internal models, which is guaranteed to exist under the generalized immersion condition. An advantage of this internal model is that it is zero input globally asymptotically stable. This fact will greatly facilitate the global stabilization of the augmented system associated with the given plant and the internal model. Then we will further utilize this class of internal models to solve the global robust output regulation problem for output feedback systems with a nonlinear exosystem.

### MSC:

 93B35 Sensitivity (robustness) 93C10 Nonlinear systems in control theory 93C15 Control/observation systems governed by ordinary differential equations
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### References:

 [1] Byrnes, Structurally stable output regulation of nonlinear systems, Automatica 33 (3) pp 369– (1997) · Zbl 0873.93043 [2] Cheng, On the design of output regulators for nonlinear systems, Systems & Control Letters 43 (3) pp 167– (2001) · Zbl 0978.93028 [3] Huang, On a robust nonlinear servomechanism problem, IEEE Transactions on Automatic Control 39 (7) pp 1510– (1994) · Zbl 0800.93290 [4] Huang, Nonlinear Output Regulation: Theory and Application (2004) · Zbl 1087.93003 [5] Khalil, On the design of robust servomechansums for minimum phase nonlinear systems, International Journal of Robust and Nonlinear Control 10 (5) pp 339– (2000) [6] Pavlov, Global nonlinear output regulation: convergence-based controller design, Automatica 43 (3) pp 456– (2007) · Zbl 1137.93027 [7] Serrani, Global robust output regulation for a class of nonlinear systems, Systems & Control Letters 39 (2) pp 133– (2000) · Zbl 0948.93027 [8] Huang, Remarks on the robust output regulation problem for nonlinear systems, IEEE Transactions on Automatic Control 46 (12) pp 2028– (2001) · Zbl 1006.93031 [9] Chen, Robust output regulation with nonlinear exosystems, Automatica 41 (8) pp 1447– (2005) · Zbl 1086.93013 [10] Ding, Output regulation of uncertain nonlinear systems with nonlinear exosystems, IEEE Transactions on Automatic Control 51 (3) pp 498– (2006) · Zbl 1366.93568 [11] Sun W Global robust output regulation for a class of output feedback systems with nonlinear exosystems and its application Proceedings of the 8th World Congress on Intelligent Control and Automation Jinan, China 2010 1635 1640 [12] Xi, Global adaptive output regulation of a class of nonlinear systems with nonlinear exosystem, Automatica 43 (1) pp 143– (2007) [13] Zhou G Restricted global robust output regulation for output feedback systems with nonlinear exosystems Proceedings of the 2007 IEEE International Conference on Control and Automation Guangzhou 2007 3259 3264 [14] Castillo-Toledo, Generalized immersion and nonlinear robust output regulation problem, Kybernetika 40 (2) pp 207– (2004) · Zbl 1249.93055 [15] Zhang, Global robust regulation with generalized immersion, Dynamics of Continuous, Discrete and Impulsice Systems, Series A: Mathematical Analysis 17 (6) pp 909– (2010) [16] Nikiforov, Adaptive non-linear tracking with complete compensation of unknown disturbances, European Journal of Control 4 (2) pp 132– (1998) · Zbl 1047.93550 [17] Chen, Global robust output regulation for output feedback systems, IEEE Transactions on Automatic Control 50 (1) pp 117– (2005) · Zbl 1365.93437 [18] Xu, Robust adaptive control of a class of nonlinear systems and its applications, IEEE Transactions on Circuits and Systems I: Regular Papers 57 (3) pp 691– (2010) [19] Liu, Global robust output regulation of output feedback systems with unknown high-frequency gain sign, IEEE Transactions on Automatic Control 51 (4) pp 625– (2006) · Zbl 1366.93209 [20] Nassbaum, Some remarks on a conjecture in parameter adaptive control, Systems & Control Letters 3 (5) pp 243– (1983) [21] Ilchmann, Universal {$$\lambda$$}-tracking for nonlinearly perturbed systems in the presence of noise, Automatica 30 (2) pp 337– (1994) · Zbl 0800.93793 [22] Sontag, Changing supply function in input/state stable systems, IEEE Transactions on Automatic Control 40 (8) pp 1476– (1995) · Zbl 0832.93047
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