A time-varying forgetting factor stochastic gradient combined with Kalman filter algorithm for parameter identification of dynamic systems

Parameter estimation problem of a class of observer canonical state-space system is considered in this paper. By means of the property of the shift operator, the space-state model is transformed into the input–output representations. Then, a time-varying forgetting factor stochastic gradient combined with Kalman filter algorithm is proposed. The proposed algorithm is based on interactively estimating unknown parameters to achieve all the parameters identification of the system. A numerical example is provided to verify the effectiveness of the proposed algorithm.     

Technical stability of nonlinear time-varying systems with small parameters

ＩｎｔｒｏｄｕｃｔｉｏｎＳｔａｂｉｌｉｔｙｐｒｏｂｌｅｍｓａｒｉｓｉｎｇｆｒｏｍｅｎｇｉｎｅｅｒｉｎｇａｐｐｌｉｃａｔｉｏｎｓａｒｅｕｓｕａｌｌｙｒｅｌａｔｅｄｔｏｃｅｒｔａｉｎｑｕａｎｔｉｔｉｅｓｔｈａｔｓｐｅｃｉｆｙｔｈｅｓｔｒｅｎｇｔｈｏｆａｄｍｉｓｓｉｂｌｅｄｉｓｔｕｒｂａｎｃｅｓａｎｄｔｈｅｌｉｍｉｔｓｏｎｄｅｖｉａｔｉｏｎｓｏｆｍｏｔｉｏｎｏｆｔｈｅｄｉｓｔｕｒｂｅｄｓｙｓｔｅｍ .Ｉｎｔｈｉｓｒｅｇａｒｄ ,ｔｈｅｃｏｎｖｅｎｔｉｏｎａｌＬｉａｐｕｎｏｖｓｔａｂｉｌｉｔｙｃｏｎｃｅｐｔ…     

On the dynamic shakedown stability

Summary Starting from a Benvenuto's sufficient stability Criterion, in the elastic-plastic range, on the load paths which will systematically exclude elastic returns in the actual state, and adopting a suitable incremental formulation of the Ceradini's theorem on the dynamic shakedown, the dynamic shakedown stability property may be proven, if the comparison material is assumed absolutely stable.

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Sommario Partendo da un noto risultato di Benvenuto circa un criterio sufficiente di stabilità elastoplastica su percorsi dei carichi che sistematicamente escludono ritorni elastici nello stato attuale, e adottando una opportuna formulazione incrementale del teorema di Ceradini sull'adattamento dinamico dei materiali, è possibile provare la stabilità dell'adattamento dinamico se il materiale fittizio di confronto è in fase stabile.

     

Efficient computation for dynamic responses of systems with time-varying characteristics

Based on Neumman series and epsilon-algorithm, an efficient computation for dynamic responses of systems with arbitrary time-varying characteristics is investigated. Avoiding the calculation for the inverses of the equivalent stiffness matrices in each time step, the computation effort of the proposed method is reduced compared with the full analysis of Newmark method. The validity and applications of the proposed method are illustrated by a 4-DOF spring-mass system with periodical time-varying stiffness properties and a truss structure with arbitrary time-varying lumped mass. It shows that good approximate results can be obtained by the proposed method compared with the responses obtained by the full analysis of Newmark method.     

On dynamic stability and quasi-bifurcation

In this paper, a dynamic stability concept and a quasi-bifurcation criterion introduced in a recent paper [1] are clarified. A simple dynamic system of four degrees of freedom is employed to illustrate the concept and the significance of the criterion.     

Improved delay-dependent stability conditions for recurrent neural networks with multiple time-varying delays

This paper investigates the global asymptotic stability problem for recurrent neural networks with multiple time-varying delays. Using the free-weighting matrix technique, and incorporating the interconnected information between the upper bounds of multiple time-varying delays, two less conservative delay-dependent asymptotic stability conditions are proposed, which are expressed by linear matrix inequalities, and can be conveniently solved by the existing softwares. Numerical examples show the reduce conservatism of the obtained conditions.     

Robust stability of nonlinear model-based networked control systems with time-varying transmission times

Robust stability of a class of model-based networked control systems (MB-NCSs, for short) with nonlinear perturbation is analyzed. Based on the model-based networked control algorithm, a linear model of the plant is used to estimate the plant state behavior between transmission times. The case that the nonlinear plant and the linear plant model are connected via a network channel with transmission times that are varying within a time interval is of particular interest. Sufficient condition on stability of MB-NCSs with nonlinear perturbation is given. One advantage of the proposed method is that the maximum transmission interval and the robustness bound on nonlinear perturbation can be computed. Finally, numerical simulation is worked out to show our main result.     

Energy determines multiple stability in time-delayed systems

Nonlinear Dynamics - Infinite dimensions always challenge the analysis of multiple stability in nonlinear time-delayed systems, as the computation and visualization of conventional basin of...     

On the stability boundary of hamiltonian systems

The criterion for the points in the parameter space being on the stability boundary of linear Hamiltonian system depending on arbitrary numbers of parameters was given, through the sensitivity analysis of eigenvalues and eigenvectors. The results show that multiple eigenvalues with Jordan chain take a very important role in the stability of Hamiltonian systems. Foundation item: the National Natural Science Foundation of China (10072012); the National Natural Science Foundation of Russia Biography: QI Zhao-hui (1964-)     

