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43
Range Identification for Perspective Dynamic Systems Using Linear Approximation
"... Abstract — This paper presents linear approximation ideas to range identification problem for a perspective dynamic system (PDS). Using a recently introduced linear approximation technique, the perspective dynamic system, which is a special class of nonlinear systems, can be approximated by a sequen ..."
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Cited by 14 (1 self)
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Abstract — This paper presents linear approximation ideas to range identification problem for a perspective dynamic system (PDS). Using a recently introduced linear approximation technique, the perspective dynamic system, which is a special class of nonlinear systems, can be approximated by a sequence of linear, timevarying (LTV) subsystems. Observer design problem of the original nonlinear PDS reduces to the observer design of this sequence of LTV subsystems. For each LTV subsystem, existing standard observer methods can be applied. I.
Existence and Learning of Oscillations in Recurrent Neural Networks
, 1999
"... In this paper we study a particular class of nnode recurrent neural networks (RNNs). In the 3node case we use monotone dynamical systems theory to show, for a welldefined set of parameters, that, generically, every orbit of the RNN is asymptotic to a periodic orbit. Then, within the usual `learni ..."
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Cited by 13 (0 self)
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In this paper we study a particular class of nnode recurrent neural networks (RNNs). In the 3node case we use monotone dynamical systems theory to show, for a welldefined set of parameters, that, generically, every orbit of the RNN is asymptotic to a periodic orbit. Then, within the usual `learning' context of Neural Networks, we investigate whether RNNs of this class can adapt their internal parameters so as to `learn' and then replicate autonomously certain external periodic signals. Our learning algorithm is similar to identification algorithms in adaptive control theory. The main feature of the adaptation algorithm is that global exponential convergence of parameters is guaranteed. We also obtain partial convergence results in the nnode case.
Model Reference Adaptive Control of Distributed Parameter Systems
 SIAM J. CONTROL OPTIM
, 1995
"... A model reference adaptive control law is defined for nonlinear distributed parameter systems. The reference model is assumed to be governed by a strongly coercive linear operator defined with respect to a Gelfand triple of reflexive Banach and Hilbert spaces. The resulting nonlinear closed loop sys ..."
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Cited by 13 (1 self)
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A model reference adaptive control law is defined for nonlinear distributed parameter systems. The reference model is assumed to be governed by a strongly coercive linear operator defined with respect to a Gelfand triple of reflexive Banach and Hilbert spaces. The resulting nonlinear closed loop system is shown to be well posed. The tracking error is shown to converge to zero, and regularity results for the control input and the output are established. With an additional richness, or persistence of excitation assumption, the parameter error is shown to converge to zero as well. A finite dimensional approximation theory is developed. Examples involving both first (parabolic) and second (hyperbolic) order systems and linear and nonlinear systems are discussed, and numerical simulation results are presented.
On the stabilization of persistently excited linear systems
 SIAM J. Control Optim
"... We consider control systems of the type ˙x = Ax+α(t)bu, where u ∈ R, (A, b) is a controllable pair and α is an unknown timevarying signal with values in [0, 1] satisfying a persistent excitation condition i.e., ∫ t+T t α(s)ds ≥ µ for every t ≥ 0, with 0 < µ ≤ T independent on t. We prove that s ..."
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Cited by 12 (8 self)
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We consider control systems of the type ˙x = Ax+α(t)bu, where u ∈ R, (A, b) is a controllable pair and α is an unknown timevarying signal with values in [0, 1] satisfying a persistent excitation condition i.e., ∫ t+T t α(s)ds ≥ µ for every t ≥ 0, with 0 < µ ≤ T independent on t. We prove that such a system is stabilizable with a linear feedback depending only on the pair (T, µ) if the eigenvalues of A have nonpositive real part. We also show that stabilizability does not hold for arbitrary matrices A. Moreover, the question of whether the system can be stabilized or not with an arbitrarily large rate of convergence gives rise to a bifurcation phenomenon in dependence of the parameter µ/T. 1
ON CONDITIONS FOR ASYMPTOTIC STABILITY OF DISSIPATIVE INFINITEDIMENSIONAL SYSTEMS WITH INTERMITTENT DAMPING
, 2012
"... Abstract. We study the asymptotic stability of a dissipative evolution in a Hilbert space subject to intermittent damping. We observe that, even if the intermittence satisfies a persistent excitation condition, if the Hilbert space is infinitedimensional then the system needs not being asymptotical ..."
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Cited by 8 (3 self)
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Abstract. We study the asymptotic stability of a dissipative evolution in a Hilbert space subject to intermittent damping. We observe that, even if the intermittence satisfies a persistent excitation condition, if the Hilbert space is infinitedimensional then the system needs not being asymptotically stable (not even in the weak sense). Exponential stability is recovered under a generalized observability inequality, allowing for timedomains that are not intervals. Weak asymptotic stability is obtained under a similarly generalized unique continuation principle. Finally, strong asymptotic stability is proved for intermittences that do not necessarily satisfy some persistent excitation condition, evaluating their total contribution to the decay of the trajectories of the damped system. Our results are discussed using the example of the wave equation, Schrödinger’s equation and, for strong stability, also the special case of finitedimensional systems.
OnLine Parameter Estimation For InfiniteDimensional Dynamical Systems
, 1997
"... The online or adaptive identification of parameters in abstract linear and nonlinear infinitedimensional dynamical systems is considered. An estimator in the form of an infinitedimensional linear evolution system having the state and parameter estimates as its states is defined. Convergence of th ..."
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Cited by 5 (0 self)
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The online or adaptive identification of parameters in abstract linear and nonlinear infinitedimensional dynamical systems is considered. An estimator in the form of an infinitedimensional linear evolution system having the state and parameter estimates as its states is defined. Convergence of the state estimator is established via a Lyapunov estimate. The finitedimensional notion of a plant being sufficiently rich or persistently excited is extended to infinite dimensions. Convergence of the parameter estimates is established under the additional assumption that the plant is persistently excited. A finitedimensional approximation theory is developed, and convergence results are established. Numerical results for examples involving the estimation of both constant and functional parameters in onedimensional linear and nonlinear heat or diffusion equations and the estimation of sti#ness and damping parameters in a onedimensional wave equation with KelvinVoigt viscoelastic damping ...
Stabilization of twodimensional persistently excited linear control systems with arbitrary rate of convergence
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Towards uniform linear timeinvariant stabilization of systems with persistency of excitation
, 2007
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Indirect adaptive control of a class of interconnected nonlinear dynamical systems
 International Journal of Control
, 1993
"... This paper has been mechanically scanned. Some errors may have been inadvertently introduced. ..."
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Cited by 4 (1 self)
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This paper has been mechanically scanned. Some errors may have been inadvertently introduced.