Control Theory & Systems
Shiva Karimi; Elyas Shivanian; Zahra Barikbin
Abstract
This paper presents a novel numerical method for solving variable-order fractional integro-differential equations using two-dimensional fractional-order Fibonacci wavelets. The proposed approach employs fractional-order Fibonacci wavelets together with their associated integral and derivative operational ...
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This paper presents a novel numerical method for solving variable-order fractional integro-differential equations using two-dimensional fractional-order Fibonacci wavelets. The proposed approach employs fractional-order Fibonacci wavelets together with their associated integral and derivative operational matrices. First, new integral and derivative operational matrices are derived. These matrices, which exhibit improved accuracy in the numerical examples reported herein, are then employed to transform the governing equation into a system of algebraic equations. The collocation method is subsequently applied to solve this system and determine the unknown coefficients. Finally, error analysis, convergence results based on relevant theorems, and numerical examples are provided to demonstrate the accuracy, reliability, and efficiency of the proposed method.
Control Theory & Systems
Majid Akbarian; Javad Zanganeh
Abstract
This paper proposes a novel observer-based adaptive neural command filter (CF) output-feedback tracking control scheme for uncertain nonlinear multiple-input multiple-output (MIMO) stochastic systems subject to constrained partial tracking errors (PTEs). The key contributions are threefold. First, a ...
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This paper proposes a novel observer-based adaptive neural command filter (CF) output-feedback tracking control scheme for uncertain nonlinear multiple-input multiple-output (MIMO) stochastic systems subject to constrained partial tracking errors (PTEs). The key contributions are threefold. First, a linear Luenberger-type state observer is designed to handle unmeasured states, and radial basis function neural networks (RBFNNs) are employed to approximate unknown nonlinear functions. Second, a dynamic surface control (DSC) strategy augmented with compensating signals simultaneously eliminates the "explosion of complexity" inherent in conventional backstepping and rectifies filter-output errors in the DSC framework. Third, a minimal learning parameter (MLP) technique — based on Young's inequality — reduces the number of online-tunable parameters to a single scalar per subsystem, yielding a computationally efficient adaptive law. The closed-loop system is rigorously proven to be semi-globally uniformly ultimately bounded (SGUUB) in probability via Lyapunov-based stochastic stability analysis, and all PTEs remain within prescribed performance bounds throughout transient and steady-state operation. Comparative simulations on a second-order MIMO stochastic benchmark demonstrate that the proposed approach achieves significantly lower root mean square and integral absolute tracking errors than existing methods, while maintaining bounded and smooth control effort. Current limitations, including the restriction to strict-feedback topologies and the assumption of bounded external disturbances, motivate future extensions to multi-agent and event-triggered control frameworks.
Control Theory & Systems
Ghania Idiri
Abstract
In this paper, a systematic design approach for the parametric optimization of uncertain dynamical systems with bounded parameter uncertainties is proposed. The methodology proceeds in two stages. In the first stage, the control input is expressed as a finite linear combination of polynomial basis functions, ...
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In this paper, a systematic design approach for the parametric optimization of uncertain dynamical systems with bounded parameter uncertainties is proposed. The methodology proceeds in two stages. In the first stage, the control input is expressed as a finite linear combination of polynomial basis functions, and an approximate analytical solution of the state equation is derived using the Variational Iteration Method, which is a semi-analytical iterative technique that avoids discretization and linearization. Substituting this approximate trajectory into the performance index yields a robust min–max optimization problem parameterized by the control coefficients. In the second stage, the robust optimization problem is converted into a tractable scenario optimization problem by drawing a finite number of independent and identically distributed samples from the uncertainty set. The resulting problem is solved using a genetic algorithm. The effectiveness of the proposed approach is demonstrated through two application examples. The first example concerns an uncertain linear-quadratic regulator, and the second addresses an uncertain nonlinear optimal control problem. Optimal control and state trajectories are provided for a set of samples. In addition, the optimal value of the performance index is reported, showing that this value does not exceed the threshold imposed by the proposed approach. The paper concludes by discussing limitations, including dependence on the accuracy of the Variational Iteration Method approximation and the assumption of a known probability distribution over the uncertainty set, and identifies directions for future research.
