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Output feedback adaptive robust control of uncertain linear systems with disturbances
 ASME Journal of Dynamic Systems, Measurement, and Control
, 2006
"... In this paper, a discontinuous projection based output feedback adaptive robust control (ARC) scheme is constructed for a class of linear systems subjected to both parametric uncertainties and disturbances that might be output dependent. An observer is first designed to provide exponentially converg ..."
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Cited by 13 (5 self)
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In this paper, a discontinuous projection based output feedback adaptive robust control (ARC) scheme is constructed for a class of linear systems subjected to both parametric uncertainties and disturbances that might be output dependent. An observer is first designed to provide exponentially convergent estimates of the unmeasured states. This observer has an extended filter structure so that online parameter adaptation can be utilized to reduce the effect of possible large disturbances that have known shapes but unknown amplitudes. Estimation errors that come from initial state estimates and uncompensated disturbances are dealt with via certain robust feedback at each step of the backstepping design. Compared to other existing output feedback robust adaptive control schemes, the proposed method explicitly takes into account the effect of disturbances and uses both parameter adaptation and robust feedback to attenuate their effects for an improved tracking performance. Experimental results on the control of an iron core linear motor are presented to illustrate the effectiveness and achievable performance of the proposed scheme. �DOI: 10.1115/1.2363413�
UGAS and ULES of Nonautonomous Systems: Applications to Integral Control of Ships and Manipulators
 In Proc. 5th. European Contr. Conf
, 1998
"... Nonlinear, adaptive backstepping design is applied to the tracking control problem for a class of mechanical systems with constant disturbances. The adaptive algorithm provides integral action that guarantees zero steadystate tracking error. The main contribution of this paper is to show that the ( ..."
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Cited by 7 (4 self)
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Nonlinear, adaptive backstepping design is applied to the tracking control problem for a class of mechanical systems with constant disturbances. The adaptive algorithm provides integral action that guarantees zero steadystate tracking error. The main contribution of this paper is to show that the (timevarying) closedloop tracking error system has an equilibrium, corresponding to zero steadystate tracking error, that is uniformly globally asymptotically stable (UGAS) and uniformly locally exponentially stable (ULES). These properties (and a uniform local Lipschitz condition) guarantee robustness of stability while weaker properties, like uniform global stability plus global convergence, do not. Notation: k\Deltak stands for the Euclidean norm of vectors and induced norm of matrices. k\Deltak 1 denotes the L1 norm. We denote by B r the set B r 4 = fx 2 IR n : kxk rg. A continuous function ff : IR 0 ! IR 0 is said to be of class K, ff 2 K, if ff(s) is strictly increasing and ff...
Nonlinearities Enhance Parameter Convergence in OutputFeedback Systems
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 1998
"... While the parameter convergence properties of standard adaptive algorithms for linear systems are well established, there are no similar results on the parameter convergence of adaptive controllers for nonlinear systems, which have gained popularity in recent years. In this paper we focus on a recen ..."
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Cited by 6 (1 self)
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While the parameter convergence properties of standard adaptive algorithms for linear systems are well established, there are no similar results on the parameter convergence of adaptive controllers for nonlinear systems, which have gained popularity in recent years. In this paper we focus on a recently developed class of adaptive schemes for outputfeedback nonlinear systems and show that parameter convergence is guaranteed if and only if an appropriately defined signal vector, which does not depend on closedloop signals, is persistently exciting. Then we develop an analytic procedure which allows us, given a specific nonlinear system and a specific reference signal, to determine a priori whether or not this vector is persistently exciting (PE), and, hence, whether or not the parameter estimates will converge. In the process we show that the presence of nonlinearities usually reduces the sufficient richness (SR) requirements on the reference signals, and hence enhances parameter conver...
Nonlinearities Enhance Parameter Convergence in StrictFeedback Systems
 IEEE Transactions on Automatic Control
, 1998
"... Following the development of a parameter convergence analysis procedure for outputfeedback nonlinear systems, we shift our attention to strictfeedback nonlinear systems in this paper. We develop an analytic procedure which allows us, given a specific nonlinear system and a specific reference signa ..."
