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.
Control and Optimization
Maryam Yaghoubi; Fatemeh Dadmand
Abstract
Natural disasters, such as earthquakes, result in significant financial and human losses. Rescue operations play a crucial role in managing such crises. However, the lack of precise information and the damage or destruction of urban transportation routes ...
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Natural disasters, such as earthquakes, result in significant financial and human losses. Rescue operations play a crucial role in managing such crises. However, the lack of precise information and the damage or destruction of urban transportation routes following earthquakes introduces uncertainty into these operations. This study presents a multi-objective humanitarian logistics model that utilizes a mixed-integer nonlinear programming (MINLP) approach. The model considers the reliability of transportation routes after an earthquake, the standard response time for allocating personnel and relief equipment, and the coverage maximization. This model incorporates various uncertainties, including the reliability of the transportation network. Real data from the city of Gonabad, Iran, was used to evaluate the proposed model. The results and sensitivity analysis demonstrated that the model exhibits desirable performance.
Control and Optimization
Ahmad Sharif
Abstract
In this study, we explore soliton solutions for the conformable time-fractional Boussinesq equation utilizing the three-wave method. To validate the precision of our findings, we discuss specific special cases by adjusting certain potential parameters and also present the ...
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In this study, we explore soliton solutions for the conformable time-fractional Boussinesq equation utilizing the three-wave method. To validate the precision of our findings, we discuss specific special cases by adjusting certain potential parameters and also present the graphical representations of our results. The results achieved in this research align closely with those from previous studies, demonstrating enhanced accuracy and simplicity. Given the extensive applications of this equation in particle physics, understanding its dynamics is crucial. Consequently, employing methods that encompass a broad spectrum of solutions is imperative. The versatility of this method in yielding diverse solutions is evident in the results we have obtained. The solutions derived in this paper are novel and offer greater precision compared to previous works.
Control and Optimization
Atefeh Hassani Bafrani
Abstract
The primary objective of this paper is to enhance several well-known geometric constraint qualifications and necessary optimality conditions for nonsmooth semi-infinite optimization problems (SIPs). We focus on defining novel algebraic Mangasarian-Fromovitz type constraint qualifications, and on presenting ...
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The primary objective of this paper is to enhance several well-known geometric constraint qualifications and necessary optimality conditions for nonsmooth semi-infinite optimization problems (SIPs). We focus on defining novel algebraic Mangasarian-Fromovitz type constraint qualifications, and on presenting two Karush-Kuhn-Tucker type necessary optimality conditions for nonsmooth SIPs defined by locally Lipschitz functions. Then, by employing a new type of generalized invex functions, we present sufficient conditions for the optimality of a feasible point of the considered problems. It is noteworthy that the new class of invex functions we considered encompasses several classes of invex functions introduced previously. Our results are based on the Michel-Penot subdifferential.
Control and Optimization
Seyed Mohsen Izadyar; Mohammad Eshaghnezhad; Hossein Davoodi Yeganeh
Abstract
This study presents a model of a quantum dot laser with a planar cavity, employing numerical methods and artificial neural networks for simulation purposes. The investigation focuses on the influence of critical parameters, including the injection current into the active layer of the quantum dot ...
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This study presents a model of a quantum dot laser with a planar cavity, employing numerical methods and artificial neural networks for simulation purposes. The investigation focuses on the influence of critical parameters, including the injection current into the active layer of the quantum dot laser and the carrier relaxation time to a lower energy state level. The model delves into the intricate carrier and photon dynamics within the laser, solving a system of coupled equations that describe these interactions. The fourth-order Runge-Kutta method is utilized to solve these equations numerically. The results indicate that increased pumping power enhances the stable power levels and the peak power output of the laser. Additionally, analysis of the power versus intensity of current ($P-I$) characteristic curve reveals that a longer carrier relaxation time to a lower energy state leads to a higher threshold current and a reduction in the quantum efficiency of the device. The study also examines the laser switch-on time against the injection current. Finally, the deterioration in the quality of quantum dots and quantum wells is scrutinized. To gain deeper insights into the effect of increased pumping current on laser switch-on time, the study complements numerical findings with the application of artificial neural networks, yielding significant results.
