Control Theory & Systems
Sommayeh Sheykhi; Mashallah Matinfar; Mohammad Arab Firoozjaee
Abstract
The advection-dispersion, variable-order differential equations have a vast application in fluid physics and energy systems. In this study, we propose a Ritz-approximation method using shifted Legendre polynomials to construct approximate numerical solutions for these equations. The ...
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The advection-dispersion, variable-order differential equations have a vast application in fluid physics and energy systems. In this study, we propose a Ritz-approximation method using shifted Legendre polynomials to construct approximate numerical solutions for these equations. The proposed method discretizes the original problem, converting it into a system of nonlinear algebraic equations that can be solved numerically at selected points. We discuss the error characteristics of the proposed method. For validation, the presented examples are compared with exact solutions and with prior results. The results indicate that the proposed method is highly effective.
Control Theory & Systems
Masrour Dowlatabadi; Maryam Nikbakht
Abstract
This study analyzes the growth dynamics of melanoma tumor cells and develops a model predictive controller (MPC) using four well-known optimizers to suppress tumor growth, proposing an MPC framework that integrates multiple metaheuristic algorithms for regulating tumor size. All modelling, control design, ...
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This study analyzes the growth dynamics of melanoma tumor cells and develops a model predictive controller (MPC) using four well-known optimizers to suppress tumor growth, proposing an MPC framework that integrates multiple metaheuristic algorithms for regulating tumor size. All modelling, control design, and simulations are performed in MATLAB, and results indicate that a PSO-based MPC offers satisfactory response and rapid convergence, achieving effective tracking and disturbance rejection. The study assumes precise drug dosing is feasible and demonstrates substantial tumor-size reduction through the integration of MPC with metaheuristic optimization. Simulation findings reveal that the PSO-based MPC achieves notable improvement in tumor reduction and overall control performance, outperforming other metaheuristic approaches, as evidenced by comparative error metrics: ITAE ≈ 1.9377 × 10^3, IAE ≈ 244.45, MSE ≈ 4.6863 × 10^3.
Control Theory & Systems
Ali Dehghani Filabadi; Hossein Nahid Titkanlue
Abstract
This paper addresses multi-attribute group decision-making (MAGDM) where linguistic assessments are represented by both positive and negative interval type-2 fuzzy numbers (IT2FNs), capturing the intrinsic uncertainty of group evaluations more accurately. We introduce a novel ranking method ...
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This paper addresses multi-attribute group decision-making (MAGDM) where linguistic assessments are represented by both positive and negative interval type-2 fuzzy numbers (IT2FNs), capturing the intrinsic uncertainty of group evaluations more accurately. We introduce a novel ranking method for IT2FNs that simultaneously utilizes the mean and standard deviation of the upper and lower membership functions, as well as the IT2FN's height. This enhances its discriminatory capability. The theoretical foundations of this ranking— encompassing zero, unity, and symmetry properties— are rigorously established, and its superiority over existing techniques is demonstrated through comparative analyses on seven benchmark datasets. Building on this ranking, we develop an integrated fuzzy MAGDM framework that can handle both positive and negative IT2FN assessments for criteria and weights. The framework’s practicality and effectiveness are validated through two case studies: one with exclusively positive linguistic terms and another with mixed positive and negative scales. Results indicate that the proposed ranking and decision framework yield more rational and robust group decisions under substantial uncertainty. They outperform conventional fuzzy methods and offer a nuanced solution for real-world MAGDM scenarios.
Control Theory & Systems
Subramani Magudeeswaran; Muthurathinam Sivabalan; Mehmet Yavuz; Dharmendra Kumar Singh; Kannimuthu Giridharan
Abstract
In this study, we fabricate and investigate a three-species intraguild predation model with a ratio-dependent functional response. We also incorporate harvesting efforts into both intraguild prey and intraguild predators. Then, we analyze the dynamical behavior ...
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In this study, we fabricate and investigate a three-species intraguild predation model with a ratio-dependent functional response. We also incorporate harvesting efforts into both intraguild prey and intraguild predators. Then, we analyze the dynamical behavior of the proposed model by taking the harvesting rate as the bifurcation parameter. We precisely outline the prerequisites for the proposed model's existence, stability, and bifurcation near the equilibrium points. It contributes to a better understanding of the impacts of harvesting on the survival or extinction of one or more species in the proposed model. Furthermore, we derive the suggested model's bionomic equilibrium and optimum harvesting policy by using the \textit{Pontryagin's maximum principle}. Finally, we provide some numerical simulations to validate the analytical results. In addition, we give some graphical representations to validate our results.
