Mostafa Tavakolli
Abstract
Let $S= \{e_1,\,e_2, \ldots,\,e_m\}$ be an ordered subset of edges of a connected graph $G$. The edge $S$-representation of an edge set $M\subseteq E(G)$ with respect to $S$ is the vector $r_e(M|S) = (d_1,\,d_2,\ldots,\,d_m)$, where $d_i=1$ if $e_i\in M$ and $d_i=0$ ...
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Let $S= \{e_1,\,e_2, \ldots,\,e_m\}$ be an ordered subset of edges of a connected graph $G$. The edge $S$-representation of an edge set $M\subseteq E(G)$ with respect to $S$ is the vector $r_e(M|S) = (d_1,\,d_2,\ldots,\,d_m)$, where $d_i=1$ if $e_i\in M$ and $d_i=0$ otherwise, for each $i\in\{1,\ldots , k\}$. We say $S$ is a global forcing set for maximal matchings of $G$ if $r_e(M_1|S)\neq r_e(M_2|S)$ for any two maximal matchings $M_1$ and $M_2$ of $G$. A global forcing set for maximal matchings of $G$ with minimum cardinality is called a minimum global forcing set for maximal matchings, and its cardinality, denoted by $\varphi_{gm}$, is the global forcing number (GFN for short) for maximal matchings. Similarly, for an ordered subset $F = \{v_1,\,v_2, \ldots,\,v_k\}$ of $V(G)$, the $F$-representation of a vertex set $I\subseteq V(G)$ with respect to $F$ is the vector $r(I|F) = (d_1,\,d_2,\ldots,\,d_k)$, where $d_i=1$ if $v_i\in I$ and $d_i=0$ otherwise, for each $i\in\{1,\ldots , k\}$. We say $F$ is a global forcing set for independent dominatings of $G$ if $r(D_1|F)\neq r(D_2|F)$ for any two maximal independent dominating sets $D_1$ and $D_2$ of $G$. A global forcing set for independent dominatings of $G$ with minimum cardinality is called a minimum global forcing set for independent dominatings, and its cardinality, denoted by $\varphi_{gi}$, is the GFN for independent dominatings. In this paper, we study the GFN for maximal matchings under several types of graph products. Also, we present some upper bounds for this invariant. Moreover, we present some bounds for $\varphi_{gm}$ of some well-known graphs.
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.
Farshid Pouralizadeh Moghaddam; Hossein Gholizade Narm
Abstract
In this paper, a synthesis method based on robust model predictive control is developed for compensation of uncertain time-delays in networked control systems with bounded disturbance. The proposed method uses linear matrix inequalities and uncertainty polytope to model uncertain ...
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In this paper, a synthesis method based on robust model predictive control is developed for compensation of uncertain time-delays in networked control systems with bounded disturbance. The proposed method uses linear matrix inequalities and uncertainty polytope to model uncertain time-delays and system disturbances. The continuous system with time-delay is discretized using uncertainty polytope. Then, the discretized model together with model disturbance is compensated. Uncertain parameters and additive disturbances are included in the controller design explicitly and robust stability is guaranteed in this method. The proposed method is applied to a level process. It is simulated by applying conventional RMPC as well. The simulation results show the effectiveness of the proposed method compared with the conventional algorithm of the RMPC\footnote{Robust Model Predictive Control} method.
Mohammad Gholami Baladezaei; Morteza Gachpazan; Akbar Hashemi Borzabadi
Abstract
In this paper, the benefits of 1/G'-expansion technique are utilized to create a direct scheme for extracting approximate solutions for a class of optimal control problems. In the given approach, first state and control functions have been parameterized as a power series, ...
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In this paper, the benefits of 1/G'-expansion technique are utilized to create a direct scheme for extracting approximate solutions for a class of optimal control problems. In the given approach, first state and control functions have been parameterized as a power series, which is constructed according to the solutions of a Bernoulli differential equation, where the number of terms in produced power series is determined by the balance method. A proportionate replacement and solving the created optimization problem lead to suitable solutions close to the analytical ones for the main problem. Numerical experiments are given to evaluate the quality of the proposed method.
