Search results for "nonlinear system"

A nonlocal problem arising from heat radiation on non-convex surfaces

1997

We consider both stationary and time-dependent heat equations for a non-convex body or a collection of disjoint conducting bodies with Stefan-Boltzmann radiation conditions on the surface. The main novelty of the resulting problem is the non-locality of the boundary condition due to self-illuminating radiation on the surface. Moreover, the problem is nonlinear and in the general case also non-coercive. We show that the non-local boundary value problem admits a maximum principle. Hence, we can prove the existence of a weak solution assuming the existence of upper and lower solutions. This result is then applied to prove existence under some hypotheses that guarantee the existence of sub- and…

A kriging interpolation strategy for the optimization of Acidithiobacillus ferrooxidans biomass production using fed-batch bioreactors

2008

In this work, a procedure for the optimization of Acidithiobacillus ferrooxidans biomass production in fed-batch reactors using a model based on optimal spatial interpolation of experimental data is proposed. The approach is useful in those cases where specific growth and substrate consumption rates are unknown. Based on interpolation, the optimal values of biomass and substrate concentrations set points are obtained at the minimum of 2-dimensional cost function. In the fed-batch reactor biomass and substrate concentrations are controlled at their set points by changing the input flow and its concentration. We propose a minimum variance control strategy which improves the classical proporti…

Linear parameter estimation and predictive constrained control of wiener/hammerstein systems

2003

Abstract A new, analytical, orthonormal basis functions (OBF)-based design methodology for adaptive predictive constrained control of open-loop stable, possibly nonminimum phase, time-varying Wiener and Hammerstein systems is presented. A linear adaptive least-squares parameter estimation algorithm is applied both to a nonlinear static part and a linear dynamic, OBF-modeled factor of the Wiener/Hammerstein system. A notion of inverse systems is crucial for linear estimation of both Wiener and Hammerstein systems, with in verses of the nonlinear or linear parts respectively involved. The adaptive estimator is coupled with a simple but robust, predictive control strategy called Extended Horiz…

FINITE ELEMENT APPROXIMATION OF NONLOCAL HEAT RADIATION PROBLEMS

1998

This paper focuses on finite element error analysis for problems involving both conductive and radiative heat transfers. The radiative heat exchange is modeled with a nonlinear and nonlocal term that also makes the problem non-monotone. The continuous problem has a maximum principle which suggests the use of inverse monotone discretizations. We also estimate the error due to the approximation of the boundary by showing continuous dependence on the geometric data for the continuous problem. The final result of this paper is a rigorous justification and error analysis for methods that use the so-called view factors for numerical modeling of the heat radiation.

Signal Denoising with Harten’s Multiresolution Using Interpolation and Least Squares Fitting

2014

Harten’s multiresolution has been successfully applied to the signal compression using interpolatory reconstructions with nonlinear techniques. Here we study the applicability of these techniques to remove noise to piecewise smooth signals. We use two reconstruction types: interpolatory and least squares, and we introduce ENO and SR nonlinear techniques. The standard methods adaptation to noisy signals and the comparative of the different schemes are the subject of this paper.

Verifications of Primal Energy Identities for Variational Problems with Obstacles

2018

We discuss error identities for two classes of free boundary problems generated by obstacles. The identities suggest true forms of the respective error measures which consist of two parts: standard energy norm and a certain nonlinear measure. The latter measure controls (in a weak sense) approximation of free boundaries. Numerical tests confirm sharpness of error identities and show that in different examples one or another part of the error measure may be dominant.

Nonlinear coefficient measurement in highly dispersive fibers

2018

We present a novel approach for measuring nonlinear coefficients in fibers with significant pulse broadening. We perform a proof-of-concept demonstration for 200-m-long polarization-maintaining and single-mode fibers pumped at 1060 nm with ps pulses.

All-fiber based chaotic polarization scrambler

2014

We present a fiber-based polarization scrambler founded on the nonlinear interaction between a signal and its backward replica generated and amplified by a reflective loop. The output polarization dynamic turns out to be chaotic.

Refinement of the Dispersion Equations of the Nonlinear Biaxial Crystals KTiOAsO/sub 4/, RbTiOAsO/sub 4/ and CsTiOAsO/sub 4/. Method and Measurements

2005

Robust finite-time fuzzy H∞ control for uncertain time-delay systems with stochastic jumps

2014

Abstract This paper investigates the problem of robust finite-time H ∞ control for a class of uncertain discrete-time Markovian jump nonlinear systems with time-delays represented by Takagi–Sugeno (T–S) model. Initially, the concepts of stochastic finite-time boundedness and stochastic finite-time H ∞ stabilization are presented. Then, by using stochastic Lyapunov–Krasovskii functional approach, sufficient conditions are derived such that the resulting close-loop system is stochastically finite-time bounded and satisfies a prescribed H ∞ disturbance attenuation level in a given finite-time interval. Furthermore, sufficient criteria on stochastic finite-time H ∞ stabilization using a fuzzy s…