Abstract This work offers a systematic technique to achieve reduced order synchronization (ROS) between two different order general classes of chaotic systems in a master-slave configuration. In this study, the dynamics of the master and slave systems are assumed to follow a special class of strict-feedback form, namely, the generalized triangular feedback form. The main objective is to design a suitable scalar controller using a Lyapunov theory-based back-stepping approach such that the mth order slave system gets synchronized with the nth order master system. Due to the difference in the order of the systems (m<n and m=(n−1)), it is only possible to achieve the synchronization between m numbers of states of the slave systems with (n−1) numbers of states of the master system, respectively. We cannot conclude on the stability of the nth state of the master system as there is no counterpart (state) available in the slave system to be synchronized with. Adding an additional (m+1)th state dynamics along with a nonlinear feedback controller (U1) to the slave system ensures that the nth state of the master system is synchronized with the (m+1)th state dynamics of the slave system. With the suggested technique proposed in this article, complete state-to-state synchronization can be achieved with only two controllers. The analytical results are successfully validated through numerical simulations presented in the end.
{"title":"Reduced Order Synchronization of Two Non-Identical Special Class of Strict Feedback Systems via Back-Stepping Control Technique","authors":"Riddhi Bora, Bharat Bhushan Sharma","doi":"10.1115/1.4063721","DOIUrl":"https://doi.org/10.1115/1.4063721","url":null,"abstract":"Abstract This work offers a systematic technique to achieve reduced order synchronization (ROS) between two different order general classes of chaotic systems in a master-slave configuration. In this study, the dynamics of the master and slave systems are assumed to follow a special class of strict-feedback form, namely, the generalized triangular feedback form. The main objective is to design a suitable scalar controller using a Lyapunov theory-based back-stepping approach such that the mth order slave system gets synchronized with the nth order master system. Due to the difference in the order of the systems (m&lt;n and m=(n−1)), it is only possible to achieve the synchronization between m numbers of states of the slave systems with (n−1) numbers of states of the master system, respectively. We cannot conclude on the stability of the nth state of the master system as there is no counterpart (state) available in the slave system to be synchronized with. Adding an additional (m+1)th state dynamics along with a nonlinear feedback controller (U1) to the slave system ensures that the nth state of the master system is synchronized with the (m+1)th state dynamics of the slave system. With the suggested technique proposed in this article, complete state-to-state synchronization can be achieved with only two controllers. The analytical results are successfully validated through numerical simulations presented in the end.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"75 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135088354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Despite the unconstrained thermal expansion is assumed stress-free, the conventional FE approach requires formulating elastic forces, and this in turn leads to elastic stresses. A displacement-based formulation, on the other hand, can be used to address this limitation by converting the thermal energy to kinetic energy instead of strain energy. The fundamental differences between the strain- and kinetic-energy approaches are discussed. It is shown that the unconstrained thermal expansion predicted using the kinetic-energy approach is independent of the continuum constitutive model, and consequently, such a formulation can be used for both solids and fluids. The displacement (kinetic) and strain (stress) formulations are discussed to shed light on the mechanism of thermal expansion at the macroscopic level. The thermal-expansion displacement formulation (TEDF) and position-gradient multiplicative decomposition into thermal and mechanical parts are used to compute the thermal stresses due to boundary and motion constraints (BMC). TEDF implementation issues are discussed and constant matrices evaluated at a preprocessing stage after applying sweeping matrix technique to eliminate rigid-body thermal-displacement translational modes are identified. Furthermore, the softening effect due to the constitutive-model dependence on the temperature is investigated at high temperatures. Numerical results are presented to show fundamental differences between the TEDF approach that converts heat energy to kinetic energy and conventional FE approach that converts heat energy to strain energy that produces elastic stresses.