Control and Optimization
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 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.
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.
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.
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.
Control and Optimization
Ali Valinejad; Afshin Babaei; Zahra Zarei
Abstract
This paper introduces a variable step size strategy for a stochastic time-delays Lotka-Volterra competition system. This adaptive strategy utilizes the Milstein method for numerical solutions. It employs two local error estimates, corresponding to the diffusion and drift components ...
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This paper introduces a variable step size strategy for a stochastic time-delays Lotka-Volterra competition system. This adaptive strategy utilizes the Milstein method for numerical solutions. It employs two local error estimates, corresponding to the diffusion and drift components of the model, to select and control the step sizes. The algorithm is described in detail, and numerical experiments are conducted to demonstrate the efficiency of the proposed method. The primary objective of this research is to propose a dynamic strategy for generating and controlling the step sizes in the finite difference algorithm employed. This adaptive approach accelerates the numerical procedure and improves efficiency compared to a constant-size scheme. As an analytical solution for the model is unavailable, a numerical estimation with a small fixed step size is considered a reference solution. The numerical results demonstrate the superior accuracy of the proposed strategy compared to a reference solution.
Control and Optimization
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.
Control and Optimization
Reza Akbari; Leader Navaei; Mohammad Shahriari
Abstract
This paper presents an extension of the SEIR mathematical model for infectious disease transmission to a fractional-order model. The model is formulated using the Caputo derivative of order α ∈ (0, 1]. We study the stability of equilibrium points, including ...
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This paper presents an extension of the SEIR mathematical model for infectious disease transmission to a fractional-order model. The model is formulated using the Caputo derivative of order α ∈ (0, 1]. We study the stability of equilibrium points, including the disease-free equilibrium $(E_{f})$, and the infected steady-state equilibrium $(E_{e})$ using the stability theorem of Fractional Differential Equations. The model is also analyzed under certain conditions, and it is shown that the disease-free equilibrium is locally asymptotically stable. Additionally, the extended Barbalat’s lemma is applied to the fractional-order system, and a suitable Lyapunov functional is constructed to demonstrate the global asymptotic stability of the infected steady-state equilibrium. To validate the theoretical results, a numerical simulation of the problem is conducted.
Control and Optimization
Hajar Alimorad
Abstract
While many real-world optimization problems typically involve multiple constraints, unconstrained problems hold practical and fundamental significance. They can arise directly in specific applications or as transformed versions of constrained optimization problems. Newton's method, ...
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While many real-world optimization problems typically involve multiple constraints, unconstrained problems hold practical and fundamental significance. They can arise directly in specific applications or as transformed versions of constrained optimization problems. Newton's method, a notable numerical technique within the category of line search algorithms, is widely used for function optimization. The search direction and step length play crucial roles in this algorithm. This paper introduces an algorithm aimed at enhancing the step length within the Broyden quasi-Newton process. Additionally, numerical examples are provided to compare the effectiveness of this new method with another approach.
Control and Optimization
Fatemeh Babakordi; Nemat Allah Taghi-Nezhad
Abstract
This paper presents the introduction of two novel equation types: the partial hesitant fuzzy equation and the half hesitant fuzzy equation. Additionally, an efficient method is proposed to solve these equations by defining four solution categories: Controllable, Tolerable Solution ...
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This paper presents the introduction of two novel equation types: the partial hesitant fuzzy equation and the half hesitant fuzzy equation. Additionally, an efficient method is proposed to solve these equations by defining four solution categories: Controllable, Tolerable Solution Set (TSS), Controllable Solution Set (CSS), and Algebraic Solution Set (ASS). Furthermore, the paper establishes eight theorems that explore different types of solutions and lay out the conditions for the existence and non-existence of hesitant fuzzy solutions. The practicality of the proposed method is demonstrated through numerical examples.