Control Theory & Systems
Mehdi Ramezanifard; Naser Pariz; Mohammad Bagher Naghibi Sistani; Majid Akbarian
Abstract
Non-holonomic mobile robots are widely deployed in industrial and service environments, yet designing controllers for moving-target tracking under nonholonomic constraints remains a challenging open problem. In this paper, we present a Mamdani-type fuzzy logic tracking controller specifically designed ...
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Non-holonomic mobile robots are widely deployed in industrial and service environments, yet designing controllers for moving-target tracking under nonholonomic constraints remains a challenging open problem. In this paper, we present a Mamdani-type fuzzy logic tracking controller specifically designed for non-holonomic mobile robots pursuing dynamic targets with arbitrary movement patterns. Although tailored to differential-drive platforms, the proposed architecture can be extended to other types of mobile robots and autonomous systems. A key feature of the controller is the explicit enforcement of a predefined safe distance between the robot and the target, preventing collision while simultaneously supporting covert or low-detection tracking applications. A significant advantage of this model-free architecture is its computational efficiency: the system operates on minimal sensor inputs, requires no dynamic model of the robot,and can be seamlessly deployed on low-cost sensing hardware, making it well-suited for energy-constrained platforms. Lyapunov-based stability analysis is provided for the closed-loop system, and the methodology is validated through simulation on a differential-drive robot model across multiple complex scenarios in a virtual environment, including cases with high measurement noise. The comprehensive simulation results confirm that the controller achieves robust stability and high tracking precision, demonstrating its practical acceptability for real-time target tracking applications.
Control Theory & Systems
Maha Mohsin Mohammed Ali
Abstract
A core challenge in numerically solving partial differential equations (PDEs) is achieving accuracy without sacrificing computational tractability. Globally supported methods provide high-order precision but at a computational cost that grows prohibitively with problem size, while locally supported schemes ...
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A core challenge in numerically solving partial differential equations (PDEs) is achieving accuracy without sacrificing computational tractability. Globally supported methods provide high-order precision but at a computational cost that grows prohibitively with problem size, while locally supported schemes scale more efficiently, though often with a reduction in solution accuracy. The proposed localized meshless framework resolves this tension through the integration of Radial Basis Function (RBF) approximation with the Partition of Unity (PU) decomposition, with applications to elliptic, convection-diffusion, and Helmholtz boundary value problems and their corresponding PDE-constrained optimal control problems. The domain is partitioned into overlapping subdomains, each accommodating an independent RBF expansion that is subsequently blended by compactly supported PU weight functions. This localization strategy replaces the single ill-conditioned dense system of global RBF collocation with a collection of smaller, well-conditioned local systems, reducing the theoretical computational complexity from O(N3) to O(N log N). Three canonical benchmark problems validate the framework: Poisson’s equation, a singularly perturbed convection-diffusion equation, and the Helmholtz equation on a circular domain, each embedded in a distributed optimal control formulation. The proposed scheme achieves L2-norm errors of order 10-4 at N = 1,000 nodes, outperforming both standard finite difference methods and global RBF collocation by factors of 28 to 49 in accuracy. Optimal control problems are handled through a Lagrange multiplier formulation yielding coupled state and adjoint systems, both discretized within the same RBF-PU architecture. The framework is illustrated through a detailed engineering case study — optimal heat-source regulation in a thermally loaded plate — in which the complete optimality system is derived, physically interpreted, and numerically solved. Numerical stability, current limitations, and directions for future investigation are discussed.
Control Theory & Systems
Mahnaz Abedini; Gorbanali Haghighatdoost; Hossein Kheiri
Abstract
This study develops and analyzes a four-compartment predator–prey model incorporating disease dynamics and optimal control. The first prey population follows logistic growth and is susceptible to infection, whereas the second prey population remains disease-free and exhibits greater competitive ...
