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21
Adaptive Observer for MIMO Linear Time Varying Systems
"... : The purpose of adaptive observer is to perform joint stateparameter estimation of parameterized state space system. In this paper, we propose a new approach to adaptive observer design for multiinputmultioutput (MIMO) linear time varying (LTV) or stateaffine systems. It is conceptually simpl ..."
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Cited by 10 (0 self)
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: The purpose of adaptive observer is to perform joint stateparameter estimation of parameterized state space system. In this paper, we propose a new approach to adaptive observer design for multiinputmultioutput (MIMO) linear time varying (LTV) or stateaffine systems. It is conceptually simple and computationally efficient. In the case of noise free system with constant unknown parameters, global exponential convergence for joint stateparameter estimation is established. In the presence of noises, it is proved that the estimation errors are bounded and converge in the mean to zero if the noises are bounded and have zero means. We also present a unified formulation for some known adaptive observers based on dynamic transformations. This general framework enhances the conceptual simplicity of the proposed approach. Potential applications of the adaptive observer are online continuoustime system identification, fault detection and isolation, and adaptive control. Two numerical ...
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 ...
SelfOptimizing Control and Passive Velocity Field Control of Intelligent Machines
, 1995
"... This dissertation deals with the formulation, analysis and implementation of control systems for intelligent mechanical machines. These machines must operate safely under uncertain conditions without external supervision, and must determine and achieve, through adaptation and learning, the task that ..."
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Cited by 8 (8 self)
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This dissertation deals with the formulation, analysis and implementation of control systems for intelligent mechanical machines. These machines must operate safely under uncertain conditions without external supervision, and must determine and achieve, through adaptation and learning, the task that optimizes a prescribed performance criterion. The primary application described in this dissertation is an intelligent exercise machine which is safe to operate and determines the optimal exercise routine based on the apriori unknown strength characteristics of its user. In the selfoptimizing control problem a performance criterion, which depends on the machine behavior as well as on other unknown parameters, is to be optimized. Thus, unlike standard adaptive control applications where the desired behavior is speci ed apriori, it is necessary to explicitly determine the optimal behavior as part of the adaptation process, and to control the machine so that it behaves optimally. The proposed solution consists of an adaptive controller and a reference generator in tandem. The adaptive controller is capable of tracking arbitrary behaviors and the reference generator commands the control system to alternately follow either a training behavior or the estimated optimal behavior. The reference
Output Feedback Adaptive Robust Precision Motion Control of Linear Motors
 1029–1039, the finalist for the Best Student Paper award of ASME Dynamic System and Control Division in IMECE00
, 2000
"... Linear motors oer several advantages over their rotary counterparts in many applications requiring linear motion by eliminating mechanical transmission mechanisms. However, these advantages are obtained at the expense of added diculties in controlling such a system. This paper studies the high pe ..."
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Cited by 7 (6 self)
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Linear motors oer several advantages over their rotary counterparts in many applications requiring linear motion by eliminating mechanical transmission mechanisms. However, these advantages are obtained at the expense of added diculties in controlling such a system. This paper studies the high performance robust motion control of an epoxy core linear motor, which has a negligible electrical dynamics due to the fast response of the electrical subsystem. A discontinuous projection based adaptive robust control (ARC) scheme is constructed. Since only output signal is available for measurement, an observer is designed to provide exponentially convergent estimates of the unmeasurable 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. Estimation errors that come from initial state estimates and uncompensated disturbances are eectively dealt with via certain robust...
Learning Nonlinearly Parametrized Decision Regions
 J. Math. Systems, Estimation, and Control
, 1996
"... In this paper we present a deterministic analysis of an online scheme for learning very general classes of nonlinearly parametrized decision regions. The only input required is a sequence ((xk; yk)) k2Z + of data samples, where yk =1if xkbelongs to the decision region of interest, and yk =,1 otherwi ..."
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Cited by 4 (4 self)
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In this paper we present a deterministic analysis of an online scheme for learning very general classes of nonlinearly parametrized decision regions. The only input required is a sequence ((xk; yk)) k2Z + of data samples, where yk =1if xkbelongs to the decision region of interest, and yk =,1 otherwise. Averaging results and Lyapunov theory are used to prove the stability of the scheme. In the course of this proof, conditions on both the parametrization and the sequence of input examples arise which are su cient to guarantee convergence of the algorithm. Anumber of examples are presented, including the problem of learning an intersection of half spaces using only data samples. Key words: online learning algorithm, nonlinear classi er, decision region, discriminant function, parametrization AMS Subject Classi cations: 68T05 1
Backstepping control of linear timevarying systems with known and unknown parameters
 IEEE Trans. Automat. Control
, 1908
"... Abstract—The backstepping control design procedure has been used to develop stabilizing controllers for time invariant plants that are linear or belong to some class of nonlinear systems. The use of such a procedure to design stabilizing controllers for plants with time varying parameters has been a ..."