Control and Optimization
Abbas Ali Rezaee; Hadis Ahmadian Yazdi; Mahdi Yousefzadeh Aghdam; Sahar Ghareii
Abstract
With the advancements in science and technology, the industrial and aviation sectors have witnessed a significant increase in data. A vast amount of data is generated and utilized continuously. It is imperative to employ data mining techniques to extract and uncover knowledge ...
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With the advancements in science and technology, the industrial and aviation sectors have witnessed a significant increase in data. A vast amount of data is generated and utilized continuously. It is imperative to employ data mining techniques to extract and uncover knowledge from this data. Data mining is a method that enables the extraction of valuable information and hidden relationships from datasets. However, the current aviation data presents challenges in effectively extracting knowledge due to its large volume and diverse structures. Air Traffic Management (ATM) involves handling Big data, which exceeds the capacity of conventional acquisition, matching, management, and processing within a reasonable timeframe. Aviation Big data exists in batch forms and streaming formats, necessitating the utilization of parallel hardware and software, as well as stream processing, to extract meaningful insights. Currently, the map-reduce method is the prevailing model for processing Big data in the aviation industry. This paper aims to analyze the evolving trends in aviation Big data processing methods, followed by a comprehensive investigation and discussion of data analysis techniques. We implement the map-reduce optimization of the K-Means algorithm in the Hadoop and Spark environments. The K-Means map-reduce is a crucial and widely applied clustering method. Finally, we conduct a case study to analyze and compare aviation Big data related to air traffic management in the USA using the K-Means map-reduce approach in the Hadoop and Spark environments. The analyzed dataset includes flight records. The results demonstrate the suitability of this platform for aviation Big data, considering the characteristics of the aviation dataset. Furthermore, this study presents the first application of the designed program for air traffic management.
Control and Optimization
Sajad Amirian; Maghsoud Amiri; Mohammad Taghi Taghavifard
Abstract
Integrating sustainability and reliability represents a synergistic approach that can be explored through the problem of a closed-loop supply chain network design (SCND). This study is conducted in three stages: mathematical modeling, model solution using exact methods, ...
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Integrating sustainability and reliability represents a synergistic approach that can be explored through the problem of a closed-loop supply chain network design (SCND). This study is conducted in three stages: mathematical modeling, model solution using exact methods, and evaluation of the solution methods. In the first stage, a mixed-integer linear programming (MILP) model is developed in a multi-objective, multi-product, and multi-period framework. The objectives of the proposed model aim to maximize profitability, social responsibility, and reliability. In the second stage, two methods, namely Augmented $\varepsilon$-Constraint (AEC) and Normalized Normal Constraint (NNC), are implemented in the GAMS software to solve the model and identify the optimal Pareto solutions. In the third stage, the Shannon Entropy technique is employed to determine the criteria weights, and the VIKOR technique is utilized to select the superior solution method. The overall performance accuracy of the proposed model is measured using four samples from a numerical example with randomly generated data based on the objective function coefficients. The results indicate the presence of a conflict among the three objective functions. Consequently, decision-makers should consider sacrificing some profitability to enhance environmental protection and improve reliability. In terms of three criteria, run time, diversification metric, and general distance, the NNC method is given priority over the AEC method. Even when the criteria are given equal weight, the superiority of the NNC method remains unchanged. The application of the proposed model across different industries represents a significant research direction for future research.
Control and Optimization
Ali Akbar Sohrabi; Reza Ghanbari; Khatere Ghorbani-Moghadam
Abstract
Project portfolio selection is a critical challenge for many organizations as they often face budget constraints that limit their ability to support all available projects. To address this issue, organizations seek to select a feasible subset of projects that maximizes utility. ...
