Search results for "Applied Mathematics"
showing 10 items of 4379 documents
Looking More Closely at the Rabinovich-Fabrikant System
2016
Recently, we looked more closely into the Rabinovich–Fabrikant system, after a decade of study [Danca & Chen, 2004], discovering some new characteristics such as cycling chaos, transient chaos, chaotic hidden attractors and a new kind of saddle-like attractor. In addition to extensive and accurate numerical analysis, on the assumptive existence of heteroclinic orbits, we provide a few of their approximations.
Stochastic linearization critically re-examined
1997
Abstract The stochastic linearization technique, widely used for the analysis of nonlinear dynamic systems subjected to random excitations, is revisited. It is shown that the standard procedure universally adopted for determining the so-called effective stiffness of the equivalent linear system is erroneous in all previous publications. Two error-free stochastic linearization techniques are elucidated, namely those based on (1) the force linearization and (2) energy linearization.
Numerical approach to the exact controllability of hyperbolic systems
2005
In this paper we present the numerical implementation of H.U.M. (Hilbert Uniqueness Method, J.L.Lions[1]). We restrict ourselves to the exact boundary controllability of the wave equation, with Dirichlet controls, but the numerical method presented here can be applied to other kinds of controllability. The problem is discretized by a finite elements of first order in space and by a discrete time Galerkin approximation (Dupont [1]). The efficiency of the method is illustrated by numerical results.
Time-harmonic solution for acousto-elastic interaction with controllability and spectral elements
2010
The classical way of solving the time-harmonic linear acousto-elastic wave problem is to discretize the equations with finite elements or finite differences. This approach leads to large-scale indefinite complex-valued linear systems. For these kinds of systems, it is difficult to construct efficient iterative solution methods. That is why we use an alternative approach and solve the time-harmonic problem by controlling the solution of the corresponding time dependent wave equation. In this paper, we use an unsymmetric formulation, where fluid-structure interaction is modeled as a coupling between pressure and displacement. The coupled problem is discretized in space domain with spectral el…
Quantized State-Feedback Stabilization for Delayed Markovian Jump Linear Systems with Generally Incomplete Transition Rates
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/961925 open Access This paper is concerned with the robust quantized state-feedback controller design problem for a class of continuous-time Markovian jump linear uncertain systems with general uncertain transition rates and input quantization. The uncertainties under consideration emerge in both system parameters and mode transition rates. This new uncertain model is more general than the existing ones and can be applicable to more practical situations because each transition rate can be completely unknown or only its estimate value is known. B…
Observer-Based Robust Control for Switched Stochastic Systems with Time-Varying Delay
2013
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2013/320703 Open Access This paper investigates the problem of observer-based robust H ∞ control for a class of switched stochastic systems with time-varying delay. Based on the average dwell time method, an exponential stability criterion for switched stochastic delay systems is proposed. Then, H ∞ performance analysis and observer-based robust H ∞ controller design for the underlying systems are developed. Finally, a numerical example is presented to illustrate the effectiveness of the proposed approach.
Robust fault tolerant tracking controller design for a VTOL aircraft
2013
This paper deals with the fault tolerant control (FTC) design for a Vertical Takeoff and Landing (VTOL) aircraft subject to external disturbances and actuator faults. The aim is to synthesize a fault tolerant controller ensuring trajectory tracking for the nonlinear uncertain system represented by a Takagi-Sugeno (T-S) model. In order to design the FTC law, a proportional integral observer (PIO) is adopted which estimate both of the faults and the faulty system states. Based on the Lyapunov theory and ℓ2 optimization, the trajectory tracking performance and the stability of the closed loop system are analyzed. Sufficient conditions are obtained in terms of linear matrix inequalities (LMI). …
Stabilization and controller design of 2D discrete switched systems with state delays under asynchronous switching
2013
Published version of a paper from the journal: Abstract and Applied Analysis. Also available from Hindawi:http://dx.doi.org/10.1155/2013/961870. Open Access This paper is concerned with the problem of robust stabilization for a class of uncertain two-dimensional (2D) discrete switched systems with state delays under asynchronous switching. The asynchronous switching here means that the switching instants of the controller experience delays with respect to those of the system. The parameter uncertainties are assumed to be norm-bounded. A state feedback controller is proposed to guarantee the exponential stability. The dwell time approach is utilized for the stability analysis and controller …
Singular Double Phase Problems with Convection
2020
We consider a nonlinear Dirichlet problem driven by the sum of a $p$ -Laplacian and of a $q$ -Laplacian (double phase equation). In the reaction we have the combined effects of a singular term and of a gradient dependent term (convection) which is locally defined. Using a mixture of variational and topological methods, together with suitable truncation and comparison techniques, we prove the existence of a positive smooth solution.
Modelling of EM glass convection
2008
PurposeTo develop the mathematical model, which allows predicting the temperature and flow distribution of an opaque glass melt with the temperature‐dependent properties in case it is generated by electromagnetic and thermal convection. Analysis has been done for geometry of the model crucible with the immersed rod electrodes. Numerical analysis is used as a tool for finding out the parameters of the system, which allow getting desiderated homogeneity of temperature field by EM action.Design/methodology/approachANSYS CFX software is implemented for coupling of EM, thermal and HD processes in the modelled system. Usability of non‐inductive approximation is shown using a full harmonic analysi…