{"title":"Kinetic- and Strain-Energy Approaches in the Thermal Analysis of Constrained Mechanical Systems: A Comparative Study","authors":"Moataz Abdalla, Ahmed A. Shabana","doi":"10.1115/1.4063725","DOIUrl":"https://doi.org/10.1115/1.4063725","url":null,"abstract":"Abstract Despite the unconstrained thermal expansion is assumed stress-free, the conventional FE approach requires formulating elastic forces, and this in turn leads to elastic stresses. A displacement-based formulation, on the other hand, can be used to address this limitation by converting the thermal energy to kinetic energy instead of strain energy. The fundamental differences between the strain- and kinetic-energy approaches are discussed. It is shown that the unconstrained thermal expansion predicted using the kinetic-energy approach is independent of the continuum constitutive model, and consequently, such a formulation can be used for both solids and fluids. The displacement (kinetic) and strain (stress) formulations are discussed to shed light on the mechanism of thermal expansion at the macroscopic level. The thermal-expansion displacement formulation (TEDF) and position-gradient multiplicative decomposition into thermal and mechanical parts are used to compute the thermal stresses due to boundary and motion constraints (BMC). TEDF implementation issues are discussed and constant matrices evaluated at a preprocessing stage after applying sweeping matrix technique to eliminate rigid-body thermal-displacement translational modes are identified. Furthermore, the softening effect due to the constitutive-model dependence on the temperature is investigated at high temperatures. Numerical results are presented to show fundamental differences between the TEDF approach that converts heat energy to kinetic energy and conventional FE approach that converts heat energy to strain energy that produces elastic stresses.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"75 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135088353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The generalized-αscheme has become the approach of choice for the time integration of the equations of motion of multibody systems. Despite its simplicity, this scheme presents drawbacks: the time step size cannot be changed easily, making it difficult to implement time adaptivity, and the solution of periodic problems cannot be found easily. This paper explores an alternative approach based on the finite element method in time. The basic principles underpinning the approach are presented and both time-continuous and time-discontinuous approaches are investigated. Two types of Galerkin schemes will be presented here: the time-continuous and the time-discontinuous schemes. In the former, the displacement field is continuous across inter-element boundaries, whereas discontinuities or “jumps” are allowed across inter-element boundaries for the latter. Simple problems are treated to identify the best schemes. Families of schemes of various accuracy are presented. The first family, based on time-continuous elements, features schemes that do not present numerical dissipation. Asymptotic annihilation is achieved by the time-discontinuous elements that form the second family. The problem of kinematic constraints is treated within the framework of the finite element method in time. Special emphasis is devoted to the satisfaction of the kinematic constraints and their time derivative within a time element.
{"title":"The Finite Element Method in Time For Multibody Dynamics","authors":"Olivier Bauchau","doi":"10.1115/1.4063953","DOIUrl":"https://doi.org/10.1115/1.4063953","url":null,"abstract":"Abstract The generalized-αscheme has become the approach of choice for the time integration of the equations of motion of multibody systems. Despite its simplicity, this scheme presents drawbacks: the time step size cannot be changed easily, making it difficult to implement time adaptivity, and the solution of periodic problems cannot be found easily. This paper explores an alternative approach based on the finite element method in time. The basic principles underpinning the approach are presented and both time-continuous and time-discontinuous approaches are investigated. Two types of Galerkin schemes will be presented here: the time-continuous and the time-discontinuous schemes. In the former, the displacement field is continuous across inter-element boundaries, whereas discontinuities or “jumps” are allowed across inter-element boundaries for the latter. Simple problems are treated to identify the best schemes. Families of schemes of various accuracy are presented. The first family, based on time-continuous elements, features schemes that do not present numerical dissipation. Asymptotic annihilation is achieved by the time-discontinuous elements that form the second family. The problem of kinematic constraints is treated within the framework of the finite element method in time. Special emphasis is devoted to the satisfaction of the kinematic constraints and their time derivative within a time element.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"19 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135933837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Rene Neurauter, Stefan Holzinger, Michael Neuhauser, Jan-Thomas Fischer, Johannes Gerstmayr
Abstract Motion reconstruction and navigation require accurate orientation estimation. Modern orientation estimation methods utilize filtering algorithms, such as the Kalman filter or Madgwick's algorithm. However, these methods do not address potential sensor saturation, which may occur within short time periods in highly dynamic applications, such as, e.g., particle tracking in snow avalanches, leading to inaccurate orientation estimates. In this paper, we present two algorithms for orientation estimation combining magnetometer and partially saturated gyrometer readings. One algorithm incorporates magnetic field vector observations and the full nonlinearity of the exponential map. The other, computationally more efficient algorithm builds on a linearization of the exponential map and is solved analytically. Both algorithms are then applied to measurement data from four different experiments, with two of them being snow avalanche experiments. Moreover, Madgwick's filtering algorithm was used to validate the proposed algorithms. The two algorithms improved the orientation estimation significantly in all experiments. Hence, the proposed algorithms can improve the performance of existing sensor fusion algorithms significantly.
