In this paper,we study in a constructive way the stabilization problem of fractional bilinear systems with multiple inputs.Using the quadratic Lyapunov functions and some additional hypotheses on the unit sphere,we co...In this paper,we study in a constructive way the stabilization problem of fractional bilinear systems with multiple inputs.Using the quadratic Lyapunov functions and some additional hypotheses on the unit sphere,we construct stabilizing feedback laws for the considered fractional bilinear system.A numerical example is given to illustrate the efficiency of the obtained result.展开更多
This paper studies the parameter estimation problems of the nonlinear systems described by the bilinear state space models in the presence of disturbances.A bilinear state observer is designed for deriving identificat...This paper studies the parameter estimation problems of the nonlinear systems described by the bilinear state space models in the presence of disturbances.A bilinear state observer is designed for deriving identification algorithms to estimate the state variables using the input-output data.Based on the bilinear state observer,a novel gradient iterative algorithm is derived for estimating the parameters of the bilinear systems by means of the continuous mixed p-norm cost function.The gain at each iterative step adapts to the data quality so that the algorithm has good robustness to the noise disturbance.Furthermore,to improve the performance of the proposed algorithm,a dynamicmoving window is designed which can update the dynamical data by removing the oldest data and adding the newestmeasurement data.A numerical example of identification of bilinear systems is presented to validate the theoretical analysis.展开更多
This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems(DFBS).Based on the parallel distributed compensation(PDC) approach,the sufficient co...This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems(DFBS).Based on the parallel distributed compensation(PDC) approach,the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the cost function value is no more than a certain upper bound in the presence of the additive controller gain perturbations.The non-fragile guaranteed cost controller can be obtained by solving a set of bilinear matrix inequalities(BMIs).The Van de Vusse model is utilized to demonstrate the validity and effectiveness of the proposed approach.展开更多
The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system (DFBS) is presented. Based on parallel distribution compensation method, some sufficient conditions are de...The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system (DFBS) is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality (LMI) so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.展开更多
A bilinear fault detection observer is proposed for a class of continuous time singular bilinear systems subject to unknown input disturbance and fault. By singular value decomposition on the original system, a biline...A bilinear fault detection observer is proposed for a class of continuous time singular bilinear systems subject to unknown input disturbance and fault. By singular value decomposition on the original system, a bilinear fault detection observer is proposed for the decomposed system via an algebraic Riccati equation, and the domain of attraction of the state estimation error is estimated. A design procedure is presented to determine the fault detection threshold. A model of flexible joint robot is used to demonstrate the effectiveness of the proposed method.展开更多
A bilinear observer is proposed for a class of singular bilinear system subject to unknown input disturbance. Based on singular value decomposition technique, the existence of the solution to the decomposed system is ...A bilinear observer is proposed for a class of singular bilinear system subject to unknown input disturbance. Based on singular value decomposition technique, the existence of the solution to the decomposed system is presented. Then a bilinear observer is proposed for the decomposed system based on an algebraic Riccati equation, and the domain of attraction of the state estimation error is derived. Finally, a detailed design procedure is given to design a bilinear observer for a model of flexible joint robot, which demonstrates the effectiveness of the proposed method.展开更多
In this paper, switched controllers are designed for a class of nonlinear discrete singular systems and a class of discrete singular bilinear systems. An invariant principle is presented for such switched nonlinear si...In this paper, switched controllers are designed for a class of nonlinear discrete singular systems and a class of discrete singular bilinear systems. An invariant principle is presented for such switched nonlinear singular systems. The invariant principle and the switched controllers are used to globally stabilize a class of singular bilinear systems that are not open-loop stable.展开更多
