The optimal control problem for nonlinear interconnected large-scale dynamic systems is considered. A successive approximation approach for designing the optimal controller is proposed with respect to quadratic perfor...The optimal control problem for nonlinear interconnected large-scale dynamic systems is considered. A successive approximation approach for designing the optimal controller is proposed with respect to quadratic performance indexes. By using the approach, the high order, coupling,nonlinear two-point boundary value (TPBV) problem is transformed into a sequence of linear decoupling TPBV problems. It is proven that the TPBV problem sequence uniformly converges to the optimal control for nonlinear interconnected large-scale systems. A suboptimal control law is obtained by using a finite iterative result of the optimal control sequence.展开更多
This paper studies the optimal control with zero steady-state error problem for nonlinear large-scale systems affected by external persistent disturbances.The nonlinear large-scale system is transformed into N nonline...This paper studies the optimal control with zero steady-state error problem for nonlinear large-scale systems affected by external persistent disturbances.The nonlinear large-scale system is transformed into N nonlinear subsystems with interconnect terms.Based on the internal model principle,a disturbance compensator is constructed such that the ith subsystem with external persistent disturbances is transformed into an augmented subsystem without disturbances.According to the sensitivity approach,the optimal tracking control law for the ith nonlinear subsystem can be obtained.The optimal tracking control law for the nonlinear large-scale systems can be obtained.A numerical simulation shows that the method is effective.展开更多
In this paper, a mathematic description of a class of uncertain nonlinear large scale systems based on some practical application is given. A designing method to construct observers for su...In this paper, a mathematic description of a class of uncertain nonlinear large scale systems based on some practical application is given. A designing method to construct observers for such kind of nonlinear composite systems is developed. The unknown parameters and disturbances are assumed to be neither linear nor matched. A numerical example is used to illustrate the efficiency of our results.展开更多
A new type controller, BP neural-networks-based sliding mode controller is developed for a class of large-scale nonlinear systems with unknown bounds of high-order interconnections in this paper. It is shown that dece...A new type controller, BP neural-networks-based sliding mode controller is developed for a class of large-scale nonlinear systems with unknown bounds of high-order interconnections in this paper. It is shown that decentralized BP neural networks are used to adaptively learn the uncertainty bounds of interconnected subsystems in the Lyapunov sense, and the outputs of the decentralized BP neural networks are then used as the parameters of the sliding mode controller to compensate for the effects of subsystems uncertainties. Using this scheme, not only strong robustness with respect to uncertainty dynamics and nonlinearities can be obtained, but also the output tracking error between the actual output of each subsystem and the corresponding desired reference output can asymptotically converge to zero. A simulation example is presented to support the validity of the proposed BP neural-networks-based sliding mode controller.展开更多
This paper first analyzes the features of two classes of numerical methods for global analysis of nonlinear dynamical systems, which regard state space respectively as continuous and discrete ones. On basis of this un...This paper first analyzes the features of two classes of numerical methods for global analysis of nonlinear dynamical systems, which regard state space respectively as continuous and discrete ones. On basis of this understanding it then points out that the previously proposed method of point mapping under cell reference (PMUCR), has laid a frame work for the development of a two scaled numerical method suitable for the global analysis of high dimensional nonlinear systems, which may take the advantages of both classes of single scaled methods but will release the difficulties induced by the disadvantages of them. The basic ideas and main steps of implementation of the two scaled method, namely extended PMUCR, are elaborated. Finally, two examples are presented to demonstrate the capabilities of the proposed method.展开更多
Time-delays,due to the information transmission between subsystems,naturally exist in large-scale systems and the existence of the delay is frequently a source of instability. This paper considers the problems of robu...Time-delays,due to the information transmission between subsystems,naturally exist in large-scale systems and the existence of the delay is frequently a source of instability. This paper considers the problems of robust non-fragile fuzzy control for a class of uncertain discrete nonlinear large-scale systems with time-delay and controller gain perturbations described by T-S fuzzy model. An equivalent T-S fuzzy model is represented for discrete-delay nonlinear large-scale systems. A sufficient condition for the existence of such non-fragile controllers is further derived via the Lyapunov function and the linear matrix inequality( LMI) approach. Simulation results demonstrate the feasibility and the effectiveness of the proposed design and the proper stabilization of the system in spite of controller gain variations and uncertainties.展开更多
In this paper, the problem of adaptive tracking control for a class of nonlinear large scale systems with unknown parameters entering linearly is discussed. Based on the theory of input output linearization of nonli...In this paper, the problem of adaptive tracking control for a class of nonlinear large scale systems with unknown parameters entering linearly is discussed. Based on the theory of input output linearization of nonlinear systems, direct adaptive control schemes are presented to achieve bounded tracking. The proposed control schemes are robust with respect to the uncertainties in interconnection structure as well as subsystem dynamics. A numerical example is given to illustrate the efficiency of this method.展开更多
