Research Article
Control and Optimization
Mohamad Reza Ramezani-al; Samira Sabeti
Abstract
Guaranteed cost control (GCC) is an impressive method of controlling nonlinear systems, incredibly uncertain switched systems. Most of the recent studies of GCC on uncertain switched linear systems have been concerned with asymptotic stability analysis. In this paper, ...
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Guaranteed cost control (GCC) is an impressive method of controlling nonlinear systems, incredibly uncertain switched systems. Most of the recent studies of GCC on uncertain switched linear systems have been concerned with asymptotic stability analysis. In this paper, a new robust switching law for time-delay uncertain switched linear systems is designed. First, the switching law is designed, and second, a state-feedback controller based on Lyapunov-Krasovskii Functional (LKF) is designed. Also, using Linear Matrix Inequality (LMI) particular condition for the existence of a solution of obtained switching law and controller is achieved. Consequently, in the presented theorems, the exponential stability of the overall system under switching law and controller is analyzed. Finally, theoretical results are verified via presenting an example.
Research Article
Control and Optimization
Jahangir Alizadeh; Hamid Khaloozadeh
Abstract
In the present study, a novel methodology is developed to enlarge the Region of Attraction (ROA) at the point of equilibrium of an input-affine nonlinear control system. Enlarging the ROA for non-polynomial dynamical systems is developed by designing a nonlinear state feedback controller ...
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In the present study, a novel methodology is developed to enlarge the Region of Attraction (ROA) at the point of equilibrium of an input-affine nonlinear control system. Enlarging the ROA for non-polynomial dynamical systems is developed by designing a nonlinear state feedback controller through the State-Dependent Riccati Equation (SDRE). Consequently, its process is defined in the form of Sum-of-Squares (SOS) optimization problem with control and non-control constraints. Of note, the proposed technique is effective in estimating the ROA for a nonlinear system functioning on polynomial or non-polynomial dynamics. In the present study, the application of the proposed scheme are shown by numerical simulations.
Applied Article
Control and Optimization
Zahra Abbasi; Nasser Akhoundi
Abstract
Product reviews in E-commerce websites such as restaurants, movies, E-commerce products, etc., are essential resources for consumers to make purchasing decisions on various items. In this paper, we model discovering groups with maximum descriptively ...
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Product reviews in E-commerce websites such as restaurants, movies, E-commerce products, etc., are essential resources for consumers to make purchasing decisions on various items. In this paper, we model discovering groups with maximum descriptively from E-commerce website of the form $<i,u,s>$, where $i\in \mathcal{I}$ (the set of items or products), $u\in \mathcal{U}$ (the set of users) and $s$ is the integer rating that user $u$ has assigned to the item $i$. Labeled groups from user's attributes are found by solving an optimization problem. The performance of the approach is examined by some experiments on real data-sets.
Research Article
Control and Optimization
Mohammad Darvisahzadeh; Ahmad Shahvarani Semnani; Hassan Alamolhodaei,; Hassan Behzadi
Abstract
Experiences of teaching Integral have indicated that the vast majorities of Iranian university students commit numerous errors while solving integral problems and have weak skills in this field; we might even say that they hide away from integral and consider it the nightmare of mathematics. On ...
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Experiences of teaching Integral have indicated that the vast majorities of Iranian university students commit numerous errors while solving integral problems and have weak skills in this field; we might even say that they hide away from integral and consider it the nightmare of mathematics. On the other hand, Integral is the base of pure and applied mathematics for all students of science, especially engineering, which some of their lessons are dependent on it directly or indirectly, so it is important to pay attention to it. Through descriptive method-exposed factor, an exam has been conducted in the form of three questions, the first of which is consisted of 4 sections on fifty students from different fields, and then interviews were conducted with a few of those students about their answers in order to study the students' behaviors when solving integral problems and to determine the type of their errors. By analyzing the performance of students in this test, we can see that students often struggle with integral and mostly have a feeble performance in solving trigonometric integrals. They want to learn computational integral instead of how to conceptualize integral in their minds correctly. The error most committed by university students was procedural errors, which arise from using derivative instead of integral. Besides most of the mistakes happen in solving definite integrals, and calculating finite areas between two curves. This is due to a lack of understanding of integrals and a lack of information in other areas of mathematics.
Research Article
Control and Optimization
Mostafa Nouri Jouybari; Yahya Talebi Rostami; Siyamak Firouzian
Abstract
In this study, $R$ and $M$ are assumed to be a commutative ring with non-zero identity $M$ and an $R$-module, respectively. Scalar Product Graph of $M$, denoted by $G_R(M)$, is a graph with the vertex-set $M$ and two different vertices $a$ and $b$ in ...
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In this study, $R$ and $M$ are assumed to be a commutative ring with non-zero identity $M$ and an $R$-module, respectively. Scalar Product Graph of $M$, denoted by $G_R(M)$, is a graph with the vertex-set $M$ and two different vertices $a$ and $b$ in $M$ are connected if and only if there exists $r$ belong to $R$ such that $a=rb$ or $b=ra$. This paper studies some properties of such weakly perfect graphs.
Research Article
Control and Optimization
Sara Mansourinasab; Mahdi Sojoodi; Seyed Reza Moghadasi
Abstract
Conventional model predictive control (MPC) methods are usually implemented to systems with discrete-time dynamics laying on smooth vector space $ \mathbf{R}^n$. In contrast, the configuration space of the majority of mechanical systems is not expressed as Euclidean space. Therefore, ...
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Conventional model predictive control (MPC) methods are usually implemented to systems with discrete-time dynamics laying on smooth vector space $ \mathbf{R}^n$. In contrast, the configuration space of the majority of mechanical systems is not expressed as Euclidean space. Therefore, the MPC method in this paper has developed on a smooth manifold as the configuration space of the attitude control of a 3D pendulum. The Lie Group Variational Integrator (LGVI) equations of motion of the 3D pendulum have been considered as the discrete-time update equations since the LGVI equations preserve the group structure and conserve quantities of motion. The MPC algorithm is applied to the linearized dynamics of the 3D pendulum according to its LGVI equations around the equilibrium using diffeomorphism. Also, as in standard MPC algorithms, convex optimization is solved at each iteration to compute the control law. In this paper, the linear matrix inequality (LMI) is used to solve the convex optimization problem under constraints. A numerical example illustrates the design procedure.