Control Theory & Systems
Mohammad Zangouei; Naser Pariz; Reihaneh Kardehi Moghaddam
Abstract
In this paper, we present an event-triggered fault-tolerant control framework for nonlinear affine multi-agent systems, together with a state-observer–based fault detection scheme. The proposed approach integrates an event-triggered controller that reduces communication and computation while guaranteeing ...
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In this paper, we present an event-triggered fault-tolerant control framework for nonlinear affine multi-agent systems, together with a state-observer–based fault detection scheme. The proposed approach integrates an event-triggered controller that reduces communication and computation while guaranteeing closed-loop stability, with a robust fault-detection mechanism capable of identifying sensor faults, including current-sensor faults, under bus and load disturbances, and leveraging sensor redundancy to enable rapid recovery. A rigorous stability and robustness assessment based on eigenvalue analysis of the observer matrix is complemented by extensive MATLAB simulations that demonstrate resilience to parameter variations and external disturbances. Open-loop analyses under unconventional inputs reveal high sensitivity to fault types while exhibiting insensitivity to load disturbances, underscoring the detector’s discriminative capability. To mitigate startup and transient effects, a low-pass filter is implemented at the detector output, reducing transients and improving fault-detection accuracy for real-time identification of current sensor faults. The overall results show reliable fault detection, rapid recovery, and maintained performance in the presence of sensor faults and load disturbances, thereby enhancing the robustness of nonlinear affine multi-agent systems.
Control Theory & Systems
Salam Mcheik; Elyas Shivanian; Youssef El Seblani
Abstract
In this paper, we investigate the existence and uniqueness of solutions for a high-order boundary value problem involving non-integer derivatives, specifically utilizing the Caputo fractional derivative. The problem is subject to non-local boundary conditions. To ...
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In this paper, we investigate the existence and uniqueness of solutions for a high-order boundary value problem involving non-integer derivatives, specifically utilizing the Caputo fractional derivative. The problem is subject to non-local boundary conditions. To tackle this, we introduce the fractional Green's function as an analytical tool. The Banach contraction fixed-point theorem serves as the fundamental method to establish our main results. To support the theoretical findings, we provide illustrative examples. Furthermore, we develop a numerical semi-analytical approach to approximate the unique solution with the desired accuracy.
Control Theory & Systems
Ali Dehghani Filabadi; Hossein Nahid Titkanlue
Abstract
Addressing complex decision-making scenarios, particularly those involving multiple criteria and expert perspectives, often requires robust frameworks capable of managing uncertainty and qualitative assessments. The Qualitative Absolute Order-of-Magnitude (QAOM) model offers ...
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Addressing complex decision-making scenarios, particularly those involving multiple criteria and expert perspectives, often requires robust frameworks capable of managing uncertainty and qualitative assessments. The Qualitative Absolute Order-of-Magnitude (QAOM) model offers a flexible approach for expressing subjective evaluations through linguistic terms with adjustable levels of detail. However, practical challenges remain in applying QAOM, including the absence of an inherent system for deriving attribute weights, limitations in coherently synthesizing the judgments from multiple experts, and the lack of systematic normalization procedures for negatively oriented attributes. To address these issues, this paper proposes an advanced multi-attribute group decision-making (MAGDM) framework fully embedded within the QAOM paradigm. The proposed solution introduces a mathematically consistent metric for comparing linguistic assessments, an entropy-based attribute weighting approach rooted in qualitative information, and an aggregation process that reflects expert diversity. Furthermore, a specialized normalization protocol is developed to handle negative attributes across heterogeneous scales. The feasibility and advantages of the method are validated through comprehensive examples and comparative analyses, highlighting improvements over traditional techniques in terms of objectivity, flexibility, and analytical depth. Overall, these developments markedly enhance the capabilities of QAOM-based MAGDM, equipping decision-makers with more nuanced and reliable tools for tackling complex problems characterized by imprecision and divergent expert opinions.
Control Theory & Systems
Maha Mohsin Mohammed Ali; Mahmoud Mahmoudi; Majid Darehmiraki
Abstract
This study addresses the numerical solution of an optimal control problem governed by a fractional convection–reaction–diffusion partial differential equation. The approach utilizes Radial Basis Function–Partition of Unity (RBF-PU) methods combined with the Grünwald-Letnikov approximation ...