A novel H∞ tracking-based decentralized indirect adaptive output feedback fuzzy controller for a class of uncertain large-scale nonlinear systems is developed. By virtue of the proper filtering of the observation err...A novel H∞ tracking-based decentralized indirect adaptive output feedback fuzzy controller for a class of uncertain large-scale nonlinear systems is developed. By virtue of the proper filtering of the observation error dynamics, the observer-based decentralized indirect adaptive fuzzy control scheme is presented for a class of large-scale nonlinear systems using the combination of H∞ tracking technique, a fuzzy adaptive observer and fuzzy inference systems. The output feedback and adaptation mechanisms are both robust and implementable indeed owing to their freedom from the unavailable observation error vector. All the signals of the closed-loop largescale system are guaranteed to stay uniformly bounded and the output errors take on H∞ tracking performance. Simulation results substantiate the effectiveness of the proposed scheme.展开更多
In this paper, two types of mathematical models are developed to describe the dynamics of large-scale nonlinear systems, which are composed of several interconnected nonlinear subsystems. Each subsystem can be describ...In this paper, two types of mathematical models are developed to describe the dynamics of large-scale nonlinear systems, which are composed of several interconnected nonlinear subsystems. Each subsystem can be described by an input-output nonlinear discrete-time mathematical model, with unknown, but constant or slowly time-varying parameters. Then, two recursive estimation methods are used to solve the parametric estimation problem for the considered class of the interconnected nonlinear systems. These methods are based on the recursive least squares techniques and the prediction error method. Convergence analysis is provided using the hyper-stability and positivity method and the differential equation approach. A numerical simulation example of the parametric estimation of a stochastic interconnected nonlinear hydraulic system is treated.展开更多
The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations . T...The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations . The asymptotic expansions of solution were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application of the method of boundary layer with multiple scales .展开更多
Harmonic, subharmonic, superharmonic, simultaneous sub/super harmonic, and combination resonances of the additive type of self-excited two coupled-second order systems to multi-frequency excitation are investigated. T...Harmonic, subharmonic, superharmonic, simultaneous sub/super harmonic, and combination resonances of the additive type of self-excited two coupled-second order systems to multi-frequency excitation are investigated. The theoretical results are obtained by the multiple-scales method. The steady state amplitudes for each resonance are plotted, showing the influence of the different parameters. Analysis for each figure is given. Approximate solution corresponding to each type of resonance is determined. Stability analyses are carried out for each case.展开更多
Electric power infrastructure has recently undergone a comprehensive transformation from electromagnetics to semiconductors. Such a development is attributed to the rapid growth of power electronic converter applicati...Electric power infrastructure has recently undergone a comprehensive transformation from electromagnetics to semiconductors. Such a development is attributed to the rapid growth of power electronic converter applications in the load side to realize energy conservation and on the supply side for renewable generations and power transmissions using high voltage direct current transmission. This transformation has altered the fundamental mechanism of power system dynamics, which demands the establishment of a new theory for power system control and protection. This paper presents thoughts on a theoretical framework for the coming semiconducting power systems.展开更多
This work concerns the representation and stability properties of impulsive solutions for a class of time-delay and measure nonlinear large scale systems. On the basis of fundamental solution of the correspollding ord...This work concerns the representation and stability properties of impulsive solutions for a class of time-delay and measure nonlinear large scale systems. On the basis of fundamental solution of the correspollding ordinary time-delay nonlinear large scale systems is established.By lumped Picard and Gauss-Seidel iteration methods which avoided the difficulties of constructing lyapunov functin, the explicit algebraic criteria of exponential stability for the impulsive and time-delay system are obtained.展开更多
In this paper,we discuss the existence of stationary oscillations of certain large-scale nonlinear time-delay systems by weighted vector Liapunov functions and obtain a simple sufficiency criterion,which is independen...In this paper,we discuss the existence of stationary oscillations of certain large-scale nonlinear time-delay systems by weighted vector Liapunov functions and obtain a simple sufficiency criterion,which is independent of delays.展开更多
This paper deals with the study of the temperature effect on the nonlinear vibration behavior of nanoplate-based nano electromechanical systems（NEMS） subjected to hydrostatic and electrostatic actuations. Using Erin...This paper deals with the study of the temperature effect on the nonlinear vibration behavior of nanoplate-based nano electromechanical systems（NEMS） subjected to hydrostatic and electrostatic actuations. Using Eringen＇s nonlocal elasticity and Gurtin–Murdoch theory, the nonlocal plate model is derived through Hamilton＇s principle. The governing equation which is extremely nonlinear due to the geometrical nonlinearity and electrostatic attraction forces is solved numerically using the differential quadrature method（DQM）. The accuracy of the present method is veriied by comparing the obtained results with the experimental data and those in the literature and very good agreement is obtained. Finally a comprehensive study is carried out to determine the inluence of temperature on the nonlinear vibration characteristics of NEMS made of two different materials including aluminum（Al）and silicon（Si） and some conclusions are drawn.展开更多
基金Supported by National Natural Science Foundation of P. R. China (60074001)the Natural Science Foundation of Shandong Province (Y2000G02)
文摘The optimal control problem for nonlinear interconnected large-scale dynamic systems is considered. A successive approximation approach for designing the optimal controller is proposed with respect to quadratic performance indexes. By using the approach, the high order, coupling,nonlinear two-point boundary value (TPBV) problem is transformed into a sequence of linear decoupling TPBV problems. It is proven that the TPBV problem sequence uniformly converges to the optimal control for nonlinear interconnected large-scale systems. A suboptimal control law is obtained by using a finite iterative result of the optimal control sequence.
