Definition
A central problem in control theory is the design offeedback controllers so as to have certain outputs ofa given plant to trackprescribed reference trajectories. In any realistic scenario,this control goal has to be achieved in spite of a goodnumber of phenomena which would cause the system to behavedifferently than expected. These phenomena could be endogenous, for instanceparameter variations, or exogenous, such as additional undesiredinputs affecting the behavior of the plant. In numerous designproblems, exogenous inputs are not available for measurement,nor are known ahead of time, but rather can only be seen asunspecified members of a given family of functions.Embedding a suitable “internal model” of sucha family in the controller is a design strategy thathas proven to be quite successful in handling uncertainties inthe controlled plant as well as in the exogenous inputs.
Introduction
The problem of controlling the output of a system soas to achieve asymptotic tracking...
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Abbreviations
- Exosystem:
-
A dynamical system modeling the set of all exogenous inputs (command/disturbances) affecting a controlled plant.
- Internal model:
-
A model of the exogenous inputs (command/disturbances) affecting a controlled plant, embedded in the interior of the controller.
- Generalized tracking problem:
-
The problem of designing a controller able to asymptotically track/reject any exogenous command/disturbance in a fixed set of functions.
- Observer:
-
A device designed to asymptotically track the state of a dynamical system on the basis of measured observations.
- Steady state:
-
A family of behaviors, in a dynamical system, that are asymptotically approached, as actual time tends to infinity or as initial time tends to minus infinity.
Bibliography
AndrieuV, Praly L (2006) On the existence ofa Kazantis-Kravaris/Luenberger observer. SIAM J Contr Optim45:432–456
BirkhoffGD (1927) Dynamical systems. American Mathematical Society,Providence
ByrnesCI, Delli Priscoli F, Isidori A, Kang W (1997) Structurallystable output regulation of nonlinear systems. Automatica33:369–385
ByrnesCI, Isidori A (2003) Limit Sets, Zero dynamics and internalmodels in the problem of nonlinear output regulation. IEEE TransAutom Contr 48:1712–1723
ByrnesCI, Isidori A (2004) Nonlinear internal models for outputregulation. IEEE Trans Autom Contr49:2244–2247
ByrnesCI, Isidori A, Praly L (2003) On the asymptotic properties ofa system Arising in non-equilibrium theory of outputregulation, preprint of the Mittag-Leffler Institute. 18,Stockholm
IsidoriA, Byrnes CI (2007) The steady-state response ofa nonlinear system: ideas, tools and applications,preprint
DavisonEJ (1976) The robust control of a servomechanism problemfor linear time-invariant multivariable systems. IEEE TransAutom Contr AC-21:25–34
DelliPriscoli F, Marconi L, Isidori A (2006) A new approach toadaptive nonlinear regulation. SIAM J Contr Optim45:829–855
FrancisBA (1977) The linear multivariable regulator problem. SIAM JContr Optim 14:486–505
FrancisBA, Wonham WM (1976) The internal model principle of controltheory. Automatica12:457–465
GauthierJP, Kupka I (2001) Deterministic observation theory andapplications. Cambridge University Press,Cambridge
HahnW (1967) Stability of motions. Springer, NewYork
HaleJK, Magalhães LT, Oliva WM (2002) Dynamics in infinitedimensions. Springer, New York
HuangJ, Lin CF (1994) On a robust nonlinear multivariableservomechanism problem. IEEE Trans Autom Contr39:1510–1513
HuangJ, Rugh WJ (1990) On a nonlinear multivariableservomechanism problem. Automatica26:963–972
IsidoriA (1995) Nonlinear Control Systems. Springer,London
IsidoriA (2000), A tool for semiglobal stabilization of uncertainnon-minimum-phase nonlinear systems via output feedback. IEEETrans Autom ContrAC-45:1817–1827
IsidoriA, Byrnes CI (1990) Output regulation of nonlinear systems. IEEETrans Autom Contr 25:131–140
IsidoriA, Marconi L, Serrani A (2003) Robust autonomous guidance: Aninternal model-based approach. Springer,London
KhalilH (1994) Robust servomechanism output feedback controllers forfeedback linearizable systems. Automatica30:587–1599
MarconiL, Praly L, Isidori A (2006) Output stabilization via nonlinearluenberger observers. SIAM J Contr Optim45:2277–2298
SerraniA, Isidori A, Marconi L (2001) Semiglobal nonlinear outputregulation with adaptive internal model. IEEE Trans Autom Contr46:1178–1194
TeelAR, Praly L (1995) Tools for semiglobal stabilization by partialstate and output feedback. SIAM J Control Optim33:1443–1485
WillemsJC (1991) Paradigms and puzzles in the theory of dynamicalsystems, IEEE Transaction on Automatic Control36:259–294
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Isidori, A., Marconi, L. (2009). System Regulation and Design, Geometric and Algebraic Methods in. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_545
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