ON THE STABILITY BOUNDARY OF HAMILTONIAN SYSTEMS

ＩｎｔｒｏｄｕｃｔｉｏｎＭａｎｙｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍｓｃａｎｂｅｖｉｅｗｅｄａｓｌｉｎｅａｒＨａｍｉｌｔｏｎｉａｎｓｙｓｔｅｍｓ.Ｗｈｅｎｗｅｓｔｕｄｙｔｈｅｅｆｆｅｃｔｓｏｆｓｙｓｔｅｍｐａｒａｍｅｔｅｒｓｏｎｔｈｅｂｅｈａｖｉｏｒｏｆｔｈｅｓｙｓｔｅｍｓ,ｔｈｅｓｙｓｔｅｍｃａｎｂｅｒｅｇａｒｄｅｄａｓｔｈｅｓｙｓｔｅｍｄｅｐｅｎｄｉｎｇｏｎｐａｒａｍｅｔｅｒｓ.Ｖｅｒｙｉｍｐｏｒｔａｎｔｓｙｓｔｅｍｐａｒａｍｅｔｅｒｓ ,ｓｕｃｈａｓｃｒｉｔｉｃａｌｌｏａｄ ,ｃｒｉｔｉｃａｌａｎｇ…     

On the stability of stochastic difference systems

In this paper the stability of linear stochastic difference equations and a class of weakly non-linear stochastic difference equations is considered. For the linear systems explicit criteria are derived for the stability of the moments of any order. We also show how the moments of a linear stochastic difference system can be computed when a certain Lie-algebraic condition is satisfied.     

Systematic closed form modeling of hybrid parameter multiple body systems

Presented in this paper is a systematic approach to modeling non-holonomic hybrid parameter multiple body systems. The continuum bodies are represented with the postulates usually associated to the non-linear theories, the Timoshenko (like) beam theories, the higher order plate and shell theories, and the rational theories (e.g. rods) with intrinsic rotary inertia properties.The methodology is an extension of previous work. It is founded in variational principles, but uses vector algebra to eliminate tedium. The variational nature of the methodology allows rigorous equation formulation providing not only the complete non-linear hybrid differential equations, but also the boundary conditions. The methodology is formulated satisfying general non-holonomic constraints; it produces a minimal realization. The spatial dimensions of the continuua are not restricted and the inter-body connections are completely general.To demonstrate the application of the technique, a two-link elastic pendulum or manipulator is modeled. The algorithmic modeling steps are demonstrated. Numerical simulations are presented.     

A survey of some recent results in the stability and instability analyses of time-varying systems

After formulating the problem of stability and instability of linear and non-linear time varying feedback systems, we give a concise survey of a few known stability results for non-linear time invariant and time varying systems. This serves as motivation for the establishment of general frequency domain stability and instability criteria for time varying linear and non-linear feedback systems. All the details are omitted in an attempt to give an overall view. Finally some comments are made on the stability analysis of systems governed by partial differential equations.     

The effect of damping on the dynamic stability of nonconservative systems

Summary A study of the effect of vanishing viscous damping on the stability of nonconservative linear elastic systems, with special reference to systems that lose stability statically through the emergence of new equilibrium configurations close to the principal one, i. e. by divergence. It is shown that in this case slight damping presents a wide range of effects on the stability of the system.

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Sommario Si studia l'effetto della presenza di smorzamenti viscosi tendenti a zero sulla stabilità di sistemi elastici lineari soggetti a forze posizionali non conservative, con particolare riguardo a quei sistemi che perdono stabilità staticamente, per la comparsa di nuove configurazioni di equilibrio prossime a quella principale, od anche, come si usa dire, per « divergenza ». Si mostra come in tal caso deboli smorzamenti viscosi presentino un'ampia casistica di effetti sulla stabilità del sistema.

     

On the stability of motion of uncertain systems

The basic theorem of the direct Lyapunov method on the stability of solutions of uncertain systems with respect to a moving invariant set is generalized. A corollary of general assertion is cited in terms of scalar Lyapunov functions. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 2, pp. 105–109, February, 1999.     

On the stability of equilibrium of continuous systems

Summary A sufficiency theorem for the stability of a linearly viscoelastic solid subjected to partial follower surface tractions is established. It is shown that an appropriately defined functional metric space must be introduced in order to formulate a well-posed problem. The usual energy method, if applicable, and the Galerkin method, if convergent, yield stability conditions only in a functional space whose metric is defined in an average

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Übersicht Es wird ein hinreichendes Kriterium für die Stabilität eines viskoelastischen festen Körpers abgeleitet, der Kräften unterworfen wird, die teilweise den Verformungen der Oberfläche folgen. Es wird gezeigt, daß ein geeignet definierter metrischer Funktionalraum eingeführt werden muß, um das Problem vernünftig formulieren zu können. Die übliche Energie-Methode, sofern sie anwendbar ist, sowie das GalerkinVerfahren, wenn es konvergiert, ergeben lediglich Stabilitätsbedingungen in einem Funktionalraum, dessen Metrik im Mittel definiert ist.

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This research was supported by the National Aeronautics and Space Administration under Grant NsG 605.     

The dynamic stability of degenerate systems under parametric excitation

Summary The parametric resonance in a system having two modes of the same frequency is studied. The simultaneous occurence of the instabilities of the first and second kind is examined, by using a generalized perturbation procedure. The region of instability in the first approximation is obtained by using the Sturm's theorem for the roots of a polynomial equation.

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Übersicht Es wird die parametrische Resonanz eines Systems betrachtet, dessen zwei Eigenfrequenzen gleich sind. Das gleichzeitige Auftreten von Instabilitäten erster und zweiter Art wird durch eine verallgemeinerte Störungsrechnung untersucht. Der Instabilitätsbereich läßt sich dann in erster Näherung unter Benutzung des Sturmschen Satzes über die Wurzeln eines Polynoms berechnen.

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The author is indebted to Prof. Dr. E. Mettler, Universität Karlsruhe, for his useful suggestions. The author's grateful thanks are due to the German Academic Exchange Service (DAAD) for the financial support at the Institut für Mechanik, Universität Karlsruhe.