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Project portfolio selection is a critical challenge for many organizations as they often face budget constraints that limit their ability to support all available projects. To address this issue, organizations seek to select a feasible subset of projects that maximizes utility. While several models for project portfolio selection based on multiple criteria have been proposed, they are typically NP-hard problems. In this study, we propose an efficient Variable Neighborhood Search (VNS) algorithm to solve these problems. Our algorithm includes a formula for computing the difference value of the objective function, which enhances its accuracy and ensures that selected projects meet desired criteria. We demonstrate the effectiveness of our algorithm through rigorous testing and comparison with a genetic algorithm (GA) and CPLEX. The results of the Wilcoxon non-parametric test confirm that our algorithm outperforms both GA and CPLEX in terms of speed and accuracy. Moreover, the variance of the relative error of our algorithm is less than that of GA.
Control and Optimization
Zeinab Barary; AllahBakhsh Yazdani Cherati; Somayeh Nemati
Abstract
This paper proposes and analyzes an applicable approach for numerically computing the solution of fractional optimal control-affine problems. The fractional derivative in the problem is considered in the sense of Caputo. The approach is based on a fractional-order hybrid of block-pulse functions and ...
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This paper proposes and analyzes an applicable approach for numerically computing the solution of fractional optimal control-affine problems. The fractional derivative in the problem is considered in the sense of Caputo. The approach is based on a fractional-order hybrid of block-pulse functions and Jacobi polynomials. First, the corresponding Riemann-Liouville fractional integral operator of the introduced basis functions is calculated. Then, an approximation of the fractional derivative of the unknown state function is obtained by considering an approximation in terms of these basis functions. Next, using the dynamical system and applying the fractional integral operator, an approximation of the unknown control function is obtained based on the given approximations of the state function and its derivatives. Subsequently, all the given approximations are substituted into the performance index. Finally, the optimality conditions transform the problem into a system of algebraic equations. An error upper bound of the approximation of a function based on the fractional hybrid functions is provided. The method is applied to several numerical examples, and the experimental results confirm the efficiency and capability of the method. Furthermore, they demonstrate a good agreement between the approximate and exact solutions.
Control and Optimization
Farid Pourofoghi; Davood Darvishi Salokolaei
Abstract
Fractional programming is a significant nonlinear planning tool within operation research. It finds applications in diverse domains such as resource allocation, transportation, production programming, performance evaluation, and finance. In ...
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Fractional programming is a significant nonlinear planning tool within operation research. It finds applications in diverse domains such as resource allocation, transportation, production programming, performance evaluation, and finance. In practical scenarios, uncertainties often make it challenging to determine precise coefficients for mathematical models. Consequently, utilizing indefinite coefficients instead of definite ones is recommended in such cases. Grey systems theory, along with probability theory, randomness, fuzzy logic, and rough sets, is an approach that addresses uncertainty. In this study, we address the problem of linear fractional programming with grey coefficients in the objective function. To tackle this problem, a novel approach based on the variable change technique proposed by Charnes and Cooper, along with the convex combination of intervals, is employed. The article presents an algorithm that determines the solution to the grey fractional programming problem using grey numbers, thus capturing the uncertainty inherent in the objective function. To demonstrate the effectiveness of the proposed method, an example is solved using the suggested approach. The result is compared with solutions obtained using the whitening method, employing Hu and Wong's technique and the Center and Greyness Degree Ranking method. The comparison confirms the superiority of the proposed method over the whitening method, thus suggesting adopting the grey system approach in such situations.
Control and Optimization
Hanifa Mosawi; Mostafa Tavakolli; Khatere Ghorbani-Moghadam
Abstract
Graph coloring is a crucial area of research in graph theory, with numerous algorithms proposed for various types of graph coloring, particularly graph p-distance coloring. In this study, we employ a recently introduced graph coloring algorithm to develop a hybrid algorithm approximating the chromatic ...
