Abstract
A classical problem in control theory is the design of feedback laws such that the effect of exogenous inputs on selected output variables is asymptotically rejected. This includes problems of asymptotic tracking and disturbance rejection. In this entry, the fundamentals of the theory are presented, as well as constructive procedures for the design of a controller, which embeds an “internal model” of the generator of the exogenous inputs. Current and future research directions are also discussed.
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Bibliography
Byrnes CI, Isidori A (2003) Limit sets, zero dynamics and internal models in the problem of nonlinear output regulation. IEEE Trans Autom Control 48:1712–1723
Byrnes CI, Isidori A (2004) Nonlinear internal models for output regulation. IEEE Trans Autom Control 49:2244–2247
Byrnes CI, Delli Priscoli F, Isidori A, Kang W (1997) Structurally stable output regulation of nonlinear systems. Automatica 33:369–385
Chen Z, Huang J (2004) Global robust servomechanism problem of lower triangular systems in the general case. Syst Control Lett 52:209–220
Delli Priscoli F (2004) Output regulation with nonlinear internal models. Syst Control Lett 53: 177–185
Delli Priscoli F, Marconi L, Isidori A (2006a) A new approach to adaptive nonlinear regulation. SIAM J Control Optim 45:829–855
Delli Priscoli F, Marconi L, Isidori A (2006b) Nonlinear observers as nonlinear internal models. Syst Control Lett 55:640–649
Francis BA, Wonham WM (1976) The internal model principle of control theory. Automatica 12:457–465
Hale JK, Magalhães LT, Oliva WM (2002) Dynamics in infinite dimensions. Springer, New York
Huang J (2004) Nonlinear output regulation: theory and applications. SIAM, Philadelphia
Huang J, Lin CF (1994) On a robust nonlinear multivariable servomechanism problem. IEEE Trans Autom Control 39:1510–1513
Isidori A (1995) Nonlinear control systems, 3rd edn. Springer, Berlin/New York
Isidori A (2013) Nonlinear zero dynamics. In: Encyclopedia of systems and control. Springer
Isidori A, Byrnes CI (1990) Output regulation of nonlinear systems. IEEE Trans Autom Control 25:131–140
Isidori A, Byrnes CI (2008) Steady-state behaviors in nonlinear systems with an application to robust disturbance rejection. Ann Rev Control 32:1–16
Isidori A, Marconi L (2008) System regulation and design, geometric and algebraic methods’. In: Encyclopedia of complexity and system science. Section control and dynamical systems. Springer, Heidelberg
Isidori A, Marconi L (2012) Shifting the internal model from control input to controlled output in nonlinear output regulation. In: Proceedings of the 51th IEEE conference on decision and control, Maui
Isidori A, Marconi L, Serrani A (2003) Robust autonomous guidance: an internal model-based approach. Limited series advances in industrial control. Springer, London
Khalil H (1994) Robust servomechanism output feedback controllers for feedback linearizable systems. Automatica 30:587–1599
Marconi L, Praly L (2008) Uniform practical output regulation. IEEE Trans Autom Control 53(5):1184–1202
Marconi L, Praly L, Isidori A (2007) Output stabilization via nonlinear luenberger observers. SIAM J Control Optim 45(6):2277–2298
Pavlov A, van de Wouw N, Nijmeijer H (2006) Uniform output regulation of nonlinear systems: a convergent dynamics approach. Birkhauser, Boston
Serrani A, Isidori A, Marconi L (2000) Semiglobal output regulation for minimum-phase systems. Int J Robust Nonlinear Control 10:379–396
Serrani A, Isidori A, Marconi L (2001) Semiglobal nonlinear output regulation with adaptive internal model. IEEE Trans Autom Control 46:1178–1194
Teel AR, Praly L (1995) Tools for semiglobal stabilization by partial state and output feedback. SIAM J Control Optim 33:1443–1485
Wieland P (2010) From static to dynamic couplings in consensus and synchronization among identical and non-identical systems. PhD thesis, Universität Stuttgart
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Marconi, L. (2013). Regulation and tracking of nonlinear systems. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_86-1
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DOI: https://doi.org/10.1007/978-1-4471-5102-9_86-1
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