The origin of the Kilometric Continuum(KC)is usually attributed to the linear mode conversion window theory,yet direct evidence has been lacking.Here we present an event where electrostatic waves,Z-mode,and KC were ob...The origin of the Kilometric Continuum(KC)is usually attributed to the linear mode conversion window theory,yet direct evidence has been lacking.Here we present an event where electrostatic waves,Z-mode,and KC were observed simultaneously near the magnetic equator by the Van Allen Probes.We identify the radio window(the region for mode conversion taking place)at L=4.059 by solving the fully-thermal dispersion relation.Ray tracing simulations show that the backward-propagating electrostatic mode can smoothly transition to Z-mode.Then,Z-mode can convert to KC when its direction shifts to parallel or anti-parallel propagation at the radio window,which aligns with observations.This study provides direct evidence that supports the linear mode conversion theory as an effective mechanism for KC generation.展开更多
A decoupled nonsingular terminal sliding mode control（DNTSMC） approach is proposed to address the tracking control problem of affine nonlinear systems.A nonsingular terminal sliding mode control（NTSMC） method is p...A decoupled nonsingular terminal sliding mode control（DNTSMC） approach is proposed to address the tracking control problem of affine nonlinear systems.A nonsingular terminal sliding mode control（NTSMC） method is presented,in which the nonsingular terminal sliding surface is defined as a special nonsingular terminal function and the convergence time of the system states can be specified.The affine nonlinear system is firstly decoupled into linear subsystems via feedback linearization.Then,a nonsingular terminal sliding surface is defined and the NTSMC method is applied to each subsystem separately to ensure the finite time convergence of the closed-loop system.The verification example is given to demonstrate the effectiveness and robustness of the proposed approach.The proposed approach exhibits a considerable advantage in terms of faster tracking error convergence and less chattering compared with the conventional sliding mode control（CSMC）.展开更多
In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the a...In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities （LMIs）. Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin＇s formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.展开更多
This paper focuses on sliding mode control problems for a class of nonlinear neutral systems with time-varying delays. An integral sliding surface is firstly constructed. Then it finds a useful criteria to guarantee t...This paper focuses on sliding mode control problems for a class of nonlinear neutral systems with time-varying delays. An integral sliding surface is firstly constructed. Then it finds a useful criteria to guarantee the global stability for the nonlinear neutral systems with time-varying delays in the specified switching surface, whose condition is formulated as linear matrix inequality. The synthesized sliding mode controller guarantees the reachability of the specified sliding surface. Finally, a numerical simulation validates the effectiveness and feas.ibility of the proposed technique.展开更多
We present a stable linear-cavity single longitudinal mode （SLM） erbium-doped silica fiber laser. It consists of four fiber Bragg gratings （FBGs） directly written in a section of photosensitive erbium-doped fiber ...We present a stable linear-cavity single longitudinal mode （SLM） erbium-doped silica fiber laser. It consists of four fiber Bragg gratings （FBGs） directly written in a section of photosensitive erbium-doped fiber （EDF） to form an asymmetric three-cavity structure. The stable SLM operation at a wavelength of 1545.112 nm with a 3-dB bandwidth of 0.012 nm and an optical signal-to-noise ratio （OSNR） of about 60 dB is verified experimentally. Under laboratory conditions, the performance of a power fluctuation of less than 0.05 dB observed from the power meter for 6 h and a wavelength variation of less than 0.01 nm obtained from the optical spectrum analyzer （OSA） for about 1.5 h are demonstrated. The gain fiber length is no longer limited to only several centimeters for SLM operation because of the excellent mode-selecting ability of the asymmetric three-cavity structure. The proposed scheme provides a simple and cost-effective approach to realizing a stable SLM fiber laser.展开更多
