There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Fractional Differential Equations

Theory of fuzzy integrals and its applications

This paper studies some basic properties of an SEIR (Susceptible-Exposed-Infectious-Recovered) epidemic model subject to vaccination and treatment controls. Firstly, the basic stability, boundedness, and nonnegativity of the state trajectory solution are investigated. Then, the problem of partial state reachability from a certain state value to a targeted one in finite time is focused on since it turns out that epidemic models are, because of their nature, neither (state) controllable from a given state to the origin nor reachable from a given initial condition. The particular formal statement of the partial reachability is focused on as a problem of output-reachability by defining a measurable output or lower dimension than that of the state. A special case of interest is that when the output is defined as the infectious subpopulation to be step-to-step tracked under suitable amounts being compatible with the required constraints. As a result, and provided that the output-controllability Gramian is nonsingular on a certain time interval of interest, a feedback control effort might be designed so that a prescribed value of the output can be approximately tracked. A linearization approximation is performed to simplify and facilitate the above task which is based on a point-to-point linearization of the solution trajectory. To this end, an “ad hoc” sampled approximate output trajectory is defined as control objective to be targeted through a point-wise calculated Jacobian matrix. A supervised appropriate restatement of the targeted suited sampled output values is redefined, if necessary, to make the initial proposed sampled trajectory compatible with the various needed constraints on nonnegativity and control boundedness. The design can be optionally performed under constant or adaptive sampling rates. Finally, some numerical examples are given to test the theoretical aspects and the design efficiency of the model.

/pdf/about-partial-reachability-issues-in-an-seir-epidemic-model-51mtky44dc.pdf

About Partial Reachability Issues in an SEIR Epidemic Model and Related Infectious Disease Tracking in Finite Time under Vaccination and Treatment Controls

Modern wind turbines are designed in order to work in variable speed operations. To perform this task, wind turbines are provided with adjustable speed generators, like the double feed induction generator. One of the main advantage of adjustable speed generators is improving the system efficiency compared to fixed speed generators, because turbine speed can be adjusted as a function of wind speed in order to maximize the output power. However this system requires a suitable speed controller in order to track the optimal reference speed of the wind turbine. In this work, a sliding mode control for variable speed wind turbines is proposed. An integral sliding surface is used, because the integral term avoids the use of the acceleration signal, which reduces the high frequency components in the sliding variable. The proposed design also uses the vector oriented control theory in order to simplify the generator dynamical equations. The stability analysis of the proposed controller has been carried out under wind variations and parameter uncertainties by using the Lyapunov stability theory. Finally simulated results show, on the one hand that the proposed controller provides a high-performance dynamic behavior, and on the other hand that this scheme is robust with respect to parameter uncertainties and wind speed variations, that usually appear in real systems.

Sliding mode control law for a variable speed wind turbine

We propose two new iterative algorithms for solving K-pseudomonotone variational inequality problems in the framework of real Hilbert spaces. These newly proposed methods are obtained by combining the viscosity approximation algorithm, the Picard Mann algorithm and the inertial subgradient extragradient method. We establish some strong convergence theorems for our newly developed methods under certain restriction. Our results extend and improve several recently announced results. Furthermore, we give several numerical experiments to show that our proposed algorithms performs better in comparison with several existing methods.

https://www.mdpi.com/2075-1680/9/2/51/pdf

Inertial Subgradient Extragradient Methods for Solving Variational Inequality Problems and Fixed Point Problems

In this paper, we consider a class of fractional-order differential equations and investigate two aspects of these equations. First, we consider the existence of a unique solution, and then, using a new class of control functions, we investigate the Gauss hypergeometric stability. We use Chebyshev and Bielecki norms in order to prove these aspects by the Picard method. Finally, we give some examples to illustrate our results.

/pdf/picard-method-for-existence-uniqueness-and-gauss-1hf7huv1h0.pdf

Picard Method for Existence, Uniqueness, and Gauss Hypergeomatric Stability of the Fractional-Order Differential Equations

The control of plasma in nuclear fusion has been revealed as a promising application of Control Engineering, with increasing interest in the control community during last years. In this paper it is developed a control-oriented linear model for the control of plasma current. For this purpose, it is provided a summary of the background necessary to deal with control problems in tokamak-based nuclear fusion reactors as it is the case of the future ITER tokamak. Besides, it is also given a review of the most used simulators and plasma models, with the aim of providing an adequate background for control engineers to derive their own control-oriented model or to choose the appropriate existing one. Finally, the proposed plasma model performance is proven in a current drive profile trajectory tracking problem using a modified anti-windup PID-based control scheme.

Manuel De la Sen

Papers

About Partial Reachability Issues in an SEIR Epidemic Model and Related Infectious Disease Tracking in Finite Time under Vaccination and Treatment Controls

Sliding mode control law for a variable speed wind turbine

Inertial Subgradient Extragradient Methods for Solving Variational Inequality Problems and Fixed Point Problems

Picard Method for Existence, Uniqueness, and Gauss Hypergeomatric Stability of the Fractional-Order Differential Equations

Linear models for plasma current control in tokamak reactors