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Cited by 5 (0 self)
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Following the development of a parameter convergence analysis procedure for outputfeedback nonlinear systems, we shift our attention to strictfeedback nonlinear systems in this paper. We develop an analytic procedure which allows us, given a specific nonlinear system and a specific reference signal, to determine a priori whether or not the parameter estimates will converge to their true values, simply by checking the linear independence of the rows of a constant real matrix. Moreover, we show that this convergence is exponential. Finally, we prove that even if the rows of this constant matrix are not linearly independent, partial parameter convergence is still achieved, in the sense that the parameter error vector converges asymptotically to the left nullspace of this matrix. Index TermsNonlinear systems, adaptive control, parameter convergence, strictfeedback form. I. INTRODUCTION In linear control theory, there exist many results and design methods which deal with the case of ...
Uniform Exponential Stability for Families of Linear TimeVarying Systems
, 2000
"... We present sufficient conditions for uniform exponential stability of families of linear time varying (LTV) systems. That is, LTV systems characterized bycertain parameter. Our conditions are in the form of classical concepts in adaptive control, such as persistency of excitation. However, our proo ..."
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Cited by 1 (0 self)
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We present sufficient conditions for uniform exponential stability of families of linear time varying (LTV) systems. That is, LTV systems characterized bycertain parameter. Our conditions are in the form of classical concepts in adaptive control, such as persistency of excitation. However, our proofs are based on modern tools which can be interpreted as an "integral" version of Lyapunov theorems# rather than on the concept of uniform complete observability which is most common in the literature. Uniformity is established in both, the initial conditions of the system, and the parameter whichcharacterizes each system of the `family'.
UGAS of nonlinear timevarying systems: a deltapersistency of excitation approach
"... We study the problem of stability analysis for certain nonlinear systems. Our contributions are new tools to guarantee uniform global asymptotic stability (UGAS) of nonlinear timevarying (NLTV) systems. Firstly, we provide new definitions of persistency of excitation (PE). In particular, wegive her ..."
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We study the problem of stability analysis for certain nonlinear systems. Our contributions are new tools to guarantee uniform global asymptotic stability (UGAS) of nonlinear timevarying (NLTV) systems. Firstly, we provide new definitions of persistency of excitation (PE). In particular, wegive here a new definition of uniform ffi PE (uffiPE) which, though conceptually equivalent to the original one introduced [7], is mathematically less conservative. We also provide with some properties of ffi PE pairs and contribute with a result which establishes UGAS of NLTV systems under uffiPE.
unknown title
, 2002
"... www.elsevier.com/locate/sysconle Uniform exponential stability of linear timevarying systems: revisited ..."
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www.elsevier.com/locate/sysconle Uniform exponential stability of linear timevarying systems: revisited
PROOF COPY [DS051318] 024604JDS PROOF COPY [DS051318] 024604JDS PROOF COPY [DS051318] 024604JDS
"... A great deal of effort has been devoted to the control of uncertain nonlinear systems �1–7 � and some of the results have been extended to the output feedback control. Specifically, Kanellakopoulos et al. introduced backstepping procedure to a class of nonlinear ..."
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A great deal of effort has been devoted to the control of uncertain nonlinear systems �1–7 � and some of the results have been extended to the output feedback control. Specifically, Kanellakopoulos et al. introduced backstepping procedure to a class of nonlinear
INDIRECT NEURAL NETWORK ADAPTIVE ROBUST CONTROL OF LINEAR MOTOR DRIVE SYSTEM *
"... In this paper, au indirect neural network adaptive robust control (INNARC) scheme is developed for the precision motion control of lineax motor drive systems. The proposed INNARC achieves not only good output tracking t)erformance but also excellent identifications of unknown nonlinear forces in sys ..."
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In this paper, au indirect neural network adaptive robust control (INNARC) scheme is developed for the precision motion control of lineax motor drive systems. The proposed INNARC achieves not only good output tracking t)erformance but also excellent identifications of unknown nonlinear forces in system for secondaxy purposes such as prognostics and machine health monitoring. Such dual objectives are accomplished through the complete separation of unknown nonlinem'ity estimation via neural networks and the design of baseline adaptive robust control (ARC) law for output; tracking perfi)rmance. Specifically, recurrent neural network (NN) structnre with NN weights tuned online is employed to approximate various unknown nonlinem&quot; forces of the system having unknown forms to adapt to various operating conditions. The design is actual system dynamics