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This study addresses the numerical solution of an optimal control problem governed by a fractional convection–reaction–diffusion partial differential equation. The approach utilizes Radial Basis Function–Partition of Unity (RBF-PU) methods combined with the Grünwald-Letnikov approximation for fractional derivatives, which provides a fundamental extension of classical derivatives in fractional calculus. To enhance sparsity in the control strategy, an $L_2$ norm is integrated into the objective function, along with quadratic penalties to reduce deviations from the desired state. This hybrid formulation facilitates the effective management of spatially sparse controllers, relevant in many practical applications. The RBF-PU technique offers a flexible and efficient framework by partitioning the domain into overlapping subregions, applying local RBF approximations, and synthesizing the global solution with compactly supported weight functions. Numerical experiments demonstrate the accuracy and effectiveness of this method.
Control Theory & Systems
Maria Afsharirad
Abstract
This paper presents a hybrid scheme for solving optimal control problems. Discretizing the time interval and assuming a constant control value on each sub-interval transforms the optimal control problem into an assignment problem. To cluster feasible solutions, a novel method is proposed ...
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This paper presents a hybrid scheme for solving optimal control problems. Discretizing the time interval and assuming a constant control value on each sub-interval transforms the optimal control problem into an assignment problem. To cluster feasible solutions, a novel method is proposed in this paper, which applies metaheuristic algorithms—specifically, genetic algorithms and particle swarm optimization—to generate a large number of solutions. Subsequently, the K-means clustering method is employed to classify these solutions into clusters. Enhancing the median of each cluster, using metaheuristic techniques, ultimately results in improved medians. The best median from the final iteration of the algorithm serves as an acceptable solution for the optimal control problem. In some cases, it even succeeds in discovering a new best solution.
Control Theory & Systems
Mohammad Alsaeedi; Mostafa Tavakolli; Ahmad Abouyee; Khatere Ghorbani Moghadam; Reza Ghanbari
Abstract
In this study, we proposed a novel graph partitioning problem where the edges are characterized by trapezoidal fuzzy numbers. A linear ranking function is employed to establish an order among these fuzzy numbers. We derive the necessary conditions for the existence of an ...
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In this study, we proposed a novel graph partitioning problem where the edges are characterized by trapezoidal fuzzy numbers. A linear ranking function is employed to establish an order among these fuzzy numbers. We derive the necessary conditions for the existence of an optimal solution to this problem. To address the fuzzy graph partitioning problem, we implement and compare the performance of three algorithms: Genetic Algorithm, Tabu Search, and Sequential Least Squares Programming. The algorithms are evaluated based on objective values, computational time, and the number of iterations across multiple numerical examples. Utilizing Dolan-Moré performance profiles, we demonstrate the superiority of our proposed approach relative to existing methods. The findings highlight the robustness and computational efficiency of our methodology, making a meaningful contribution to the advancement of fuzzy graph algorithms and their practical applications.
Control Theory & Systems
Reza Dehghan
Abstract
The orthogonal polynomials approximation method is widely regarded as a highly effective and versatile technique for solving optimal control problems in nonlinear systems. This powerful approach has found extensive applications in both theoretical research and practical engineering, demonstrating ...
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The orthogonal polynomials approximation method is widely regarded as a highly effective and versatile technique for solving optimal control problems in nonlinear systems. This powerful approach has found extensive applications in both theoretical research and practical engineering, demonstrating its capability to address complex dynamical behaviors. In this paper, we thoroughly investigate the optimal control problem of the Van der Pol oscillator, a classic nonlinear system with broad scientific and engineering relevance. The proposed solution follows two distinct and systematic steps. First, the state and control functions are approximated by linear combinations of shifted Chelyshkov polynomials, whose coefficients are treated as unknown parameters to be determined. Second, the resulting transformed problem is formulated as a nonlinear optimization problem and efficiently solved using advanced numerical optimization tools implemented in \textsc{Matlab}. To demonstrate the accuracy and robustness of the proposed approach, we present and analyze numerical results across several representative scenarios.
Control Theory & Systems
Mehrnoosh Salehi Chegeni; Majid Yarahmadi
Abstract
Optimal control of certain singularly perturbed systems, with slow and fast dynamics, presents notable challenges, including ill-conditioning, high dimensionality, and ill-posed algebraic Riccati equations. In this paper, we introduce a novel ...