This paper presents a robust sliding mode controller for a class of unknown nonlinear discrete-time systems in the presence of fixed time delay. A neural-network approximation and the Lyapunov-Krasovskii functional th...This paper presents a robust sliding mode controller for a class of unknown nonlinear discrete-time systems in the presence of fixed time delay. A neural-network approximation and the Lyapunov-Krasovskii functional theory into the sliding-mode technique is used and a neural-network based sliding mode control scheme is proposed. Because of the novality of Chebyshev Neural Networks (CNNs), that it requires much less computation time as compare to multi layer neural network (MLNN), is preferred to approximate the unknown system functions. By means of linear matrix inequalities, a sufficient condition is derived to ensure the asymptotic stability such that the sliding mode dynamics is restricted to the defined sliding surface. The proposed sliding mode control technique guarantees the system state trajectory to the designed sliding surface. Finally, simulation results illustrate the main characteristics and performance of the proposed approach.展开更多
In this paper, we want to make a new type linear piezoelectric motor by mode shape coating or effective electrode surface coating. The mode shape is derived from the mechanical boundary conditions of the linear piezoe...In this paper, we want to make a new type linear piezoelectric motor by mode shape coating or effective electrode surface coating. The mode shape is derived from the mechanical boundary conditions of the linear piezoelectric motor. We only have access to the first three modes of formas, the effective electrode surface coating basis, as well as with the linear piezoelectric motor of normal shape do comparison. Next, we will inspect their gain or axial velocity through theoretical analysis, simulation and experiment. According to the results of the theoretical analysis, we have found that the gain or axial velocity of the linear piezoelectric motors of mode shape is much larger than the linear piezoelectric motors of normal shape. However, according to the results of simulation and experiments, we have found that the gain or axial velocity of the linear piezoelectric motors of mode shape is much greater than the linear piezoelectric motors of normal shape, which is about 1.2 to 1.4 times. The linear piezoelectric motor of mode shape 3 has the fastest axial velocity, which is about -48 mm/s and 48 mm/s under conditions of 180 Vp-p driving voltage, 21.2 kHz driving frequency (the third vibration modal), 25 gw loading and the position of loading or mass at x = 5 mm & 45 mm respectively. And its axial velocity is about 1.4 times the linear piezoelectric motor of normal shape under the same conditions. Overall, the mode shape coating helps to enhance the gain or axial velocity of the linear piezoelectric motor.展开更多
Introducing the nonlinear Rayleigh damping into the governing equation of the Mode Ⅲ dynamic rupture for standard viscoelastic solid, this equation is a partial differential and integral equation. First, eliminating ...Introducing the nonlinear Rayleigh damping into the governing equation of the Mode Ⅲ dynamic rupture for standard viscoelastic solid, this equation is a partial differential and integral equation. First, eliminating the integral term, a PDE of third_order is obtained. Then, applying the small parameter expansion method, linearized asymptotic governing equation for each order of the small parameter is obtained. Dividing the third_order PDE into an elastic part with known solution, the rest part pertains to viscous effect which is neither a Mathieu equation nor a Hill one. The WKBJ method is still adopted to solve it analytically.展开更多
The problem of robustifying linear quadratic regulators （LQRs） for a class of uncertain affine nonlinear systems is considered. First, the exact linearization technique is used to transform an uncertain nonlinear sy...The problem of robustifying linear quadratic regulators （LQRs） for a class of uncertain affine nonlinear systems is considered. First, the exact linearization technique is used to transform an uncertain nonlinear system into a linear one and an optimal LQR is designed for the corresponding nominal system. Then, based on the integral sliding mode, a design approach to robustifying the optimal regulator is studied. As a result, the system exhibits global robustness to uncertainties and the ideal sliding mode dynamics is the same as that of the optimal LQR for the nominal system. A global robust optimal sliding mode control （GROSMC） is realized. Finally, a numerical simulation is demonstrated to show the effectiveness and superiority of the proposed algorithm compared with the conventional optimal LQR.展开更多