Bilinear singular systems can be used in the investigation of different types of engineering systems.In the past decade,considerable attention has been paid to analyzing and synthesizing singular bilinear systems.Thei...Bilinear singular systems can be used in the investigation of different types of engineering systems.In the past decade,considerable attention has been paid to analyzing and synthesizing singular bilinear systems.Their importance lies in their real world application such as economic,ecological,and socioeconomic processes.They are also applied in several biological processes,such as population dynamics of biological species,water balance,temperature regulation in the human body,carbon dioxide control in lungs,blood pressure,immune system,cardiac regulation,etc.Bilinear singular systems naturally represent different physical processes such as the fundamental law of mass action,the DC motor,the induction motor drives,the mechanical brake systems,aerial combat between two aircraft,the missile intercept problem,modeling and control of small furnaces and hydraulic rotary multimotor systems.The current research work discusses the Legendre Neural Network’s implementation to evaluate time-varying singular bilinear systems for finding the exact solution.The results were obtained from two methods namely the RK-Butcher algorithm and the Runge Kutta Arithmetic Mean(RKAM)method.Compared with the results attained from Legendre Neural Network Method for time-varying singular bilinear systems,the output proved to be accurate.As such,this research article established that the proposed Legendre Neural Network could be easily implemented in MATLAB.One can obtain the solution for any length of time from this method in time-varying singular bilinear systems.展开更多
A new multi-step adaptive predictive control algorithm for a class of bilinear systems is presented. The structure of the bilinear system is converted into a simple linear model by using nonlinear support vector machi...A new multi-step adaptive predictive control algorithm for a class of bilinear systems is presented. The structure of the bilinear system is converted into a simple linear model by using nonlinear support vector machine (SVM) dynamic approximation with analytical control law derived. The method does not need on-line parameters estimation because the system’s internal model has been transformed into an off-line global model. Compared with other traditional methods, this control law reduces on-line parameter estimating burden. In addition, its overall linear behavior treating method allows an analytical control law available and avoids on-line nonlinear optimization. Simulation results are presented in the article to illustrate the efficiency of the method.展开更多
This paper considers the optimal control problem for time-delay bilinear systems affected by sinusoidal disturbances with known frequency and measurable amplitude and phase. Firstly, using the differential homeomorphi...This paper considers the optimal control problem for time-delay bilinear systems affected by sinusoidal disturbances with known frequency and measurable amplitude and phase. Firstly, using the differential homeomorphism, a time-delay bilinear system affected by sinusoidal disturbances is changed to a time-delay pseudo linear system through the coordinate transformation. Then the system with time-delay in control variable is transformed to a linear controllable system without delay using model transformation. At last based on the theory of linear quadratic optimal control, an optimal control law which is used to eliminate the influence of the disturbances is derived from a Riccati equation and Matrix equations. The simulation results show the effectiveness of the method.展开更多
This paper considers the optimal control problem for the bilinear system based on state feedback. Based on the concept of relative order of the output with respect to the input, first we change a bilinear system to a ...This paper considers the optimal control problem for the bilinear system based on state feedback. Based on the concept of relative order of the output with respect to the input, first we change a bilinear system to a pseudo linear system model through the coordinate transformation. Then based on the theory of linear quadratic optimal control, the optimal controller is designed by solving the Riccati equation and introducing state feedback with state prediction. At last, the simulation results in CSTR Chemical reactor show the effectiveness of the method.展开更多
We study dark localized waves within a nonlinear system based on the Boussinesq approximation,describing the dynamics of shallow water waves.Employing symbolic calculus,we apply the Hirota bilinear method to transform...We study dark localized waves within a nonlinear system based on the Boussinesq approximation,describing the dynamics of shallow water waves.Employing symbolic calculus,we apply the Hirota bilinear method to transform an extended Boussinesq system into a bilinear form,and then use the multiple rogue wave method to obtain its dark rational solutions.Exploring the first-and second-order dark solutions,we examine the conditions under which these localized solutions exist and their spatiotemporal distributions.Through the selection of various parameters and by utilizing different visualization techniques(intensity distributions and contour plots),we explore the dynamical properties of dark solutions found:in particular,the first-and second-order dark rogue waves.We also explore the methods of their control.The findings presented here not only deepen the understanding of physical phenomena described by the(1+1)-dimensional Boussinesq equation,but also expand avenues for further research.Our method can be extended to other nonlinear systems,to conceivably obtain higher-order dark rogue waves.展开更多