基金Supported by National Natural Science Foundation of China （F030101-60574021） and National ＂985＂ Project of China Executed in Xi＇an Jiaotong University
基金supported by the National Natural Science Foundation of China(No.60574023)the Natural Science Foundation of Shandong Province(No.Z2005G01)
文摘This paper studies the optimal control with zero steady-state error problem for nonlinear large-scale systems affected by external persistent disturbances.The nonlinear large-scale system is transformed into N nonlinear subsystems with interconnect terms.Based on the internal model principle,a disturbance compensator is constructed such that the ith subsystem with external persistent disturbances is transformed into an augmented subsystem without disturbances.According to the sensitivity approach,the optimal tracking control law for the ith nonlinear subsystem can be obtained.The optimal tracking control law for the nonlinear large-scale systems can be obtained.A numerical simulation shows that the method is effective.
文摘In this paper, a mathematic description of a class of uncertain nonlinear large scale systems based on some practical application is given. A designing method to construct observers for such kind of nonlinear composite systems is developed. The unknown parameters and disturbances are assumed to be neither linear nor matched. A numerical example is used to illustrate the efficiency of our results.
基金The National Natural Science Foundations of China(50505029)
文摘A new type controller, BP neural-networks-based sliding mode controller is developed for a class of large-scale nonlinear systems with unknown bounds of high-order interconnections in this paper. It is shown that decentralized BP neural networks are used to adaptively learn the uncertainty bounds of interconnected subsystems in the Lyapunov sense, and the outputs of the decentralized BP neural networks are then used as the parameters of the sliding mode controller to compensate for the effects of subsystems uncertainties. Using this scheme, not only strong robustness with respect to uncertainty dynamics and nonlinearities can be obtained, but also the output tracking error between the actual output of each subsystem and the corresponding desired reference output can asymptotically converge to zero. A simulation example is presented to support the validity of the proposed BP neural-networks-based sliding mode controller.
基金supported by the National Natural Science Foundation of China (NSFC) (10872155)
文摘This paper first analyzes the features of two classes of numerical methods for global analysis of nonlinear dynamical systems, which regard state space respectively as continuous and discrete ones. On basis of this understanding it then points out that the previously proposed method of point mapping under cell reference (PMUCR), has laid a frame work for the development of a two scaled numerical method suitable for the global analysis of high dimensional nonlinear systems, which may take the advantages of both classes of single scaled methods but will release the difficulties induced by the disadvantages of them. The basic ideas and main steps of implementation of the two scaled method, namely extended PMUCR, are elaborated. Finally, two examples are presented to demonstrate the capabilities of the proposed method.
文摘Time-delays,due to the information transmission between subsystems,naturally exist in large-scale systems and the existence of the delay is frequently a source of instability. This paper considers the problems of robust non-fragile fuzzy control for a class of uncertain discrete nonlinear large-scale systems with time-delay and controller gain perturbations described by T-S fuzzy model. An equivalent T-S fuzzy model is represented for discrete-delay nonlinear large-scale systems. A sufficient condition for the existence of such non-fragile controllers is further derived via the Lyapunov function and the linear matrix inequality( LMI) approach. Simulation results demonstrate the feasibility and the effectiveness of the proposed design and the proper stabilization of the system in spite of controller gain variations and uncertainties.
