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Output Feedback Adaptive Robust Control of Uncertain Linear Systems with Disturbances
 IN PROC. OF AMERICAN CONTROL CONFERENCE
, 1999
"... In this paper, a discontinuous projection based adaptive robust control (ARC) scheme is constructed for a class of linear systems subjected to both parametric uncertainties and bounded disturbances. The plant parameters are assumed to be unknown but belong to a known bounded region. Parameter pro ..."
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Cited by 9 (5 self)
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In this paper, a discontinuous projection based adaptive robust control (ARC) scheme is constructed for a class of linear systems subjected to both parametric uncertainties and bounded disturbances. The plant parameters are assumed to be unknown but belong to a known bounded region. Parameter projection is used to ensure that the parameter estimates are within the known region to solve the design conict between adaptive control (AC) and deterministic robust control (DRC). Since only output signal is available for measurement, an observer is designed to provide exponentially convergent estimates of the unmeasured states. This observer has an extended lter structure so that online parameter adaptation can be utilized to reduce the eect of the possible large nominal disturbance that has a known shape but unknown amplitude. Estimation errors that come from initial state estimates and uncompensated disturbances are eectively dealt with via certain robust feedback at each step ...
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 5 (3 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 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 3 (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 ...
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 2 (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...
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. Notations. We denote the open ball B r := fx 2 R n : kxk !rg. A continuous function ff : R0 ! R0 is of class K (ff 2K), if ff(s) is strictly increasing and ff(0)=0#ff 2K 1 if in addition, ff(s) !1as s !1. A continuous function fi : R0 \Theta R0 ! R0 is of class KL if fi(\Delta#t) 2Kfor each fixed t 0 and fi(s# t) ! 0ast !1for each s 0. V (#) (t# x) is the time derivativeoftheLyapunov function V...
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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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'.