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Graph coloring is a crucial area of research in graph theory, with numerous algorithms proposed for various types of graph coloring, particularly graph p-distance coloring. In this study, we employ a recently introduced graph coloring algorithm to develop a hybrid algorithm approximating the chromatic number p-distance, where $p$ represents a positive integer number. We apply our algorithm to molecular graphs as practical applications of our findings.
Control and Optimization
Fahimeh Akhavan Ghassabzade; Mina Bagherpoorfard
Abstract
This paper aims to demonstrate the flexibility of mathematical models in analyzing carbon dioxide emissions and account for memory effects. The use of real data amplifies the importance of this study. This research focuses on developing a mathematical model utilizing fractional-order ...
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This paper aims to demonstrate the flexibility of mathematical models in analyzing carbon dioxide emissions and account for memory effects. The use of real data amplifies the importance of this study. This research focuses on developing a mathematical model utilizing fractional-order differential equations to represent carbon dioxide emissions stemming from the energy sector. By comparing simulation results with real-world data, it is determined that the fractional model exhibits superior accuracy when contrasted with the classical model. Additionally, an optimal control strategy is proposed to minimize the levels of carbon dioxide, CO2, and associated implementation costs. The fractional optimal control problem is addressed through the utilization of an iterative algorithm, and the effectiveness of the model is verified by presenting comparative results.
Control and Optimization
Ali Asghar Hojatifard; Nader Kanzi; Shahriar Farahmand Rad
Abstract
This paper aims to establish first-order necessary optimality conditions for non-smooth multi-objective generalized semi-infinite programming problems. These problems involve inequality constraints whose index set depends on the decision vector, and all emerging functions are assumed ...
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This paper aims to establish first-order necessary optimality conditions for non-smooth multi-objective generalized semi-infinite programming problems. These problems involve inequality constraints whose index set depends on the decision vector, and all emerging functions are assumed to be locally Lipschitz. We introduce a new constraint qualification for these problems. Building upon this qualification, we derive an upper estimate for the Clarke sub-differential of the value function of the problem. Furthermore, we demonstrate the necessary optimality conditions for properly efficient solutions to the problem.
Control and Optimization
Mohamad Reza Ramezani-al; Samira Sabeti
Abstract
Guaranteed cost control (GCC) is an impressive method of controlling nonlinear systems, incredibly uncertain switched systems. Most of the recent studies of GCC on uncertain switched linear systems have been concerned with asymptotic stability analysis. In this paper, ...
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Guaranteed cost control (GCC) is an impressive method of controlling nonlinear systems, incredibly uncertain switched systems. Most of the recent studies of GCC on uncertain switched linear systems have been concerned with asymptotic stability analysis. In this paper, a new robust switching law for time-delay uncertain switched linear systems is designed. First, the switching law is designed, and second, a state-feedback controller based on Lyapunov-Krasovskii Functional (LKF) is designed. Also, using Linear Matrix Inequality (LMI) particular condition for the existence of a solution of obtained switching law and controller is achieved. Consequently, in the presented theorems, the exponential stability of the overall system under switching law and controller is analyzed. Finally, theoretical results are verified via presenting an example.
Control and Optimization
Jahangir Alizadeh; Hamid Khaloozadeh
Abstract
In the present study, a novel methodology is developed to enlarge the Region of Attraction (ROA) at the point of equilibrium of an input-affine nonlinear control system. Enlarging the ROA for non-polynomial dynamical systems is developed by designing a nonlinear state feedback controller ...
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In the present study, a novel methodology is developed to enlarge the Region of Attraction (ROA) at the point of equilibrium of an input-affine nonlinear control system. Enlarging the ROA for non-polynomial dynamical systems is developed by designing a nonlinear state feedback controller through the State-Dependent Riccati Equation (SDRE). Consequently, its process is defined in the form of Sum-of-Squares (SOS) optimization problem with control and non-control constraints. Of note, the proposed technique is effective in estimating the ROA for a nonlinear system functioning on polynomial or non-polynomial dynamics. In the present study, the application of the proposed scheme are shown by numerical simulations.