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This study develops and analyzes a four-compartment predator–prey model incorporating disease dynamics and optimal control. The first prey population follows logistic growth and is susceptible to infection, whereas the second prey population remains disease-free and exhibits greater competitive ability. The model incorporates an epidemic process within the first prey population and considers two control measures: reducing disease transmission and treating or removing infected individuals. We investigate the resulting system theoretically to assess the effects of these interventions on disease prevalence, prey persistence, predator dynamics, and ecosystem stability. In particular, stability analysis, sensitivity analysis, and optimal control theory are employed to characterize the model dynamics and identify the most influential parameters. The results indicate that the carrying capacity (k), infection rate (γ), and disease-induced mortality rate (µ) play major roles in determining the persistence of infection. Moreover, the optimal isolation (u1) and treatment (u2) strategies substantially reduce disease prevalence, increase the healthy prey population, and promote predator stability compared with the uncontrolled scenario. Numerical simulations further demonstrate the effectiveness of the proposed control strategies in mitigating infection and maintaining ecological balance. These findings demonstrate that the model provides a unified framework for examining the interactions between heterogeneous prey populations, disease transmission, predation, and targeted control interventions.
Control Theory & Systems
Fidelis Nofertinus Zai; Rian Kurnia; Juan Prihanda Nainggolan
Abstract
In this study, we examine solutions to Optimal Tracking Control (OTC) problems for both Linear Quadratic (LQ) and nonlinear systems. Classical approaches to OTC rely on formulating and solving the Hamilton-Jacobi-Bellman (HJB) equation, which typically requires numerical solutions of the state, co-state, ...
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In this study, we examine solutions to Optimal Tracking Control (OTC) problems for both Linear Quadratic (LQ) and nonlinear systems. Classical approaches to OTC rely on formulating and solving the Hamilton-Jacobi-Bellman (HJB) equation, which typically requires numerical solutions of the state, co-state, and stationary equations using the forward-backward method. Such methods often involve intricate mathematical analysis and substantial computational effort. To address these challenges, we explored the use of Physics Informed Neural Networks (PINN) as an alternative framework for solving OTC problems. The PINN approach is implemented by constructing a problem-specific loss function that directly incorporates the governing dynamics and control objectives. This method is comparatively simpler and more flexible to implement. The performance of PINNs is evaluated through quantitative error analysis and benchmarked against the classical Runge-Kutta (RK) method. A detailed comparison is presented using tabulated error metrics and time-domain plots of absolute errors. Numerical results demonstrate that PINNs achieve lower approximation errors than Runge-Kutta method for both LQ and nonlinear tracking problems, indicating their effectiveness as a viable alternative solution strategy for OTC problems.
Control Theory & Systems
Muhammed Hassanein Al-Hakeem; Mahmoud Mahmoudi; Ahmed Sabah Ahmed Al-Jilawi
Abstract
This paper presents a novel hybrid orthogonal polynomial method for solving optimal control problems governed by fractional parabolic PDEs. By strategically weighting and combining these polynomial bases, the method adaptively leverages their respective strengths to achieve superior approximation properties. ...
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This paper presents a novel hybrid orthogonal polynomial method for solving optimal control problems governed by fractional parabolic PDEs. By strategically weighting and combining these polynomial bases, the method adaptively leverages their respective strengths to achieve superior approximation properties. The proposed approach combines the spectral accuracy of Legendre polynomials, the minimax properties of Chebyshev polynomials, and the flexibility of Jacobi polynomials to create a robust numerical framework. The hybrid orthogonal polynomial method is applied to discretize the fractional parabolic PDEs, and an efficient numerical scheme is developed to solve the resulting optimal control problem. Numerical experiments demonstrate the accuracy, efficiency, and applicability of the proposed approach, showing significant improvements over traditional radial basis function methods. The results highlight the potential of the hybrid orthogonal polynomial method for solving complex optimal control problems in science and engineering.
Control Theory & Systems
Roohallah Daneshpayeh; Sirous Jahanpanah
Abstract
This paper offers the idea of (anti) (m, n)-fuzzy BL-subalgebras as a novel extension of classical BL-algebras within the fuzzy mathematical framework. The proposed structures generalize various types of fuzzy subalgebras, including (anti) intuitionistic, (anti) Pythagorean, (anti) Fermatean, ...