The estimation of residual displacements in a structure due to an anticipated earthquake event has increasingly become an important component of performance-based earthquake engineering because controlling these displ...The estimation of residual displacements in a structure due to an anticipated earthquake event has increasingly become an important component of performance-based earthquake engineering because controlling these displacements plays an important role in ensuring cost-feasible or cost-effective repairs in a damaged structure after the event.An attempt is made in this study to obtain statistical estimates of constant-ductility residual displacement spectra for bilinear and pinching oscillators with 5%initial damping,directly in terms of easily available seismological,site,and model parameters.None of the available models for the bilinear and pinching oscillators are useful when design spectra for a seismic hazard at a site are not available.The statistical estimates of a residual displacement spectrum are proposed in terms of earthquake magnitude,epicentral distance,site geology parameter,and three model parameters for a given set of ductility demand and a hysteretic energy capacity coefficient in the case of bilinear and pinching models,as well as for a given set of pinching parameters for displacement and strength at the breakpoint in the case of pinching model alone.The proposed scaling model is applicable to horizontal ground motions in the western U.S.for earthquake magnitudes less than 7 or epicentral distances greater than 20 km.展开更多
Controllable canonical forms play important roles in the analysis and design of control systems.In this paper,a fundamental class of discrete-time bilinear systems are considered.Such systems are of interest since,on ...Controllable canonical forms play important roles in the analysis and design of control systems.In this paper,a fundamental class of discrete-time bilinear systems are considered.Such systems are of interest since,on one hand,they have the most complete controllability theory.On the other hand,they can be nearly-controllable even if controllability fails.Firstly,controllability of the systems with positive control inputs is studied and necessary and sufficient algebraic criteria for positive-controllability and positive-near-controllability are derived.Then,controllable canonical forms and nearly-controllable canonical forms of the systems are presented,respectively,where the corresponding transformation matrices are also explicitly constructed.Examples are given to demonstrate the effectiveness of the derived controllability criteria and controllable canonical forms.展开更多
This paper is concerned with the output stabilisation for a class of distributed bilinear system evolving in a spatial domain.We give sufficient conditions for strong and weak output stabilisation.Also,the output sta...This paper is concerned with the output stabilisation for a class of distributed bilinear system evolving in a spatial domain.We give sufficient conditions for strong and weak output stabilisation.Also,the output stabilisation is discussed using a minimisation problem.Examples and simulations are given.展开更多
The aim of this paper is to study approximate controllability for bilinear systems in the general case. The existence and uniqueness of solutions to bilinear evolution equations are obtained. The paper shows that the ...The aim of this paper is to study approximate controllability for bilinear systems in the general case. The existence and uniqueness of solutions to bilinear evolution equations are obtained. The paper shows that the approximate controllability of the bilinear control problem is equivalent to the approximate controllability of a discrete problem, using the method developed by Loreti and Siconolfi to approximate the bilinear control problem in an infinite-dimensional Banach space by means of a sequence of discrete problems. Finally, the necessary conditions for the bilinear system to be approximately controllable are stste and proved.展开更多
Under harmonic wave excitation, the dynamic response of a bilinear SDOF system can be expressed by the Hilbert spectrum. The Hilbert spectrum can be formulated by (1) the inter-wave combination mechanism between the s...Under harmonic wave excitation, the dynamic response of a bilinear SDOF system can be expressed by the Hilbert spectrum. The Hilbert spectrum can be formulated by (1) the inter-wave combination mechanism between the steady response and the transient response when the system behaves linearly, or (2) the intra-wave modulation mechanism embedded in one intrinsic mode function (IMF) component when the system behaves nonlinearly. The temporal variation of the instantaneous frequency of the IMF component is consistent with the system nonlinear behavior of yielding and unloading. As a thorough study of this fundamental structural dynamics problem, this article investigates the influence of the amplitude of the harmonic wave excitation on the Hilbert spectrum and the intrinsic oscillatory mode of the dynamic response of a bilinear SDOF system.展开更多
文摘In this paper,we study in a constructive way the stabilization problem of fractional bilinear systems with multiple inputs.Using the quadratic Lyapunov functions and some additional hypotheses on the unit sphere,we construct stabilizing feedback laws for the considered fractional bilinear system.A numerical example is given to illustrate the efficiency of the obtained result.