{"title":"Motion Reconstruction of Fast-rotating Rigid Bodies","authors":"Rene Neurauter, Stefan Holzinger, Michael Neuhauser, Jan-Thomas Fischer, Johannes Gerstmayr","doi":"10.1115/1.4063952","DOIUrl":"https://doi.org/10.1115/1.4063952","url":null,"abstract":"Abstract Motion reconstruction and navigation require accurate orientation estimation. Modern orientation estimation methods utilize filtering algorithms, such as the Kalman filter or Madgwick's algorithm. However, these methods do not address potential sensor saturation, which may occur within short time periods in highly dynamic applications, such as, e.g., particle tracking in snow avalanches, leading to inaccurate orientation estimates. In this paper, we present two algorithms for orientation estimation combining magnetometer and partially saturated gyrometer readings. One algorithm incorporates magnetic field vector observations and the full nonlinearity of the exponential map. The other, computationally more efficient algorithm builds on a linearization of the exponential map and is solved analytically. Both algorithms are then applied to measurement data from four different experiments, with two of them being snow avalanche experiments. Moreover, Madgwick's filtering algorithm was used to validate the proposed algorithms. The two algorithms improved the orientation estimation significantly in all experiments. Hence, the proposed algorithms can improve the performance of existing sensor fusion algorithms significantly.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"2 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135934324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The aim of this article is to propose the Lerch operational matrix method to solve a stochastic fractional differential equation. In this approach, the Lerch polynomials have been used as a basis function. Then, the product operational matrix, integral operational matrix, stochastic operational matrix, and operational matrix of fractional integral based on the Lerch polynomials have been constructed. The main characteristic of this method is to reduce the stochastic fractional differential equation into a system of algebraic equations by using derived operational matrices and suitable collocation points. Moreover, the convergence and error analysis of the presented method is also discussed in detail. Additionally, the applicability of the proposed technique is also demonstrated by solving some examples. To confirm the accuracy and effectiveness of the suggested technique, a comparison between the results produced by the proposed method and those obtained by other methods has been provided.
{"title":"Numerical Treatment For The Solution Of Stochastic Fractional Differential Equation Using Lerch Operational Matrix Method","authors":"P. K. Singh, Santanu Saha Ray","doi":"10.1115/1.4063885","DOIUrl":"https://doi.org/10.1115/1.4063885","url":null,"abstract":"Abstract The aim of this article is to propose the Lerch operational matrix method to solve a stochastic fractional differential equation. In this approach, the Lerch polynomials have been used as a basis function. Then, the product operational matrix, integral operational matrix, stochastic operational matrix, and operational matrix of fractional integral based on the Lerch polynomials have been constructed. The main characteristic of this method is to reduce the stochastic fractional differential equation into a system of algebraic equations by using derived operational matrices and suitable collocation points. Moreover, the convergence and error analysis of the presented method is also discussed in detail. Additionally, the applicability of the proposed technique is also demonstrated by solving some examples. To confirm the accuracy and effectiveness of the suggested technique, a comparison between the results produced by the proposed method and those obtained by other methods has been provided.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"309 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136317941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper presents a new method of controlling the end effector position and orientation of a flexible planar three-link mechanism. The coupled dynamic model was formulated using a method based on the Udwadia–Kalaba equations of motion for constrained systems. Lyapunov's theory was used to develop a nonlinear control law using piezoelectric actuators and the unconstrained link dynamic models. Numerical simulation was used to demonstrate the system tracking performance of the end effector using a reduced order controller applied to a higher order truth dynamic model.
