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... more
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.
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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... more
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.
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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... more
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.
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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... more
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.
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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... more
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.
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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... more
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.
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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... more
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.
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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... more
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.
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The relief logistics and humanitarian supply chain in academic literature refer to the process of planning, execution, and effective controlling of the flow of costs and information and storage of necessary goods and materials from... more
The relief logistics and humanitarian supply chain in academic literature refer to the process of planning, execution, and effective controlling of the flow of costs and information and storage of necessary goods and materials from the point of origin to consumption with the primary purpose of reducing and relieving the affected people suffer. This paper discusses a multi-objective model for multi-period location-distribution-routing problems considering the evacuation of casualties and homeless people and fuzzy paths in relief logistics. Firstly, an uncertain multi-objective model of the problem was developed based on uncertain parameters of demand, time, and transport capacity, and then, using the fuzzy programming method, uncertain parameters of the problem were controlled. As the problem is NP-hard and GAMS software has not able to solve the model in larger sizes, meta-heuristic algorithms of NSGA-II and MOPSO were used to solve the problem.
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A fuzzy distance measure is introduced in this paper to evaluate the fuzzy distance between two fuzzy numbers. For this purpose, alpha-values of fuzzy numbers are used to develop an integral-based fuzzy distance measure. The... more
A fuzzy distance measure is introduced in this paper to evaluate the fuzzy distance between two fuzzy numbers. For this purpose, alpha-values of fuzzy numbers are used to develop an integral-based fuzzy distance measure. The properties of the proposed fuzzy distance measure are verified. The proposed fuzzy distance measure is also compared with other fuzzy distance measures.
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Linear programming problems have exact parameters. In most real-world, we are dealing with situations in which accurate data and complete information are not available. Uncertainty approaches such as fuzzy and random can be used to... more
Linear programming problems have exact parameters. In most real-world, we are dealing with situations in which accurate data and complete information are not available. Uncertainty approaches such as fuzzy and random can be used to deal with uncertainties in real-life. Fuzzy and stochastic theories cannot be used if the number of experts and the level of experience is so low that it is impossible to extract membership functions or the number of samples is small. To solve these problems, the grey system theory is proposed. In this paper, a linear programming problem in a grey environment with resources in interval grey numbers is considered. Most of the proposed methods for solving grey linear programming problems become common linear programming problems. However, we seek to solve the problem directly without turning it into a standard linear programming problem for the purpose of maintaining uncertainty in the original problem data in the final solution. For this purpose, we present a method based on the duality theory for solving the grey linear programming problems. This method is more straightforward and less complicated than previous methods. We emphasize that the concept presented is beneficial for real and practical conditions in management and planning problems. Therefore, we shall illustrate our method with some examples in different situations.
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In this paper, we develop general necessary optimality conditions of the KKT types for non-smooth continuous-time optimization problems with inequality constraints. The primary instrument in our study is the concept of a... more
In this paper, we develop general necessary optimality conditions of the KKT types for non-smooth continuous-time optimization problems with inequality constraints. The primary instrument in our study is the concept of a convexificator. Based on this concept, non-smooth versions of the Mangasarian-Fromovitz constraint qualification are presented. Then, we derive optimality conditions for this problem under weak assumptions. Indeed, the constraint functions and the objective function that exist in this problem are not necessarily differentiable or convex.
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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.... more
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.
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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... more
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.
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Iterative feedback tuning (IFT) is an algorithm for adjusting the coefficients of the integer-order type proportional-integral-derivative (PID) controllers without needing a system model. The IFT algorithm is performed iteratively with... more
Iterative feedback tuning (IFT) is an algorithm for adjusting the coefficients of the integer-order type proportional-integral-derivative (PID) controllers without needing a system model. The IFT algorithm is performed iteratively with the aim of optimizing the control coefficients at each stage via an objective function. In this research, for the first time, the IFT algorithm is used to adjust all the coefficients of the fractional order PID controllers, i.e., PI^α D^β controllers to have optimal performance. For this purpose, fractional order calculations and the integer-order version of the IFT algorithm are firstly presented, and the novel IFT algorithm is then used to adjust coefficients of the PI^α D^β controller. Finally, the performance of the proposed method is illustrated and verified through some examples.
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Evaluation of advertising marketing campaigns is a very important and complex task, so far no comprehensive model has been presented in this regard. The present study aims to provide a decision framework for evaluating marketing... more
Evaluation of advertising marketing campaigns is a very important and complex task, so far no comprehensive model has been presented in this regard. The present study aims to provide a decision framework for evaluating marketing campaigns. This article collects real-world data from an Iranian bank deposit marketing campaign. For this purpose, 250 cases were considered to extract the rules and 60 cases were considered as test data. Information is provided on 15 important parameters of marketing education, defaults, age, occupation, marriage, day, contact, balance, housing, loans, previous contact, previous outcome, month, call duration, and campaigns. A fuzzy expert system was designed with 12 rules after reviewing the rules and removing similar and contradictory rules by using their degree calculation. In this system, by integrating some factors, finally, 6 input variables and one output variable were considered that were used by the product inference engine, singleton fuzzifier, and center average defuzzifier. It was observed that the designed fuzzy expert system provides very good results.
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A shearlet frame approach is used to solve $n$-dimensional wave equations numerically. By the presented procedure, the shearlet coefficients are obtained via separate time-independent partial differential equations. The proposed... more
A shearlet frame approach is used to solve $n$-dimensional wave equations numerically. By the presented procedure, the shearlet coefficients are obtained via separate time-independent partial differential equations. The proposed method has the advantage of separation of spatial and temporal parameters. The issues of convergence and best approximation are also discussed.
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In view of the tremendous importance of patients’ stability in medical sciences, this paper addresses the application of a sliding mode control in medical devices. In doing so, we consider a nonlinear dynamic system that shows the... more
In view of the tremendous importance of patients’ stability in medical sciences, this paper addresses the application of a sliding mode control in medical devices. In doing so, we consider a nonlinear dynamic system that shows the mathematical model of the human immunodeficiency virus. This nonlinear model has three variable states: healthy cells, infected cells, and free viruses. The proposed controller displays the effect of medication on preventing the production of the virus and blocking the new infection. This controller ensures the stability of this dynamic system provided for HIV in the event of a bounded disturbance. The stability and convergence of this process are proved by the Lyapunov theorem. Finally, a numerical example is given to demonstrate the efficiency of the proposed method.