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Optimal control of certain singularly perturbed systems, with slow and fast dynamics, presents notable challenges, including ill-conditioning, high dimensionality, and ill-posed algebraic Riccati equations. In this paper, we introduce a novel inverse optimal control method based on the eigenvalue assignment approach to address these issues. The proposed method optimizes the objective function while ensuring system stability through the strategic placement of eigenvalues in the singular perturbed closed-loop system. To facilitate analysis and support the implementation, a new theorem is proved, and a corresponding algorithm is developed. The proposed algorithm is free of ill-conditioned numerical problems, making it more robust in terms of numerical diffusion and perturbation measurement. Finally, two simulation examples are presented to illustrate the advantages of the proposed method, demonstrating improvement in controller robustness, substantial reductions in cost functions, and decreased control amplitudes.
Control Theory & Systems
Alireza Fakharzadeh Jahromi; Mahin Azizi Karachi; Hajar Alimorad
Abstract
Cancer is a class of diseases characterized by uncontrolled cell growth that affects immune cells. There are several treatment options available, including surgery, chemotherapy, hormonal therapy, radiation therapy, targeted therapy, and ...
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Cancer is a class of diseases characterized by uncontrolled cell growth that affects immune cells. There are several treatment options available, including surgery, chemotherapy, hormonal therapy, radiation therapy, targeted therapy, and palliative care. Among these, chemotherapy is one of the most widely used and recognized methods. This paper presents a novel model designed to control cancer cell growth based on a system of nonlinear fractional differential equations with delay in chemotherapy. The model focuses on the competition between tumor and immune cells to minimize the number of tumor cells and determine the optimal dosage of the administered drug. It can simulate various scenarios and predict the outcomes of different chemotherapy regimens. By employing discretization and the Grunwald-Letnikov method, we aim to gain insights into why some patients respond well to chemotherapy while others do not. The results may also help identify potential drug targets and optimize existing treatments.
Control Theory & Systems
Maryam Najimi; Akbar Hashemi Borzabadi
Abstract
This paper addresses the challenges of power control, radar assignment, and signal timing to improve the detection and tracking of multiple targets within a mono-static cognitive radar network. A fusion center is utilized to integrate target velocity ...
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This paper addresses the challenges of power control, radar assignment, and signal timing to improve the detection and tracking of multiple targets within a mono-static cognitive radar network. A fusion center is utilized to integrate target velocity data gathered by radars. The primary objective is to minimize the mean square error in target velocity estimation while adhering to constraints related to global detection probability and total radar power consumption for effective target detection and tracking. The optimization problem is formulated and a low-complexity method is proposed using the genetic algorithm (GA). In this approach, the radars and their transmission powers are represented as chromosomes and the network's quality of service (QoS) requirements serve as inputs to the GA. The output of the GA is the mean error square of the target velocity estimation. Once the problem is resolved, the power allocation for each radar assigned to a specific target is determined. Simulation results demonstrate the effectiveness of the proposed algorithm in enhancing detection performance and improving tracking accuracy when compared to other benchmark algorithms.
Control Theory & Systems
Mohsen Sayadi; Hasan Barzegar; Saeid Alikhani; Nima Ghanbari
Abstract
An irregularity measure (IM) of a connected graph $G$ is defined as a non-negative graph invariant that satisfies the condition $IM(G) = 0$ if and only if $G$ is a regular graph. Among the prominent degree-based irregularity measures are Bell's degree variance, denoted as ...
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An irregularity measure (IM) of a connected graph $G$ is defined as a non-negative graph invariant that satisfies the condition $IM(G) = 0$ if and only if $G$ is a regular graph. Among the prominent degree-based irregularity measures are Bell's degree variance, denoted as $Var_B(G)$, and degree deviation, represented as $S(G)$. Specifically, they are defined by the equations $Var_B(G) = \frac{1}{n} \sum_{i=1}^{n} \left( d_i - \frac{2m}{n} \right)^2$ and $S(G)=\sum_{i=1}^n \left|d_i- \frac{2m}{n}\right |$, where $m$ is the number of edges and $n$ is the number of vertices in $G$. This paper studies the properties of Bell's degree-variance and degree deviation for acyclic, unicyclic, and cactus graphs. Our analysis shows how these measures relate to graph topology and structure, influencing the overall irregularity. Additionally, we identify and analyze optimal graphs that minimize both irregularity measures, providing insights into their implications for network design, data structure optimization, and real-world applications. This study contributes to the understanding of graph irregularity and offers a framework for future research into irregularity measures across different classes of graphs.
Control Theory & Systems
Rasoul Hatamian; Seyed Amjad Samareh Hashemi
Abstract
This paper presents an iterative computational method for addressing constrained nonlinear optimal control problems, specifically those involving terminal state, state saturation, and control saturation constraints. The proposed approach reformulates the original ...