Mahmoud Mahmoudi; Delaram Ahmad Ghondaghsaz
Abstract
In this paper, we present a new approach to solving stochastic differential equations and the Vasicek equation by using Brownian wavelets and multiple Ito-integral. Firstly, the calculation of the multiple Ito-integral based on the structure of Brownian motion is presented ...
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In this paper, we present a new approach to solving stochastic differential equations and the Vasicek equation by using Brownian wavelets and multiple Ito-integral. Firstly, the calculation of the multiple Ito-integral based on the structure of Brownian motion is presented and the error of Ito-integrate computation is minimized under this condition. Then, the Brownian wavelets 1D and 3D based on coefficients Brownian motion are introduced. After that, a system of linear and nonlinear equations of coefficients Brownian motion is obtained such that by solving this system the approximate solution of the Vasicek equation is obtained. In the last section, some numerical examples are given.
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.
Amir Hosein Mohajerzadeh; Abbas Ali Rezaee; Morteza Bigdeli
Abstract
Estimating the target parameter while the prior distribution function is known, and several observations which are provided by the sensor node is the main goal in this paper. In wireless sensor networks (WSN), nodes sense the environment and send data to a sink node called ...
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Estimating the target parameter while the prior distribution function is known, and several observations which are provided by the sensor node is the main goal in this paper. In wireless sensor networks (WSN), nodes sense the environment and send data to a sink node called Fusion Center (FC). FC collects data and estimates the observed parameter with user-defined precision. The proposed algorithm increases network lifetime and has an efficient estimation process. For this purpose, the proposed algorithm schedules node’s activity and determines the multihop path between nodes and FC. Simulation and performance analysis demonstrates proposed algorithm fulfills its goals.
Ghasem Ahmadi
Abstract
Rough extreme learning machines (RELMs) are rough-neural networks with one hidden layer where the parameters between the inputs and hidden neurons are arbitrarily chosen and never updated. In this paper, we propose RELMs with a stable online learning algorithm for the identification ...
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Rough extreme learning machines (RELMs) are rough-neural networks with one hidden layer where the parameters between the inputs and hidden neurons are arbitrarily chosen and never updated. In this paper, we propose RELMs with a stable online learning algorithm for the identification of continuous-time nonlinear systems in the presence of noises and uncertainties, and we prove the global asymptotically convergence of the proposed learning algorithm using the Lyapunov stability theory. Then, we use the proposed methodology to identify the chaotic systems of Duffing's oscillator and Lorentz system. Simulation results show the efficiency of the proposed model.
Hamed Soroush
Abstract
In this paper, we study nonsmooth optimization problems with quasiconvex functions using topological subdifferential. We present some necessary and sufficient optimality conditions and characterize topological pseudoconvex functions. Finally, the Mond-Weir type ...
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In this paper, we study nonsmooth optimization problems with quasiconvex functions using topological subdifferential. We present some necessary and sufficient optimality conditions and characterize topological pseudoconvex functions. Finally, the Mond-Weir type weak and strong duality results are stated for the problems.
Sayed Kahlil Ekrami
Abstract
In this paper, we prove that every orthogonally higher ring derivation is a higher ring derivation. Also we find the general solution of the pexider orthogonally higher ring derivations\begin{align*}\left\{\begin{array}{lr}f_n(x+y)=g_n(x)+h_n(y), ...
