Research Article
Control and Optimization
Akbar Hashemi Borzabadi; Mohammad Gholami Baladezaei; Morteza Ghachpazan
Abstract
This paper explores the advantages of Sub-ODE strategy in deriving near-exact solutions for a class of linear and nonlinear optimal control problems (OCPs) that can be transformed into nonlinear partial differential equations (PDEs). Recognizing that converting an OCP into ...
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This paper explores the advantages of Sub-ODE strategy in deriving near-exact solutions for a class of linear and nonlinear optimal control problems (OCPs) that can be transformed into nonlinear partial differential equations (PDEs). Recognizing that converting an OCP into differential equations typically increases the complexity by adding constraints, we adopt the Sub-ODE method, as a direct method, thereby negating the need for such transformations to extract near exact solutions. A key advantage of this method is its ability to produce control and state functions that closely resemble the explicit forms of optimal control and state functions. We present results that demonstrate the efficacy of this method through several numerical examples, comparing its performance to various other approaches, thereby illustrating its capability to achieve near-exact solutions.
Research Article
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.
Research Article
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.
Research Article
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.
Research Article
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.
Research Article
Control and Optimization
Sharifeh Rezagholi; Arash Farhadi Hikooee
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.
Research Article
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.
Research Article
Control and Optimization
Masoomeh Ebrahimipour; Saeed Nezhadhosein; Seyed Mehdi Mirhosseini-Alizamini
Abstract
This paper presents an optimal robust adaptive technique for controlling a certain class of uncertain nonlinear affine systems. The proposed approach combines sliding mode control, a linear quadratic regulator for optimality, and gradient descent as an adaptive controller. ...
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This paper presents an optimal robust adaptive technique for controlling a certain class of uncertain nonlinear affine systems. The proposed approach combines sliding mode control, a linear quadratic regulator for optimality, and gradient descent as an adaptive controller. The convergence of the sliding mode control process is proven using two theorems based on the Lyapunov function. Simulation results for pendulum and inverted pendulum systems demonstrate that the proposed method outperforms both the linear quadratic regulator technique and the sliding mode control regarding reduced chattering and improved reaching time.
Research Article
Control and Optimization
Hadi Adib; Akbar Mirzapour Babajan; Beitollah Akbari Moghaddam; Roozbeh Balounejad Nouri
Abstract
This paper explores the resilience optimization of Iran's banking sector in the face of exchange rate shocks---critical macroeconomic disturbances with extensive consequences. We develop a multi-sector macro-dynamic stochastic general equilibrium model encompassing essential economic components, ...
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This paper explores the resilience optimization of Iran's banking sector in the face of exchange rate shocks---critical macroeconomic disturbances with extensive consequences. We develop a multi-sector macro-dynamic stochastic general equilibrium model encompassing essential economic components, including firms, government, central bank, and the banking sector. This framework facilitates the simulation of the macroeconomic environment and allows for a thorough analysis of the banking sector's adaptive responses to exchange rate fluctuations. Our findings reveal optimization strategies that effectively mitigate the adverse effects of these shocks while maintaining equilibrium in the broader economy. Specifically, we discover that while an initial positive exchange rate shock can enhance banking sector performance, it ultimately triggers inflationary pressures that threaten profitability and operational stability in the medium to long term.
Research Article
Hossein Kheiri; Mehdi Zavieh; Bashir Naderi
Abstract
In this paper, we use a graphical algorithm to control and synchronization of a chaotic system. Most of the controllers designed for synchronizing chaotic systems are complex, but the controllers designed using contraction and graphical methods are often simple and linear. ...
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In this paper, we use a graphical algorithm to control and synchronization of a chaotic system. Most of the controllers designed for synchronizing chaotic systems are complex, but the controllers designed using contraction and graphical methods are often simple and linear. Therefore, we explain the relationship between contraction analysis and the graphical method for controlling and synchronizing chaotic systems. We apply this approach to control and synchronize the chaotic Genesio-Tesi system. The stability of the error system in synchronization is investigated using the contraction method. Finally, we provide numerical simulations to demonstrate the effectiveness of the proposed method.
Research Article
Control and Optimization
Ahmad Rezaee
Abstract
This paper introduces several Abadie-type constraint qualifications and derives necessary optimality conditions in the Karush-Kuhn-Tucker for both weakly efficient solutions and efficient solutions of a nonsmooth multi-objective semi-infinite programming problem characterized by locally Lipschitz ...
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This paper introduces several Abadie-type constraint qualifications and derives necessary optimality conditions in the Karush-Kuhn-Tucker for both weakly efficient solutions and efficient solutions of a nonsmooth multi-objective semi-infinite programming problem characterized by locally Lipschitz data. The findings are expressed in terms of the Micheal-Penot subdifferential.
Research Article
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.