A new proportional-integral （PI） sliding surface is designed for a class of uncertain nonlinear state-delayed systems. Based on this, an adaptive sliding mode controller （ASMC） is synthesized, which guarantees the...A new proportional-integral （PI） sliding surface is designed for a class of uncertain nonlinear state-delayed systems. Based on this, an adaptive sliding mode controller （ASMC） is synthesized, which guarantees the occurrence of sliding mode even when the system is undergoing parameter uncertainties and external disturbance. The resulting sliding mode has the same order as the original system, so that it becomes easy to solve the H∞ control problem by designing a memoryless H∞ state feedback controller. A delay-dependent sufficient condition is proposed in terms of linear matrix inequalities （LMIs）, which guarantees the sliding mode robust asymptotically stable and has a noise attenuation level γ in an H∞ sense. The admissible state feedback controller can be found by solving a sequential minimization problem subject to LMI constraints by applying the cone complementary linearization method. This design scheme combines the strong robustness of the sliding mode control with the H∞ norm performance. A numerical example is given to illustrate the effectiveness of the proposed scheme.展开更多
This paper is concerned with the problem of robust sliding-mode filtering for a class of uncertain nonlinear discrete-time systems with time-delays. The nonlinearities are assumed to satisfy global Lipschitz condition...This paper is concerned with the problem of robust sliding-mode filtering for a class of uncertain nonlinear discrete-time systems with time-delays. The nonlinearities are assumed to satisfy global Lipschitz conditions and parameter uncertainties are supposed to reside in a polytope. The resulting filter is of the Luenberger type with the discontinuous form. A sufficient condition with delay-dependency is proposed for existence of such a filter. And the desired filter can be found by solving a set of matrix inequalities. The resulting filter adapts for the systems whose noise input is real functional bounded and not be required to be energy bounded. A numerical example is given to illustrate the effectiveness of the proposed design method.展开更多
This paper is concerned with the stability and robust stability of switched positive linear systems(SPLSs) whose subsystems are all unstable. By means of the mode-dependent dwell time approach and a class of discretiz...This paper is concerned with the stability and robust stability of switched positive linear systems(SPLSs) whose subsystems are all unstable. By means of the mode-dependent dwell time approach and a class of discretized co-positive Lyapunov functions, some stability conditions of switched positive linear systems with all modes unstable are derived in both the continuous-time and the discrete-time cases, respectively. The copositive Lyapunov functions constructed in this paper are timevarying during the dwell time and time-invariant afterwards. In addition, the above approach is extended to the switched interval positive systems. A numerical example is proposed to illustrate our approach.展开更多
基金supported by the National Natural Science Foundation of China grants 42074198,42230209 and 42374215the Scientific Research Fund of Hunan Provincial Education Department Grants 21A0212,Post-graduate Scientific Research Innovation Project of Hunan Province CX20240804.
文摘The origin of the Kilometric Continuum(KC)is usually attributed to the linear mode conversion window theory,yet direct evidence has been lacking.Here we present an event where electrostatic waves,Z-mode,and KC were observed simultaneously near the magnetic equator by the Van Allen Probes.We identify the radio window(the region for mode conversion taking place)at L=4.059 by solving the fully-thermal dispersion relation.Ray tracing simulations show that the backward-propagating electrostatic mode can smoothly transition to Z-mode.Then,Z-mode can convert to KC when its direction shifts to parallel or anti-parallel propagation at the radio window,which aligns with observations.This study provides direct evidence that supports the linear mode conversion theory as an effective mechanism for KC generation.
基金supported by the National Natural Science Foundation of China(11502288)
文摘A decoupled nonsingular terminal sliding mode control（DNTSMC） approach is proposed to address the tracking control problem of affine nonlinear systems.A nonsingular terminal sliding mode control（NTSMC） method is presented,in which the nonsingular terminal sliding surface is defined as a special nonsingular terminal function and the convergence time of the system states can be specified.The affine nonlinear system is firstly decoupled into linear subsystems via feedback linearization.Then,a nonsingular terminal sliding surface is defined and the NTSMC method is applied to each subsystem separately to ensure the finite time convergence of the closed-loop system.The verification example is given to demonstrate the effectiveness and robustness of the proposed approach.The proposed approach exhibits a considerable advantage in terms of faster tracking error convergence and less chattering compared with the conventional sliding mode control（CSMC）.