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This paper presents an iterative computational method for addressing constrained nonlinear optimal control problems, specifically those involving terminal state, state saturation, and control saturation constraints. The proposed approach reformulates the original problem into a sequence of constrained linear time-varying quadratic optimal control problems. This is achieved by iteratively approximating the nonlinear dynamic system using constrained linear time-varying models. Each reformulated problem is then converted into a standard quadratic programming problem by applying Chelyshkov polynomials in conjunction with a collocation method. Finally, the resulting problems are solved to obtain optimal control solutions
Control Theory & Systems
Afrah Kadhim Saud Al-tameemi; Mahmoud Mahmoudi; Majid Darehmiraki
Abstract
This study introduces an innovative approach for addressing optimal control problems related to parabolic partial differential equations (PDEs) through the application of rational radial basis functions (RBFs). Parabolic PDEs, which are instrumental in modeling time-dependent processes such as heat transfer ...
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This study introduces an innovative approach for addressing optimal control problems related to parabolic partial differential equations (PDEs) through the application of rational radial basis functions (RBFs). Parabolic PDEs, which are instrumental in modeling time-dependent processes such as heat transfer and diffusion, pose significant computational challenges in optimal control due to the requirement for precise approximations of both state and adjoint equations. The proposed approach exploits the adaptability and spectral accuracy of rational RBFs within a meshless framework, effectively addressing the limitations of traditional discretization methods. By enhancing the accuracy and efficiency of control strategies, this method significantly contributes to advancing the theory and application of optimal control in dynamic systems. The tunable shape parameters of rational RBFs allow for accurate representation of solution characteristics, including steep gradients and localized behaviors. Additionally, their meshless framework adeptly accommodates complex geometries and boundary conditions, ensuring computational efficiency through the generation of sparse and well-conditioned system matrices. This paper also introduces a novel hybrid rational RBF, termed the Gaussian rational hybrid RBF. The efficacy of the proposed approach is validated through a series of benchmark tests and practical applications, highlighting its ability to achieve high accuracy with reduced computational effort. The findings illustrate the potential of rational RBFs as a robust and versatile tool for solving optimal control problems governed by parabolic PDEs, paving the way for further exploration of advanced rational RBF-based techniques in the field of computational optimal control.
Control Theory & Systems
Amal Kumar Adak; Nil Kamal
Abstract
The incorporation of Pythagorean fuzzy sets into credit risk assessment represents a relatively innovative approach for predicting loan defaults, offering a more precise and adaptable tool for financial institutions. Key customer information—such as credit history, credit ...
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The incorporation of Pythagorean fuzzy sets into credit risk assessment represents a relatively innovative approach for predicting loan defaults, offering a more precise and adaptable tool for financial institutions. Key customer information—such as credit history, credit mix, credit utilization, duration of credit history, income level, and employment stability—is obtained as linguistic variables. These linguistic assessments are then transformed into Pythagorean fuzzy numbers. The combined Pythagorean fuzzy information is subsequently processed using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). This approach employs a modified accuracy function to determine the Pythagorean fuzzy positive ideal solution and the Pythagorean fuzzy negative ideal solution. For distance calculations within the TOPSIS framework, spherical distance measurements are utilized. Alternatives are ranked based on the relative closeness coefficient and an adjusted index, collectively facilitating decision-making. The practical applicability of the proposed model is demonstrated through an illustrative numerical example.
Control Theory & Systems
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.
Control Theory & Systems
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 Theory & Systems
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.
Control Theory & Systems
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.
Control Theory & Systems
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.
Control Theory & Systems
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 Theory & Systems
Negar Izadi; Mohammad Taghi Dastjerdi
Abstract
In this paper, we present a new approach for achieving leader-follower consensus in a network of nonlinear dynamic agents with an undirected graph topology, using a fuzzy sliding mode controller (FSMC) for Multi-Agent Systems (MASs). Our proposed sliding mode controller ...
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In this paper, we present a new approach for achieving leader-follower consensus in a network of nonlinear dynamic agents with an undirected graph topology, using a fuzzy sliding mode controller (FSMC) for Multi-Agent Systems (MASs). Our proposed sliding mode controller is based on a separating hyperplane that effectively addresses the consensus problem in MASs. Additionally, we design a fuzzy controller to eliminate the chattering phenomenon. According to the communication graph topology and the Lyapunov stability condition, the proposed FSMC satisfies the consensus condition. One significant advantage of our approach is that the system states converge to the sliding surface quickly and remain on the surface, thereby ensuring better tracking performance. We validate the effectiveness of our proposed approach through simulation results.