{"title":"Dynamic Modeling and Control of a Flexible Planar Three Link Mechanism Using Joint and Piezoelectric Actuators","authors":"Daniel Hill","doi":"10.1115/1.4063563","DOIUrl":"https://doi.org/10.1115/1.4063563","url":null,"abstract":"Abstract This paper presents a new method of controlling the end effector position and orientation of a flexible planar three-link mechanism. The coupled dynamic model was formulated using a method based on the Udwadia–Kalaba equations of motion for constrained systems. Lyapunov's theory was used to develop a nonlinear control law using piezoelectric actuators and the unconstrained link dynamic models. Numerical simulation was used to demonstrate the system tracking performance of the end effector using a reduced order controller applied to a higher order truth dynamic model.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135824013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Two predator-prey model describing the guava borers and natural enemies are studied in this paper. Positivity, existence, and uniqueness of the solution, global and local stability analysis of the fixed points of the first model based on the Caputo fractional operator are studied. By adding piecewise constant functions to the second model including conformable fractional operator allows us to transition discrete dynamical system via discretization process. Applying Schur-Cohn criterion to the discrete system, we hold some regions where the equilibrium points in the discretized model are local asymptotically stable. We prove that discretized model displays supercritical Neimark–Sacker bifurcation at the equilibrium point. Theoretical and numerical results show that the discretized system demonstrates richer dynamic properties such as quasi-periodic solutions, bifurcation, and chaotic dynamics than the fractional order model with Caputo operator. All theoretical results are interpreted biologically and the optimum time interval for the harvesting of the guava fruit is given.
{"title":"Caputo and Conformable Fractional Order Guava Model for Biological Pest Control: Discretization, Stability and Bifurcation","authors":"Senol Kartal","doi":"10.1115/1.4063555","DOIUrl":"https://doi.org/10.1115/1.4063555","url":null,"abstract":"Abstract Two predator-prey model describing the guava borers and natural enemies are studied in this paper. Positivity, existence, and uniqueness of the solution, global and local stability analysis of the fixed points of the first model based on the Caputo fractional operator are studied. By adding piecewise constant functions to the second model including conformable fractional operator allows us to transition discrete dynamical system via discretization process. Applying Schur-Cohn criterion to the discrete system, we hold some regions where the equilibrium points in the discretized model are local asymptotically stable. We prove that discretized model displays supercritical Neimark–Sacker bifurcation at the equilibrium point. Theoretical and numerical results show that the discretized system demonstrates richer dynamic properties such as quasi-periodic solutions, bifurcation, and chaotic dynamics than the fractional order model with Caputo operator. All theoretical results are interpreted biologically and the optimum time interval for the harvesting of the guava fruit is given.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135824174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Understanding the effects of panic on crowd dynamics in emergency situations has long been considered necessary for pedestrian evacuation control. In the case of disasters, stampedes caused by panic behaviors occur with high possibility, and pedestrians are crushed or trampled, leading to enormous casualties. To eliminate the computational errors accumulated in the traditional macromodel, a macro-microconversion model based on the SF (social force) model and the AR (Aw-Rascle) model is proposed in this paper. The purpose is to use the crowd parameters of the microscopic model as the input part of the macroscopic model and to combine the advantages of the two models to ensure accuracy and improve calculation performance. The concept of the “pressure term” is defined to measure the panic level of the crowd. In addition, a flowchart of the numerical simulation is designed based on the road network conditions at the trampling site. To validate the conversion model, a numerical simulation is conducted in a case study of the Mecca Hajj stampede in 2015. The simulation results display the whole process of crowd marching and meeting with the dynamic variations of the “pressure term.” The simulation results are compared with the traditional simulation results based on a Gaussian distribution, which verifies that the simulation results obtained by the proposed method are closer to the real situation. Moreover, in this study, a new micromacro transformation method for crowd evaluation dynamics, which can enhance computing speed and execution efficiency, is provided.
{"title":"Panic-Pressure Conversion Model From Microscopic Pedestrian Movement to Macroscopic Crowd Flow","authors":"Wenjie Zhu, Rongyong Zhao, Hao Zhang, Cuiling Li, Ping Jia, Yunlong Ma, Dong Wang, Miyuan Li","doi":"10.1115/1.4063505","DOIUrl":"https://doi.org/10.1115/1.4063505","url":null,"abstract":"Abstract Understanding the effects of panic on crowd dynamics in emergency situations has long been considered necessary for pedestrian evacuation control. In the case of disasters, stampedes caused by panic behaviors occur with high possibility, and pedestrians are crushed or trampled, leading to enormous casualties. To eliminate the computational errors accumulated in the traditional macromodel, a macro-microconversion model based on the SF (social force) model and the AR (Aw-Rascle) model is proposed in this paper. The purpose is to use the crowd parameters of the microscopic model as the input part of the macroscopic model and to combine the advantages of the two models to ensure accuracy and improve calculation performance. The concept of the “pressure term” is defined to measure the panic level of the crowd. In addition, a flowchart of the numerical simulation is designed based on the road network conditions at the trampling site. To validate the conversion model, a numerical simulation is conducted in a case study of the Mecca Hajj stampede in 2015. The simulation results display the whole process of crowd marching and meeting with the dynamic variations of the “pressure term.” The simulation results are compared with the traditional simulation results based on a Gaussian distribution, which verifies that the simulation results obtained by the proposed method are closer to the real situation. Moreover, in this study, a new micromacro transformation method for crowd evaluation dynamics, which can enhance computing speed and execution efficiency, is provided.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135824175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A second-order numerical scheme is proposed to solve the generalized time-fractional Burgers' equation. Time-fractional derivative is considered in the Caputo sense. First, the quasilinearization process is used to linearize the time-fractional Burgers'; equation, which gives a sequence of linear partial differential equations (PDEs). The Crank-Nicolson scheme is used to discretize the sequence of PDEs in the temporal direction, followed by the central difference formulae for both the first and second-order spatial derivatives. The established error bounds (in the $L^2-$norm) obtained through the meticulous theoretical analysis show that the method is the second-order convergent in both space and time. The technique is also shown to be conditionally stable. Some numerical experiments are presented to confirm the theoretical results.