基金funded by the National Natural Science Foundation of China(No.61773182)the 111 Project(B12018).
文摘This paper studies the parameter estimation problems of the nonlinear systems described by the bilinear state space models in the presence of disturbances.A bilinear state observer is designed for deriving identification algorithms to estimate the state variables using the input-output data.Based on the bilinear state observer,a novel gradient iterative algorithm is derived for estimating the parameters of the bilinear systems by means of the continuous mixed p-norm cost function.The gain at each iterative step adapts to the data quality so that the algorithm has good robustness to the noise disturbance.Furthermore,to improve the performance of the proposed algorithm,a dynamicmoving window is designed which can update the dynamical data by removing the oldest data and adding the newestmeasurement data.A numerical example of identification of bilinear systems is presented to validate the theoretical analysis.
基金supported by the National Natural Science Foundation of China(60374015)
文摘This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems(DFBS).Based on the parallel distributed compensation(PDC) approach,the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the cost function value is no more than a certain upper bound in the presence of the additive controller gain perturbations.The non-fragile guaranteed cost controller can be obtained by solving a set of bilinear matrix inequalities(BMIs).The Van de Vusse model is utilized to demonstrate the validity and effectiveness of the proposed approach.
文摘The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system (DFBS) is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality (LMI) so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.
基金This work was supported in part by National Nature Science Foundation of China (No. 60325311, 60534010, 60572070)the Funds for Creative Research Groups of China (No. 60521003)the Program for Changjiang Scholars and Innovative Research Team in University (No. IRT0421).
文摘A bilinear fault detection observer is proposed for a class of continuous time singular bilinear systems subject to unknown input disturbance and fault. By singular value decomposition on the original system, a bilinear fault detection observer is proposed for the decomposed system via an algebraic Riccati equation, and the domain of attraction of the state estimation error is estimated. A design procedure is presented to determine the fault detection threshold. A model of flexible joint robot is used to demonstrate the effectiveness of the proposed method.
基金This work was supported by the National Natural Science Foundation of China (No.60244017, 60325311).
文摘A bilinear observer is proposed for a class of singular bilinear system subject to unknown input disturbance. Based on singular value decomposition technique, the existence of the solution to the decomposed system is presented. Then a bilinear observer is proposed for the decomposed system based on an algebraic Riccati equation, and the domain of attraction of the state estimation error is derived. Finally, a detailed design procedure is given to design a bilinear observer for a model of flexible joint robot, which demonstrates the effectiveness of the proposed method.
基金This work was supported by the Science Technical Foundation of Liaoning of China (No. 2001401041)
文摘In this paper, switched controllers are designed for a class of nonlinear discrete singular systems and a class of discrete singular bilinear systems. An invariant principle is presented for such switched nonlinear singular systems. The invariant principle and the switched controllers are used to globally stabilize a class of singular bilinear systems that are not open-loop stable.
