In this paper, a new rumor spreading model in social networks has been investigated. We propose a new version primarily based on the cholera model in order to take into account the expert pages specialized in the dissemination of rumors from an existing IRCSS model. In the second part, we recommend an optimal control strategy to fight against the spread of the rumor, and the study aims at characterizing the three optimal controls which minimize the number of spreader users, fake pages, and corresponding costs; theoretically, we have proved the existence of optimal controls, and we have given a characterization of controls in terms of states and adjoint functions based on a discrete version of Pontryagin’s maximum principle. To illustrate the theoretical results obtained, we propose numerical simulations for several scenarios applying the forward-backward sweep method (FBSM) to solve our optimality system in an iterative process.

In this work, we propose a multifishing area prey-predator discrete-time model which describes the interaction between the prey and middle and top predators in various areas, which are connected by their movements to their neighbors, to provide realistic description prey effects of two predators. A grid of colored cells is presented to illustrate the entire domain; each cell may represent a subdomain or area. Next, we propose two harvesting control strategies that focus on maximizing the biomass of prey, in the targeted area, and minimizing the biomass of middle and top predators coming from the neighborhood of this targeted area to ensure sustainability and maintain a differential chain system. Theoretically, we have proved the existence of optimal controls, and we have given a characterization of controls in terms of states and adjoint functions based on a discrete version of Pontryagin’s maximum principle. To illustrate the theoretical results obtained, we propose numerical simulations for several scenarios applying the forward-backward sweep method (FBSM) to solve our optimality system in an iterative process.

This paper studies a finite-dimensional discrete linear system whose initial state $x_0$ is unknown. We assume that the system is augmented by two output equations, the first one $z_i$ being representing measurements made on the unknown state of the system and the other $y_i$ being representing the corresponding output. The purpose of our work is to introduce two control laws, both in closed-loop of measurements $z_i$ and whose goal is to reduce asymptotically the effects of the unknown part of the initial state $x_0$. The approach that we present consists of both theoretical and algorithmic characterization of the set of such controls. To illustrate our theoretical results, we give a number of examples and numerical simulations.

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In this paper, we consider an infinite dimensional linear systems. It is assumed that the initial state of system is not known throughout all the domain Ω ⊂ R n , the initial state x 0 ∈ L 2 (Ω) is supposed known on one part of the domain Ω and uncertain on the rest. That meanswhere the values α 1 , . . . , α r are supposed known and α r+1 , . . . , α t unknown and 1 ω i is the indicator function. The uncertain part (α 1 , . . . , α r ) of the initial state x 0 is said to be (ε 1 , . . . , ε r )-admissible if the sensitivity of corresponding output signal (y i ) i 0 relatively to uncertainties (α k ) 1 k r is less to the tresholdThe main goal of this paper is to determine the set of all possible gain operators that makes the system insensitive to all uncertainties. The characterization of this set is investigated and an algorithmic determination of each gain operators is presented. Some examples are given.