{"title":"A Second-order Scheme for the Generalized Time-fractional Burgers' Equation","authors":"Reetika Chawla, Devendra Kumar, Satpal Singh","doi":"10.1115/1.4063792","DOIUrl":"https://doi.org/10.1115/1.4063792","url":null,"abstract":"Abstract A second-order numerical scheme is proposed to solve the generalized time-fractional Burgers' equation. Time-fractional derivative is considered in the Caputo sense. First, the quasilinearization process is used to linearize the time-fractional Burgers'; equation, which gives a sequence of linear partial differential equations (PDEs). The Crank-Nicolson scheme is used to discretize the sequence of PDEs in the temporal direction, followed by the central difference formulae for both the first and second-order spatial derivatives. The established error bounds (in the $L^2-$norm) obtained through the meticulous theoretical analysis show that the method is the second-order convergent in both space and time. The technique is also shown to be conditionally stable. Some numerical experiments are presented to confirm the theoretical results.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"184 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136112406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Dynamical systems that have a chaotic underlying structure have a sensitive dependency on the initial conditions and the values of their parameters. In this piece of work, a straightforward method for solving the synchronization issue in master-slave arrangement for a category of chaotic or hyperchaotic systems, in which perturbations are present in the parameters of the response system, is discussed. The desired control signal is bounded by the initial state when the controller is activated. There is just one control input that is used, and it is derived from Lyapunov&#39;s concept of stability. In general, it is tricky to synchronize hyperchaotic or chaotic systems with single controller, and the work turns out to be significantly more complex when the parameters of the slave system are perturbed. The feedback controller using single input that has been constructed makes certain that the state variables of the response system are in synchronization with the state variables that correspond to them in the drive system. In order to attain the desired level of synchronization, the required conditions that must be satisfied to do so have been identified utilizing Lyapunov's stability analysis in a simple manner. In addition, numerical illustrations have been provided in order to support and confirm the theoretical findings of the paper.
{"title":"Novel Single Bounded Input Control Synchronization Criterion for a Category of Hyperchaotic & Chaotic Systems in Presence of Uncertainties","authors":"None Pallav, Himesh Handa, Bharat Bhushan Sharma","doi":"10.1115/1.4063723","DOIUrl":"https://doi.org/10.1115/1.4063723","url":null,"abstract":"Abstract Dynamical systems that have a chaotic underlying structure have a sensitive dependency on the initial conditions and the values of their parameters. In this piece of work, a straightforward method for solving the synchronization issue in master-slave arrangement for a category of chaotic or hyperchaotic systems, in which perturbations are present in the parameters of the response system, is discussed. The desired control signal is bounded by the initial state when the controller is activated. There is just one control input that is used, and it is derived from Lyapunov&amp;#39;s concept of stability. In general, it is tricky to synchronize hyperchaotic or chaotic systems with single controller, and the work turns out to be significantly more complex when the parameters of the slave system are perturbed. The feedback controller using single input that has been constructed makes certain that the state variables of the response system are in synchronization with the state variables that correspond to them in the drive system. In order to attain the desired level of synchronization, the required conditions that must be satisfied to do so have been identified utilizing Lyapunov's stability analysis in a simple manner. In addition, numerical illustrations have been provided in order to support and confirm the theoretical findings of the paper.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135855426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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