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In this paper, we prove that every orthogonally higher ring derivation is a higher ring derivation. Also we find the general solution of the pexider orthogonally higher ring derivations\begin{align*}\left\{\begin{array}{lr}f_n(x+y)=g_n(x)+h_n(y), \;\left\langle x,y \right\rangle =0,\\f_n(xy) = \sum_{i+j=n} g_i(x)h_j(y).\end{array}\right.\end{align*}Then we prove that for any approximate pexider orthogonally higher ring derivation under some control functions $ \varphi(x,y) $ and $ \psi(x,y) $, there exists a unique higher ring derivation $ D=\{d_n\}_{n=0}^\infty $, near $ \{f_n\}_{n=0}^\infty $, $ \{g_n\}_{n=0}^\infty $ and $ \{h_n\}_{n=0}^\infty $ estimated by $ \varphi $ and $ \psi $.
Control and Optimization
Ali Valinejad; Afshin Babaei; Zahra Zarei
Abstract
This paper introduces a variable step size strategy for a stochastic time-delays Lotka-Volterra competition system. This adaptive strategy utilizes the Milstein method for numerical solutions. It employs two local error estimates, corresponding to the diffusion and drift components ...
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This paper introduces a variable step size strategy for a stochastic time-delays Lotka-Volterra competition system. This adaptive strategy utilizes the Milstein method for numerical solutions. It employs two local error estimates, corresponding to the diffusion and drift components of the model, to select and control the step sizes. The algorithm is described in detail, and numerical experiments are conducted to demonstrate the efficiency of the proposed method. The primary objective of this research is to propose a dynamic strategy for generating and controlling the step sizes in the finite difference algorithm employed. This adaptive approach accelerates the numerical procedure and improves efficiency compared to a constant-size scheme. As an analytical solution for the model is unavailable, a numerical estimation with a small fixed step size is considered a reference solution. The numerical results demonstrate the superior accuracy of the proposed strategy compared to a reference solution.
Control and Optimization
Maryam Yaghoubi; Fatemeh Dadmand
Abstract
Natural disasters, such as earthquakes, result in significant financial and human losses. Rescue operations play a crucial role in managing such crises. However, the lack of precise information and the damage or destruction of urban transportation routes ...
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Natural disasters, such as earthquakes, result in significant financial and human losses. Rescue operations play a crucial role in managing such crises. However, the lack of precise information and the damage or destruction of urban transportation routes following earthquakes introduces uncertainty into these operations. This study presents a multi-objective humanitarian logistics model that utilizes a mixed-integer nonlinear programming (MINLP) approach. The model considers the reliability of transportation routes after an earthquake, the standard response time for allocating personnel and relief equipment, and the coverage maximization. This model incorporates various uncertainties, including the reliability of the transportation network. Real data from the city of Gonabad, Iran, was used to evaluate the proposed model. The results and sensitivity analysis demonstrated that the model exhibits desirable performance.
Control and Optimization
Atefeh Hassani Bafrani
Abstract
The primary objective of this paper is to enhance several well-known geometric constraint qualifications and necessary optimality conditions for nonsmooth semi-infinite optimization problems (SIPs). We focus on defining novel algebraic Mangasarian-Fromovitz type constraint qualifications, and on presenting ...
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The primary objective of this paper is to enhance several well-known geometric constraint qualifications and necessary optimality conditions for nonsmooth semi-infinite optimization problems (SIPs). We focus on defining novel algebraic Mangasarian-Fromovitz type constraint qualifications, and on presenting two Karush-Kuhn-Tucker type necessary optimality conditions for nonsmooth SIPs defined by locally Lipschitz functions. Then, by employing a new type of generalized invex functions, we present sufficient conditions for the optimality of a feasible point of the considered problems. It is noteworthy that the new class of invex functions we considered encompasses several classes of invex functions introduced previously. Our results are based on the Michel-Penot subdifferential.
Control and Optimization
Sharifeh Rezagholi; Arash Farhadi
Abstract
This paper examines normal cones of the feasible set for mathematical programming problems with switching constraints (MPSC). Functions involved are assumed to be continuously differentiable. The primary focus is on providing the upper estimate of the Mordukhovich normal cone for ...