文摘In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities （LMIs）. Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin＇s formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.
基金Project supported by the National Natural Science Foundation of China (Grant No 60674026)the Key Project of Chinese Ministry of Education (Grant No 107058)+1 种基金the Jiangsu Provincial Natural Science Foundation of China (Grant No BK2007016)the Jiangsu Provincial Program for Postgraduate Scientific Innovative Research of Jiangnan University (Grant No CX07B_116z)and PIRT Jiangnan
文摘This paper focuses on sliding mode control problems for a class of nonlinear neutral systems with time-varying delays. An integral sliding surface is firstly constructed. Then it finds a useful criteria to guarantee the global stability for the nonlinear neutral systems with time-varying delays in the specified switching surface, whose condition is formulated as linear matrix inequality. The synthesized sliding mode controller guarantees the reachability of the specified sliding surface. Finally, a numerical simulation validates the effectiveness and feas.ibility of the proposed technique.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61077069 and 61107094)the Innovation Foundation for Excellent Doctoral Candidates of Beijing Jiaotong University, China (Grant No. 2011YJS202)
文摘We present a stable linear-cavity single longitudinal mode （SLM） erbium-doped silica fiber laser. It consists of four fiber Bragg gratings （FBGs） directly written in a section of photosensitive erbium-doped fiber （EDF） to form an asymmetric three-cavity structure. The stable SLM operation at a wavelength of 1545.112 nm with a 3-dB bandwidth of 0.012 nm and an optical signal-to-noise ratio （OSNR） of about 60 dB is verified experimentally. Under laboratory conditions, the performance of a power fluctuation of less than 0.05 dB observed from the power meter for 6 h and a wavelength variation of less than 0.01 nm obtained from the optical spectrum analyzer （OSA） for about 1.5 h are demonstrated. The gain fiber length is no longer limited to only several centimeters for SLM operation because of the excellent mode-selecting ability of the asymmetric three-cavity structure. The proposed scheme provides a simple and cost-effective approach to realizing a stable SLM fiber laser.
文摘This paper presents a robust sliding mode controller for a class of unknown nonlinear discrete-time systems in the presence of fixed time delay. A neural-network approximation and the Lyapunov-Krasovskii functional theory into the sliding-mode technique is used and a neural-network based sliding mode control scheme is proposed. Because of the novality of Chebyshev Neural Networks (CNNs), that it requires much less computation time as compare to multi layer neural network (MLNN), is preferred to approximate the unknown system functions. By means of linear matrix inequalities, a sufficient condition is derived to ensure the asymptotic stability such that the sliding mode dynamics is restricted to the defined sliding surface. The proposed sliding mode control technique guarantees the system state trajectory to the designed sliding surface. Finally, simulation results illustrate the main characteristics and performance of the proposed approach.
文摘In this paper, we want to make a new type linear piezoelectric motor by mode shape coating or effective electrode surface coating. The mode shape is derived from the mechanical boundary conditions of the linear piezoelectric motor. We only have access to the first three modes of formas, the effective electrode surface coating basis, as well as with the linear piezoelectric motor of normal shape do comparison. Next, we will inspect their gain or axial velocity through theoretical analysis, simulation and experiment. According to the results of the theoretical analysis, we have found that the gain or axial velocity of the linear piezoelectric motors of mode shape is much larger than the linear piezoelectric motors of normal shape. However, according to the results of simulation and experiments, we have found that the gain or axial velocity of the linear piezoelectric motors of mode shape is much greater than the linear piezoelectric motors of normal shape, which is about 1.2 to 1.4 times. The linear piezoelectric motor of mode shape 3 has the fastest axial velocity, which is about -48 mm/s and 48 mm/s under conditions of 180 Vp-p driving voltage, 21.2 kHz driving frequency (the third vibration modal), 25 gw loading and the position of loading or mass at x = 5 mm & 45 mm respectively. And its axial velocity is about 1.4 times the linear piezoelectric motor of normal shape under the same conditions. Overall, the mode shape coating helps to enhance the gain or axial velocity of the linear piezoelectric motor.