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This paper offers the idea of (anti) (m, n)-fuzzy BL-subalgebras as a novel extension of classical BL-algebras within the fuzzy mathematical framework. The proposed structures generalize various types of fuzzy subalgebras, including (anti) intuitionistic, (anti) Pythagorean, (anti) Fermatean, and (anti) q-rung orthopair fuzzy BL-subalgebras for q >= 1. Fundamental algebraic properties and equivalent characterizations of (m,n)-fuzzy BL-subalgebras are established through the notion of value-cuts. Furthermore, the concept of power-implication preserving (PIP) BL-algebras is introduced, and it is shown that a PIP BL-algebra exists for every prime number. Several closure properties of (m,n)-fuzzy BL-subalgebras under combination operations are also derived within this framework. From an applied perspective, the developed theoretical results can serve as a mathematical foundation for modeling and reasoning in fuzzy control systems and optimization processes, particularly in decision-making environments characterized by uncertainty and graded information.
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
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
Mohammad Rashki-Ghalehno; Seyed Mehdi Mirhosseini-Alizamini; Bashir Naderi
Abstract
This paper introduces a robust hybrid adaptive control framework for stabilizing chaotic systems under persistent, potentially large time delays. The controller is based on an enhanced Lyapunov–Krasovskii functional that integrates an energy-capturing integral term with a bounded trigonometric ...
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This paper introduces a robust hybrid adaptive control framework for stabilizing chaotic systems under persistent, potentially large time delays. The controller is based on an enhanced Lyapunov–Krasovskii functional that integrates an energy-capturing integral term with a bounded trigonometric term. The integral term accounts for historical effects by quantifying cumulative energy over the delay period, while the trigonometric term attenuates nonlinear oscillations. Embedding these components in a single control law yields stabilization of all state variables to the equilibrium despite substantial delays. We establish Uniform Ultimate Boundedness, showing that trajectories enter a compact neighborhood of the equilibrium after a finite transient and subsequently converge. Adjustable gains enable practitioners to determine the convergence radius and the size of the attraction region according to practical requirements. The method is validated on the delayed Lorenz system; simulations with a 20-second delay demonstrate rapid convergence to a small neighborhood of the equilibrium, with the Lyapunov functional derivative remaining non-positive. A comparative study with established controllers underscores the proposed approach’s favorable trade-offs among computational cost, oscillation suppression, and explicit stability guarantees. Overall, the proposed framework delivers a practical, robust, and high-performance solution for controlling chaotic systems in the presence of large time delays.
Control Theory & Systems
Hadi Sharifi; Mostafa Akhavan-Safar; Mohammad Mohsen Sadr
Abstract
Enterprise architecture (EA) offers an integrated framework for strategic planning and organizational governance. Implementing EA effectively requires prioritizing a concise set of criteria within a complex system, leveraging mathematical modeling and optimization to inform decisions under uncertainty. ...
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Enterprise architecture (EA) offers an integrated framework for strategic planning and organizational governance. Implementing EA effectively requires prioritizing a concise set of criteria within a complex system, leveraging mathematical modeling and optimization to inform decisions under uncertainty. This study introduces a hierarchical decision-making approach using Analytic Hierarchy Process (AHP) to extract and weight the most impactful criteria from an extensive literature base and expert opinions, with a focus on control-theoretic and optimization perspectives. Using insights from 18 experts from various fields and the proposed approach, key criteria of successful enterprise architecture deployment were identified and quantified: commitment (0.1143), governance (0.1082), infrastructure (0.0751), organizational management (0.0589), and senior management support (0.0484). The methodology integrates weights with objective-function considerations, sensitivity analyses, and optimization-oriented interpretations to ensure robust prioritization under uncertainty. The resulting framework supports decision-makers in (i) controlling and steering EA initiatives, (ii) optimizing resource allocation and process efficiencies, and (iii) designing data-driven, scenario-based decision models for dynamic organizational environments. These findings offer actionable guidance for managers aiming to enhance performance, reduce costs, and secure competitive advantage through disciplined governance, rigorous modeling, and evidence-based decision support.
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
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.
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