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On the topological structure of the solution set for a semilinear ffunctional-differential inclusion in a Banach space

Giuseppe Conti, Valeri Obukhovskiĭ, Pietro Zecca (1996)

Banach Center Publications

In this paper we show that the set of all mild solutions of the Cauchy problem for a functional-differential inclusion in a separable Banach space E of the form x’(t) ∈ A(t)x(t) + F(t,xt) is an R δ -set. Here A(t) is a family of linear operators and F is a Carathéodory type multifunction. We use the existence result proved by V. V. Obukhovskiĭ [22] and extend theorems on the structure of solutions sets obtained by N. S. Papageorgiou [23] and Ya. I. Umanskiĭ [32].

On the well-posedness and regularity of the wave equation with variable coefficients

Bao-Zhu Guo, Zhi-Xiong Zhang (2007)

ESAIM: Control, Optimisation and Calculus of Variations

An open-loop system of a multidimensional wave equation with variable coefficients, partial boundary Dirichlet control and collocated observation is considered. It is shown that the system is well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. The Riemannian geometry method is used in the proof of regularity and the feedthrough operator is explicitly computed.

On time optimal control of the wave equation, its regularization and optimality system

Karl Kunisch, Daniel Wachsmuth (2013)

ESAIM: Control, Optimisation and Calculus of Variations

An approximation procedure for time optimal control problems for the linear wave equation is analyzed. Its asymptotic behavior is investigated and an optimality system including the maximum principle and the transversality conditions for the regularized and unregularized problems are derived.

On timed event graph stabilization by output feedback in dioid

B. Cottenceau, Mehdi Lhommeau, Laurent Hardouin, Jean-Louis Boimond (2003)

Kybernetika

This paper deals with output feedback synthesis for Timed Event Graphs (TEG) in dioid algebra. The feedback synthesis is done in order to (1) stabilize a TEG without decreasing its original production rate, (2) optimize the initial marking of the feedback, (3) delay as much as possible the tokens input.

On-line parameter and delay estimation of continuous-time dynamic systems

Janusz Kozłowski, Zdzisław Kowalczuk (2015)

International Journal of Applied Mathematics and Computer Science

The problem of on-line identification of non-stationary delay systems is considered. The dynamics of supervised industrial processes are usually modeled by ordinary differential equations. Discrete-time mechanizations of continuous-time process models are implemented with the use of dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures mechanized in recursive forms are applied for simultaneous identification of input delay and spectral parameters of the...

On-line wavelet estimation of Hammerstein system nonlinearity

Przemysław Śliwiński (2010)

International Journal of Applied Mathematics and Computer Science

A new algorithm for nonparametric wavelet estimation of Hammerstein system nonlinearity is proposed. The algorithm works in the on-line regime (viz., past measurements are not available) and offers a convenient uniform routine for nonlinearity estimation at an arbitrary point and at any moment of the identification process. The pointwise convergence of the estimate to locally bounded nonlinearities and the rate of this convergence are both established.

On-off intermittency in continuum systems driven by the Chen system

Qian Zhou, Zeng-Qiang Chen, Zhu Zhi Yuan (2008)

Kybernetika

Previous studies on on-off intermittency in continuum systems are generally based on the synchronization of identical chaotic oscillators or in nonlinear systems driven by the Duffing oscillator. In this paper, one-state on-off intermittency and two-state on-off intermittency are observed in two five- dimensional continuum systems, respectively, where each system has a two- dimensional subsystem driven by the chaotic Chen system. The phenomenon of intermingled basins is observed below the blowout...

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