文摘In this paper, the problem of adaptive tracking control for a class of nonlinear large scale systems with unknown parameters entering linearly is discussed. Based on the theory of input output linearization of nonlinear systems, direct adaptive control schemes are presented to achieve bounded tracking. The proposed control schemes are robust with respect to the uncertainties in interconnection structure as well as subsystem dynamics. A numerical example is given to illustrate the efficiency of this method.
基金supported by the Natural Sciences and Engineering Research Council of Canada(N00892)in part by National Natural Science Foundation of China(51405436,51375452,61573174)
基金supported by the National Natural Science Foundation of China(90510010).
文摘A novel H∞ tracking-based decentralized indirect adaptive output feedback fuzzy controller for a class of uncertain large-scale nonlinear systems is developed. By virtue of the proper filtering of the observation error dynamics, the observer-based decentralized indirect adaptive fuzzy control scheme is presented for a class of large-scale nonlinear systems using the combination of H∞ tracking technique, a fuzzy adaptive observer and fuzzy inference systems. The output feedback and adaptation mechanisms are both robust and implementable indeed owing to their freedom from the unavailable observation error vector. All the signals of the closed-loop largescale system are guaranteed to stay uniformly bounded and the output errors take on H∞ tracking performance. Simulation results substantiate the effectiveness of the proposed scheme.
基金supported by the Ministry of Higher Education and Scientific Research of Tunisia
文摘In this paper, two types of mathematical models are developed to describe the dynamics of large-scale nonlinear systems, which are composed of several interconnected nonlinear subsystems. Each subsystem can be described by an input-output nonlinear discrete-time mathematical model, with unknown, but constant or slowly time-varying parameters. Then, two recursive estimation methods are used to solve the parametric estimation problem for the considered class of the interconnected nonlinear systems. These methods are based on the recursive least squares techniques and the prediction error method. Convergence analysis is provided using the hyper-stability and positivity method and the differential equation approach. A numerical simulation example of the parametric estimation of a stochastic interconnected nonlinear hydraulic system is treated.
文摘The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations . The asymptotic expansions of solution were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application of the method of boundary layer with multiple scales .
文摘Harmonic, subharmonic, superharmonic, simultaneous sub/super harmonic, and combination resonances of the additive type of self-excited two coupled-second order systems to multi-frequency excitation are investigated. The theoretical results are obtained by the multiple-scales method. The steady state amplitudes for each resonance are plotted, showing the influence of the different parameters. Analysis for each figure is given. Approximate solution corresponding to each type of resonance is determined. Stability analyses are carried out for each case.
基金This work was supported in part by the National Basic Research Program of China （973 Program） （Grant No. 2012CB215100）, and the Major Program of the National Natural Science Foundation of China （Grant No. 51190104）.
文摘Electric power infrastructure has recently undergone a comprehensive transformation from electromagnetics to semiconductors. Such a development is attributed to the rapid growth of power electronic converter applications in the load side to realize energy conservation and on the supply side for renewable generations and power transmissions using high voltage direct current transmission. This transformation has altered the fundamental mechanism of power system dynamics, which demands the establishment of a new theory for power system control and protection. This paper presents thoughts on a theoretical framework for the coming semiconducting power systems.
文摘This work concerns the representation and stability properties of impulsive solutions for a class of time-delay and measure nonlinear large scale systems. On the basis of fundamental solution of the correspollding ordinary time-delay nonlinear large scale systems is established.By lumped Picard and Gauss-Seidel iteration methods which avoided the difficulties of constructing lyapunov functin, the explicit algebraic criteria of exponential stability for the impulsive and time-delay system are obtained.
文摘In this paper,we discuss the existence of stationary oscillations of certain large-scale nonlinear time-delay systems by weighted vector Liapunov functions and obtain a simple sufficiency criterion,which is independent of delays.
文摘This paper deals with the study of the temperature effect on the nonlinear vibration behavior of nanoplate-based nano electromechanical systems（NEMS） subjected to hydrostatic and electrostatic actuations. Using Eringen＇s nonlocal elasticity and Gurtin–Murdoch theory, the nonlocal plate model is derived through Hamilton＇s principle. The governing equation which is extremely nonlinear due to the geometrical nonlinearity and electrostatic attraction forces is solved numerically using the differential quadrature method（DQM）. The accuracy of the present method is veriied by comparing the obtained results with the experimental data and those in the literature and very good agreement is obtained. Finally a comprehensive study is carried out to determine the inluence of temperature on the nonlinear vibration characteristics of NEMS made of two different materials including aluminum（Al）and silicon（Si） and some conclusions are drawn.