文摘Introducing the nonlinear Rayleigh damping into the governing equation of the Mode Ⅲ dynamic rupture for standard viscoelastic solid, this equation is a partial differential and integral equation. First, eliminating the integral term, a PDE of third_order is obtained. Then, applying the small parameter expansion method, linearized asymptotic governing equation for each order of the small parameter is obtained. Dividing the third_order PDE into an elastic part with known solution, the rest part pertains to viscous effect which is neither a Mathieu equation nor a Hill one. The WKBJ method is still adopted to solve it analytically.
基金supported by the Doctoral Foundation of Qingdao University of Science and Technology(0022330).
文摘The problem of robustifying linear quadratic regulators （LQRs） for a class of uncertain affine nonlinear systems is considered. First, the exact linearization technique is used to transform an uncertain nonlinear system into a linear one and an optimal LQR is designed for the corresponding nominal system. Then, based on the integral sliding mode, a design approach to robustifying the optimal regulator is studied. As a result, the system exhibits global robustness to uncertainties and the ideal sliding mode dynamics is the same as that of the optimal LQR for the nominal system. A global robust optimal sliding mode control （GROSMC） is realized. Finally, a numerical simulation is demonstrated to show the effectiveness and superiority of the proposed algorithm compared with the conventional optimal LQR.
基金This project was supported by the National Natural Science Foundation of China(69874008)
文摘A new proportional-integral （PI） sliding surface is designed for a class of uncertain nonlinear state-delayed systems. Based on this, an adaptive sliding mode controller （ASMC） is synthesized, which guarantees the occurrence of sliding mode even when the system is undergoing parameter uncertainties and external disturbance. The resulting sliding mode has the same order as the original system, so that it becomes easy to solve the H∞ control problem by designing a memoryless H∞ state feedback controller. A delay-dependent sufficient condition is proposed in terms of linear matrix inequalities （LMIs）, which guarantees the sliding mode robust asymptotically stable and has a noise attenuation level γ in an H∞ sense. The admissible state feedback controller can be found by solving a sequential minimization problem subject to LMI constraints by applying the cone complementary linearization method. This design scheme combines the strong robustness of the sliding mode control with the H∞ norm performance. A numerical example is given to illustrate the effectiveness of the proposed scheme.
基金Supported by National Natural Science Foundation of P. R. China (69874008)
文摘This paper is concerned with the problem of robust sliding-mode filtering for a class of uncertain nonlinear discrete-time systems with time-delays. The nonlinearities are assumed to satisfy global Lipschitz conditions and parameter uncertainties are supposed to reside in a polytope. The resulting filter is of the Luenberger type with the discontinuous form. A sufficient condition with delay-dependency is proposed for existence of such a filter. And the desired filter can be found by solving a set of matrix inequalities. The resulting filter adapts for the systems whose noise input is real functional bounded and not be required to be energy bounded. A numerical example is given to illustrate the effectiveness of the proposed design method.
基金supported by National Natural Science Foundation of China (61703288,61603079,61873174)
文摘This paper is concerned with the stability and robust stability of switched positive linear systems(SPLSs) whose subsystems are all unstable. By means of the mode-dependent dwell time approach and a class of discretized co-positive Lyapunov functions, some stability conditions of switched positive linear systems with all modes unstable are derived in both the continuous-time and the discrete-time cases, respectively. The copositive Lyapunov functions constructed in this paper are timevarying during the dwell time and time-invariant afterwards. In addition, the above approach is extended to the switched interval positive systems. A numerical example is proposed to illustrate our approach.