文摘Bilinear singular systems can be used in the investigation of different types of engineering systems.In the past decade,considerable attention has been paid to analyzing and synthesizing singular bilinear systems.Their importance lies in their real world application such as economic,ecological,and socioeconomic processes.They are also applied in several biological processes,such as population dynamics of biological species,water balance,temperature regulation in the human body,carbon dioxide control in lungs,blood pressure,immune system,cardiac regulation,etc.Bilinear singular systems naturally represent different physical processes such as the fundamental law of mass action,the DC motor,the induction motor drives,the mechanical brake systems,aerial combat between two aircraft,the missile intercept problem,modeling and control of small furnaces and hydraulic rotary multimotor systems.The current research work discusses the Legendre Neural Network’s implementation to evaluate time-varying singular bilinear systems for finding the exact solution.The results were obtained from two methods namely the RK-Butcher algorithm and the Runge Kutta Arithmetic Mean(RKAM)method.Compared with the results attained from Legendre Neural Network Method for time-varying singular bilinear systems,the output proved to be accurate.As such,this research article established that the proposed Legendre Neural Network could be easily implemented in MATLAB.One can obtain the solution for any length of time from this method in time-varying singular bilinear systems.
基金This work was supported in part by the National High Technology Research and Development Program of China (863 Program) (2014A A06A503), the National Natural Science Foundation of China (61422 307, 61473269, 61673361, 61673350), the Scientific Research Starting Foundation for the Returned Overseas Chinese Scholars and Ministry of Education of China, the Youth Innovation Promotion Asso- ciation, Chinese Academy of Sciences, the Youth Top-notch Talent Support Program, the 1000-talent Youth Program, and the Youth Yangtze River Scholarship.
基金Supported by National Natural Science Foundation of China (60704007 60774038) the Key Scientific and Technological Project of Anhui Province (08010202038) the Science and Technological Fund of Anhui Province for Outstanding Youth
基金Project (No. 60421002) supported by the National Natural ScienceFoundation of China
文摘A new multi-step adaptive predictive control algorithm for a class of bilinear systems is presented. The structure of the bilinear system is converted into a simple linear model by using nonlinear support vector machine (SVM) dynamic approximation with analytical control law derived. The method does not need on-line parameters estimation because the system’s internal model has been transformed into an off-line global model. Compared with other traditional methods, this control law reduces on-line parameter estimating burden. In addition, its overall linear behavior treating method allows an analytical control law available and avoids on-line nonlinear optimization. Simulation results are presented in the article to illustrate the efficiency of the method.
文摘This paper considers the optimal control problem for time-delay bilinear systems affected by sinusoidal disturbances with known frequency and measurable amplitude and phase. Firstly, using the differential homeomorphism, a time-delay bilinear system affected by sinusoidal disturbances is changed to a time-delay pseudo linear system through the coordinate transformation. Then the system with time-delay in control variable is transformed to a linear controllable system without delay using model transformation. At last based on the theory of linear quadratic optimal control, an optimal control law which is used to eliminate the influence of the disturbances is derived from a Riccati equation and Matrix equations. The simulation results show the effectiveness of the method.
文摘This paper considers the optimal control problem for the bilinear system based on state feedback. Based on the concept of relative order of the output with respect to the input, first we change a bilinear system to a pseudo linear system model through the coordinate transformation. Then based on the theory of linear quadratic optimal control, the optimal controller is designed by solving the Riccati equation and introducing state feedback with state prediction. At last, the simulation results in CSTR Chemical reactor show the effectiveness of the method.
基金supported by the National Natural Science Foundation of China(Grant No.62275176)the Natural Science Foundation of Guangdong Province,China(Grant No.2022A1515010084)+1 种基金Key projects of basic research and applied basic research in universities of Guangdong province,China(Grant Nos.2021ZDZX1118 and 2022ZDZX1079)supported by the NPRP 13S-0121-200126 project with the Qatar National Research Fund(a member of Qatar Foundation)。
文摘We study dark localized waves within a nonlinear system based on the Boussinesq approximation,describing the dynamics of shallow water waves.Employing symbolic calculus,we apply the Hirota bilinear method to transform an extended Boussinesq system into a bilinear form,and then use the multiple rogue wave method to obtain its dark rational solutions.Exploring the first-and second-order dark solutions,we examine the conditions under which these localized solutions exist and their spatiotemporal distributions.Through the selection of various parameters and by utilizing different visualization techniques(intensity distributions and contour plots),we explore the dynamical properties of dark solutions found:in particular,the first-and second-order dark rogue waves.We also explore the methods of their control.The findings presented here not only deepen the understanding of physical phenomena described by the(1+1)-dimensional Boussinesq equation,but also expand avenues for further research.Our method can be extended to other nonlinear systems,to conceivably obtain higher-order dark rogue waves.
