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On the dynamics of a vaccination model with multiple transmission ways

Shu Liao, Weiming Yang (2013)

International Journal of Applied Mathematics and Computer Science

In this paper, we present a vaccination model with multiple transmission ways and derive the control reproduction number. The stability analysis of both the disease-free and endemic equilibria is carried out, and bifurcation theory is applied to explore a variety of dynamics of this model. In addition, we present numerical simulations to verify the model predictions. Mathematical results suggest that vaccination is helpful for disease control by decreasing the control reproduction number below unity....

On the Existence of Optimal Solutions for Infinite Horizon Optimal Control Problems: Nonconvex and Multicriteria Problems

Dean A. Carlson (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa Nota si continua la discussione iniziata in [4] dell'esistenza di soluzioni ottimali per problemi di ottimo controllo in [ 0 + ∞ ] . Si definiscono problemi generalizzati, e si ottengono estensioni di risultati già presentati in [4]. Si dimostrano anche varie relazioni tra le soluzioni ottimali dei problemi generalizzati e i problemi originali e non convessi di ottimo controllo. Alla fine si considerano problemi lineari nelle variabili di stato anche nel caso di costi funzionali a valori vettoriali...

On the Fattorini criterion for approximate controllability and stabilizability of parabolic systems

Mehdi Badra, Takéo Takahashi (2014)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we consider the well-known Fattorini’s criterion for approximate controllability of infinite dimensional linear systems of type y′ = Ay + Bu. We precise the result proved by Fattorini in [H.O. Fattorini, SIAM J. Control 4 (1966) 686–694.] for bounded input B, in the case where B can be unbounded or in the case of finite-dimensional controls. More precisely, we prove that if Fattorini’s criterion is satisfied and if the set of geometric multiplicities of A is bounded then approximate...

On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate

Lucas Jódar, Enrique A. Navarro (1989)

Aplikace matematiky

In this paper explicit expressions for solutions of Cauchy problems and two-point boundary value problems concerned with the generalized Riccati matrix differential equation are given. These explicit expressions are computable in terms of the data and solutions of certain algebraic Riccati equations related to the problem. The interplay between the algebraic and the differential problems is used in order to obtain approximate solutions of the differential problem in terms of those of the algebraic...

On the global stability of Takagi-Sugeno general model.

Fernando Matía, Basil M. Al-Hadithi, Agustín Jiménez (1999)

Mathware and Soft Computing

Global stability of Takagi-Sugeno (T-S) fuzzy model is presented. First, stability conditions for T-S fuzzy model presented by Tanaka and Sugeno are reviewed. Second, new theorems for the stability of the general form of T-S model is derived in the sense of Lyapunov.The T-S model we studied includes a linear equation with a constant parameter in the consequent part of each rule while other authors have analyzed the model with no constant term, which does not represent a real system. This in turn...

On the interaction between theory experiments and simulation in developing practical learning control algorithms

Richard Longman (2003)

International Journal of Applied Mathematics and Computer Science

Iterative learning control (ILC) develops controllers that iteratively adjust the command to a feedback control system in order to converge to zero tracking error following a specific desired trajectory. Unlike optimal control and other control methods, the iterations are made using the real world in place of a computer model. If desired, the learning process can be conducted both in the time domain during each iteration and in repetitions, making ILC a 2D system. Because ILC iterates with the real...

On the null-controllability of diffusion equations

Gérald Tenenbaum, Marius Tucsnak (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This work studies the null-controllability of a class of abstract parabolic equations. The main contribution in the general case consists in giving a short proof of an abstract version of a sufficient condition for null-controllability which has been proposed by Lebeau and Robbiano. We do not assume that the control operator is admissible. Moreover, we give estimates of the control cost. In the special case of the heat equation in rectangular domains, we provide an alternative way to check...

On the null-controllability of diffusion equations

Gérald Tenenbaum, Marius Tucsnak (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This work studies the null-controllability of a class of abstract parabolic equations. The main contribution in the general case consists in giving a short proof of an abstract version of a sufficient condition for null-controllability which has been proposed by Lebeau and Robbiano. We do not assume that the control operator is admissible. Moreover, we give estimates of the control cost. In the special case of the heat equation in rectangular domains, we provide an alternative way to check...

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