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For this research, the properties of the logistic growth model for independent and coexisting species were used to set definitions for the possible regulation of one or two growth variables through their coupling parameters. The present analysis is done for the single-species Verhulst model without coupling, the single-species Verhulst model coupled with an exogenous signal, and the two-species Verhulst coexistence growth model which represents six different ecological regimes of interaction. The models' parameters, such as the intrinsic growth rate and the coupling, are defined. Finally, the control results are expressed as lemmas for regulation, and they are shown using a simulation example of a fish population growing independent of human interaction (no harvesting, no fishing) and the simulation of the regulation of said population when the coupling of fish and humans is involved (harvesting, fishing). [ABSTRACT FROM AUTHOR]

Highlights • An alcoholic fermentation process is represented in a Takagi–Sugeno form. • A Takagi–Sugeno Proportional–Integral controller is designed for temperature regulation. • By means of the generated control law, the tracking of the trajectory is achieved smoothly. Abstract The objective of this work is to present a Takagi–Sugeno (T-S) controller for temperature regulation in an alcoholic fermentation process. The controller gains are computed using the second Lyapunov method in order to provide closed loop stability. The starting point to design the controller is to select a non-linear mathematical model that represents adequately the process dynamics. Then, this non-linear model is transformed into a T-S representation by using the non-linear sector approach. This new representation of the alcoholic fermentation process adequately reproduces the non-linear dynamics of the process variables and represents the first contribution of this work. The second contribution of this work is to exhibit that this approach allows to increase the range of applications of control algorithms for fermentation reactors. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for the design of a Generalized Dynamic Functional Observer (GDFO) for Takagi-Sugeno systems. A set of conditions are provided for the existence of the observer, which can be applied to the proportional functional observer that is presented as a particular case of the proposed generalized observer. Lyapunov function is used to find stability condition of the observer. Stability conditions are given in terms of linear matrix inequalities (LMIs). A glucose-insulin system example illustrates the performance and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper deals with the application of fractional derivatives in the modeling of electrical circuits RC, RL, RLC, power electronic devices and nonlinear loads, the equations are obtained by replacing the time derivative by fractional derivatives of type Riemann–Liouville, Grünwald–Letnikov, Liouville–Caputo and the fractional definition recently introduced by Caputo and Fabrizio. The fractional equations in the time domain considers derivatives in the range of α ∈ (0; 1], analytical and numerical results are presented considering different source terms introduced in the fractional equation. The resulting solutions modified the capacitance, inductance, also, the resistance exhibits fluctuations or fractality of time in different scales. Furthermore, the results showed the existence of heterogeneities in the electrical components causing irreversible dissipative effects. The classical models are recovered when the order of the fractional derivatives are equal to 1. [ABSTRACT FROM AUTHOR]

In this paper we present an alternative representation of the diffusion equation and the diffusion–advection equation using the fractional calculus approach, the spatial-time derivatives are approximated using the fractional definition recently introduced by Caputo and Fabrizio in the range β , γ ∈ ( 0 ; 2 ] for the space and time domain respectively. In this representation two auxiliary parameters σ x and σ t are introduced, these parameters related to equation results in a fractal space–time geometry provide an entire new family of solutions for the diffusion processes. The numerical results showed different behaviors when compared with classical model solutions. In the range β , γ ∈ ( 0 ; 1 ) , the concentration exhibits the non-Markovian Lévy flights and the subdiffusion phenomena; when β = γ = 1 the classical case is recovered; when β , γ ∈ ( 1 ; 2 ] the concentration exhibits the Markovian Lévy flights and the superdiffusion phenomena; finally when β = γ = 2 the concentration is anomalous dispersive and we found ballistic diffusion. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a method for monitoring the performance degradation in a heat exchanger is presented. This method is based on the use of an adaptive observer which estimates the overall heat transfer coefficient U. The monitoring of this parameter can be useful to decide when the heat exchanger needs preventive or corrective maintenance. A simplified mathematical model of the heat exchanger is used to synthesize the adaptive observer. The effectiveness of the proposed method is demonstrated via numerical simulations and through experimental results. [Copyright &y& Elsevier]