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Cited by 3 (0 self)
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Abstract—The backstepping control design procedure has been used to develop stabilizing controllers for time invariant plants that are linear or belong to some class of nonlinear systems. The use of such a procedure to design stabilizing controllers for plants with time varying parameters has been an open problem. In this paper we consider the backstepping design procedure for linear time varying (LTV) plants with known and unknown parameters. We first show that a backstepping controller can be designed for an LTV plant by following the same steps as in the linear timeinvariant (LTI) case and treating the plant parameters as constants at each time. Its stability properties however cannot be established by using the same Lyapunov function and techniques as in the LTI case. We then introduce a new parametrization and filter structure that takes into account the plant parameter variations leading to a new backstepping controller. The new
Persistence of excitation in linear systems
 Proc. Amer. Conrro/ Conf
, 1985
"... ,4hsfrac[: This paper develops output reachability characterizations of linear finite dimensional multivwiate systems, so as tt~ translate excitation properties of system inputs to excitation properties of system outputs. states, or associated regression vectors. Such properties are of fundamental c ..."
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Cited by 3 (0 self)
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,4hsfrac[: This paper develops output reachability characterizations of linear finite dimensional multivwiate systems, so as tt~ translate excitation properties of system inputs to excitation properties of system outputs. states, or associated regression vectors. Such properties are of fundamental concern for convergence of algorithms involving ontine identification, adaptive state estimation, prediction and control, Persistence of excitation guarantees convergence without a priori stability assumptions and ensures robustness properties. Keword.r: Persistence of excitation, Sufficient richness. Adaptive identification, Reachability of regression vectors. Adaptive control. 1.
A State and Parameter Identification Scheme for Linearly Parameterized Systems
 ASME Journal of Dynamic Systems, Measurement and Control
, 1998
"... This paper presents an adaptive algorithm to estimate states and unknown parameters simultaneously for nonlinear time invariant systems which depend affinely on the unknown parameters. The system output signals are filtered and reparameterized into a regression form from which the least squares err ..."
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Cited by 2 (2 self)
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This paper presents an adaptive algorithm to estimate states and unknown parameters simultaneously for nonlinear time invariant systems which depend affinely on the unknown parameters. The system output signals are filtered and reparameterized into a regression form from which the least squares error scheme is applied to identify the unknown parameters. The states are then estimated by an observer based on the estimated parameters. The major difference between this algorithm and existing adaptive observer algorithms is that the proposed algorithm does not require any special canonical forms or rank conditions. However, an output measurement condition is imposed. The stability and performance limit of this scheme are analyzed. Two examples are then presented to show the effectiveness of the proposed schemes.
Identification of linearly overparametrized nonlinear systems
 IEEE Trans. on Automatic Control
, 1992
"... AbsrracfOften, a dynamical model is nonlinear in the unknown parameters, but it can be transformed into an overparametrized linear regression model, where the components of the overparametrization vector are nonlinear functions of the smaller number of unknown parameters. We present an algorithm th ..."
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Cited by 2 (1 self)
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AbsrracfOften, a dynamical model is nonlinear in the unknown parameters, but it can be transformed into an overparametrized linear regression model, where the components of the overparametrization vector are nonlinear functions of the smaller number of unknown parameters. We present an algorithm that directly identifies the unknown parameters, we characterize the convergence domains under two different sets of assumptions on the excitation of the signals, and we compute the corresponding convergence rates. I. INTRODUCTIONSTATEMENT OF THE PROBLEM In many practical modeling and control applications, a partial prior knowledge of the structure and the parametrization of the system is available. A typical situation is where the only unknowns of the system are the values of a few physical parameters which
On the OptimizingAdaptive Control Problem
 In: Proceedings of the 1994 American Control Conference, Baltimore MD
, 1994
"... The optimizingadaptive control problem arises in applications where the desired behavior is not specified explicitly, but instead, an objective function of the plant behavior and the unknown plant itself is to be optimized. In these cases, the control task involves the explicit determination of the ..."
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Cited by 1 (1 self)
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The optimizingadaptive control problem arises in applications where the desired behavior is not specified explicitly, but instead, an objective function of the plant behavior and the unknown plant itself is to be optimized. In these cases, the control task involves the explicit determination of the optimal behavior and the control action to achieve that behavior. The difficulty with this problem is that it involves a conflict between identification and optimization on the one hand, and control on the other. In this paper, we study this problem in the context of the intelligent exercise machine application. We propose two related excitation supervisors which switch between an excitation phase and a control phase, based on an internally generated optimality error signal. 1. Introduction In most adaptive control applications, the task is to cause the parameterized unknown plant to behave according to some preassigned behavior, typically specified as a state or an output trajectory. In s...