文摘The estimation of residual displacements in a structure due to an anticipated earthquake event has increasingly become an important component of performance-based earthquake engineering because controlling these displacements plays an important role in ensuring cost-feasible or cost-effective repairs in a damaged structure after the event.An attempt is made in this study to obtain statistical estimates of constant-ductility residual displacement spectra for bilinear and pinching oscillators with 5%initial damping,directly in terms of easily available seismological,site,and model parameters.None of the available models for the bilinear and pinching oscillators are useful when design spectra for a seismic hazard at a site are not available.The statistical estimates of a residual displacement spectrum are proposed in terms of earthquake magnitude,epicentral distance,site geology parameter,and three model parameters for a given set of ductility demand and a hysteretic energy capacity coefficient in the case of bilinear and pinching models,as well as for a given set of pinching parameters for displacement and strength at the breakpoint in the case of pinching model alone.The proposed scaling model is applicable to horizontal ground motions in the western U.S.for earthquake magnitudes less than 7 or epicentral distances greater than 20 km.
基金supported by the National Natural Science Foundation of China under Grant Nos.61973014and 61573044。
文摘Controllable canonical forms play important roles in the analysis and design of control systems.In this paper,a fundamental class of discrete-time bilinear systems are considered.Such systems are of interest since,on one hand,they have the most complete controllability theory.On the other hand,they can be nearly-controllable even if controllability fails.Firstly,controllability of the systems with positive control inputs is studied and necessary and sufficient algebraic criteria for positive-controllability and positive-near-controllability are derived.Then,controllable canonical forms and nearly-controllable canonical forms of the systems are presented,respectively,where the corresponding transformation matrices are also explicitly constructed.Examples are given to demonstrate the effectiveness of the derived controllability criteria and controllable canonical forms.
基金Thiswork was supported byAcadémieHassan II des Sciences et Techniques[630/2016].
文摘This paper is concerned with the output stabilisation for a class of distributed bilinear system evolving in a spatial domain.We give sufficient conditions for strong and weak output stabilisation.Also,the output stabilisation is discussed using a minimisation problem.Examples and simulations are given.
文摘The aim of this paper is to study approximate controllability for bilinear systems in the general case. The existence and uniqueness of solutions to bilinear evolution equations are obtained. The paper shows that the approximate controllability of the bilinear control problem is equivalent to the approximate controllability of a discrete problem, using the method developed by Loreti and Siconolfi to approximate the bilinear control problem in an infinite-dimensional Banach space by means of a sequence of discrete problems. Finally, the necessary conditions for the bilinear system to be approximately controllable are stste and proved.
基金National Natural Science Foundation of China Under Grant No.50278090
文摘Under harmonic wave excitation, the dynamic response of a bilinear SDOF system can be expressed by the Hilbert spectrum. The Hilbert spectrum can be formulated by (1) the inter-wave combination mechanism between the steady response and the transient response when the system behaves linearly, or (2) the intra-wave modulation mechanism embedded in one intrinsic mode function (IMF) component when the system behaves nonlinearly. The temporal variation of the instantaneous frequency of the IMF component is consistent with the system nonlinear behavior of yielding and unloading. As a thorough study of this fundamental structural dynamics problem, this article investigates the influence of the amplitude of the harmonic wave excitation on the Hilbert spectrum and the intrinsic oscillatory mode of the dynamic response of a bilinear SDOF system.