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This paper examines normal cones of the feasible set for mathematical programming problems with switching constraints (MPSC). Functions involved are assumed to be continuously differentiable. The primary focus is on providing the upper estimate of the Mordukhovich normal cone for the feasible set of MPSCs. First, a constraint qualification, called the ``MPSC-No Nonzero Abnormal Multiplier Constraint Qualification'', is considered for the problem. Based on this qualification, the main result of the paper is presented. Finally, an optimality condition, called the ``necessary M-stationarity condition'' is proposed for optimal solutions of the considered problems. Since other optimization problems with multiplicative constraints can be rewritten in the form of MPSCs, results obtained in this paper can be extended to a wider class of problems involving multiplicative constraints.
Control and Optimization
Seyed Mohsen Izadyar; Mohammad Eshaghnezhad; Hossein Davoodi Yeganeh
Abstract
This study presents a model of a quantum dot laser with a planar cavity, employing numerical methods and artificial neural networks for simulation purposes. The investigation focuses on the influence of critical parameters, including the injection current into the active layer of the quantum dot ...
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This study presents a model of a quantum dot laser with a planar cavity, employing numerical methods and artificial neural networks for simulation purposes. The investigation focuses on the influence of critical parameters, including the injection current into the active layer of the quantum dot laser and the carrier relaxation time to a lower energy state level. The model delves into the intricate carrier and photon dynamics within the laser, solving a system of coupled equations that describe these interactions. The fourth-order Runge-Kutta method is utilized to solve these equations numerically. The results indicate that increased pumping power enhances the stable power levels and the peak power output of the laser. Additionally, analysis of the power versus intensity of current ($P-I$) characteristic curve reveals that a longer carrier relaxation time to a lower energy state leads to a higher threshold current and a reduction in the quantum efficiency of the device. The study also examines the laser switch-on time against the injection current. Finally, the deterioration in the quality of quantum dots and quantum wells is scrutinized. To gain deeper insights into the effect of increased pumping current on laser switch-on time, the study complements numerical findings with the application of artificial neural networks, yielding significant results.
Control and Optimization
Ahmad Sharif
Abstract
In this study, we explore soliton solutions for the conformable time-fractional Boussinesq equation utilizing the three-wave method. To validate the precision of our findings, we discuss specific special cases by adjusting certain potential parameters and also present the ...
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In this study, we explore soliton solutions for the conformable time-fractional Boussinesq equation utilizing the three-wave method. To validate the precision of our findings, we discuss specific special cases by adjusting certain potential parameters and also present the graphical representations of our results. The results achieved in this research align closely with those from previous studies, demonstrating enhanced accuracy and simplicity. Given the extensive applications of this equation in particle physics, understanding its dynamics is crucial. Consequently, employing methods that encompass a broad spectrum of solutions is imperative. The versatility of this method in yielding diverse solutions is evident in the results we have obtained. The solutions derived in this paper are novel and offer greater precision compared to previous works.
Control and Optimization
Majid Anjidani
Abstract
Designing dynamically stable controllers for a robot with 2r legs is challenging due to its complex hybrid dynamics (r>1). This paper proposes a technique to decompose the robot into r biped robots, where the influence of other robot parts on each biped can be modeled as external forces. This approach ...
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Designing dynamically stable controllers for a robot with 2r legs is challenging due to its complex hybrid dynamics (r>1). This paper proposes a technique to decompose the robot into r biped robots, where the influence of other robot parts on each biped can be modeled as external forces. This approach allows existing research on biped control to be applied to the quadruped robot. Time-invariant controllers, which typically ensure walking stability for planar point-footed bipeds, are selected for this purpose. For clarity, we focus on a planar point-footed quadruped for decomposition. We extend a recent reinforcement learning method to optimize these controller parameters for walking on slopes or under specific forces, while accounting for significant modeling errors in the quadruped. Simulation results demonstrate that our method achieves stable walking with the desired features and effectively compensates for modeling errors.
