Nonlinear modes in rotating double well potential with parity–time symmetry

We investigate the nonlinear modes in a rotating double well potential with 79T symmetry. Focus on the existence and stability of the nonlinear PT modes in this system, we found that five types of PT modes can stably exist by given certain parameter settings. The multistable area between these modes are studied numerically and the bistable and tristable areas are delimited. With different input trial wavefunctions, five types of solitary wave modes are identified. We found that the rotating of the potential can significantly affect the power flow of the fundamental harmonic mode, whose effect is absent for the other modes.

Time-varying Sliding Mode Controls in Rigid Spacecraft Attitude Tracking

To solve the problem of attitude tracking of a rigid spacecraft with an either known or measurable desired attitude trajectory, three types of time-varying sliding mode controls are introduced under consideration of control input constraints. The sliding surfaces of the three types initially pass arbitrary initial values of the system, and then shift or rotate to reach predetermined ones. This way, the system trajectories are always on the sliding surfaces, and the system work is guaranteed to have robustness against parameter uncertainty and external disturbances all the time. The controller parameters are optimized by means of genetic algorithm to minimize the index consisting of the weighted index of squared error （ISE） of the system and the weighted penalty term of violation of control input constraint. The stability is verified with Lyapunov method. Compared with the conventional sliding mode control, simulation results show the proposed algorithm having better robustness against inertia matrix uncertainty and external disturbance torques.

Robust control of uncertain time delay system:a novel sliding mode control design via LMI

The sliding mode control problem （SMC） is studied for a class of uncertain delay system in the presence of both parameter uncertainties and external disturbances. A novel virtual feedback control method is presented. Based on Lyapunov theory, sufficient conditions for design of the robust sliding mode plane are derived. Sliding mode controller based on reaching law concept is developed, which is to ensure system trajectories from any initial conditions asymptotically convergent to sliding mode plane. The global asymptotically stability of the closed-loop system is guaranteed. A numerical example with simulation results is given to illustrate the effectiveness of the methodology.

Finite-time robust control of uncertain fractional-order Hopfield neural networks via sliding mode control

The finite-time control of uncertain fractional-order Hopfield neural networks is investigated in this paper. A switched terminal sliding surface is proposed for a class of uncertain fractional-order Hopfield neural networks. Then a robust control law is designed to ensure the occurrence of the sliding motion for stabilization of the fractional-order Hopfield neural networks. Besides, for the unknown parameters of the fractional-order Hopfield neural networks, some estimations are made. Based on the fractional-order Lyapunov theory, the finite-time stability of the sliding surface to origin is proved well. Finally, a typical example of three-dimensional uncertain fractional-order Hopfield neural networks is employed to demonstrate the validity of the proposed method.

Uniformed model of networked control systems with long time delay

Feedback control systems wherein the control loops are closed through a real-time network are called networked control systems （NCS）. The defining feature of an NCS is that information is exchanged using a network among control system components. Two new concepts including long time delay and short time delay are proposed. The sensor is almost always clock driven. The controller or the actuator is either clock driven or event driven. Four possible driving modes of networked control systems are presented. The open loop mathematic models of networked control systems with long time delay are developed when the system is driven by anyone of the four different modes. The uniformed modeling method of networked control systems with long time delay is proposed. The simulation results are given in the end.

Disturbance observer based time-varying sliding mode control for uncertain mechanical system

It is now well known that the time-varying sliding mode control （TVSMC） is characterized by its global robustness against matched model uncertainties and disturbances. The accurate tracking problem of the mechanical system in the presence of the parametric uncertainty and external disturbance is addressed in the TVSMC framework. Firstly, an exponential TVSMC algorithm is designed and the main features are analyzed. Especially, the control parameter is obtained by solving an optimal problem. Subsequently, the global chattering problem in TVSMC is considered. To reduce the static error resulting from the continuous TVSMC algorithm, a disturbance observer based time-varying sliding mode control （DOTVSMC） algorithm is presented. The detailed design principle and the stability of the closed-loop system under the composite controller are provided. Simulation results verify the effectiveness of the proposed algorithm.

Target Tracking Algorithm Using Finite-time Convergence Smooth Second-order Sliding Mode Controller for Mobile Robots

Target tracking control for wheeled mobile robot （WMR） need resolve the problems of kinematics model and tracking algorithm.High-order sliding mode control is a valid method used in the nonlinear tracking control system,which can eliminate the chattering of sliding mode control.Currently there lacks the research of robustness and uncertain factors for high-order sliding mode control.To address the fast convergence and robustness problems of tracking target,the tracking mathematical model of WMR and the target is derived.Based on the finite-time convergence theory and second order sliding mode method,a nonlinear tracking algorithm is designed which guarantees that WMR can catch the target in finite time.At the same time an observer is applied to substitute the uncertain acceleration of the target,then a smooth nonlinear tracking algorithm is proposed.Based on Lyapunov stability theory and finite-time convergence,a finite time convergent smooth second order sliding mode controller and a target tracking algorithm are designed by using second order sliding mode method.The simulation results verified that WMR can catch up the target quickly and reduce the control discontinuity of the velocity of WMR.

Finite time convergent control using terminal sliding mode

A method for terminal sliding mode control design is discussed. As we know, one of the strong points of terminal sliding mode control is its finite-time convergence to a given equilibrium of the system under consideration, which may be useful in specific applications. The proposed method, different from many existing terminal sliding model control desin methods, is studied, and then feedback laws are designed for a class of nonlinear systems, along with illustrative examples.

Characteristic Model-based Discrete-time Sliding Mode Control for Spacecraft with Variable Tilt of Flexible Structures

In this paper, the finite-time attitude tracking control problem for the spacecrafts with variable tilt of flexible appendages in the conditions of exogenous disturbances and inertia uncertainties is addressed. First the characteristic modeling method is applied to the problem of the spacecraft modeling. Second, a novel adaptive sliding mode surface is designed based on the characteristic model. Furthermore, a discrete-time sliding mode control (DTSMC) law, which makes the tracking error converge into a predefined bound in finite time, is proposed by employing the parameters of characteristic model associated with the sliding mode surface to provide better performances, robustness, faster response, and higher control precision. The designed DTSMC includes the adaptive control architecture and is chattering-free. Finally, digital simulations of a sun synchronous orbit satellite (SSOS) are presented to illustrate effectiveness of the control strategies as well as to verify the practical feasibility of the rapid maneuver mission. © 2014 Chinese Association of Automation.

Real-time State Monitoring During Switching Mode Transitions in High Power Three-level Inverters

大功率多电平逆变器近年来在实际工业生产中得到越来越广泛的应用。多电平逆变器由于结构复杂,采用元器件较多,因此在设计和实验中,实现各个工作状态下运行参数的同步监测和分析较为困难。本文针对大功率三电平逆变器,实现开关动态特性的在线测试,在此基础上,进一步研究三电平逆变器在开关状态变化时理论与实际负载运行工况下电路拓扑的转换变化规律。通过全电路电气参数和元器件状态的实时监测,发现在三电平逆变器非正常运行状态下开关转换时额外电应力,同时,深入研究在实际工况运行条件非正常状态下该额外电应力出现的机理和原因,为三电平逆变器的故障诊断提供了参考,对于设计高可靠性的多电平逆变器系统有一定的理论和现实意义。

Finite-time Sliding Mode Control Design for a Class of Uncertain Conic Nonlinear Systems

This paper studies the sliding mode controller design problems for a class of nonlinear system. The nonlinear function is considered to satisfy conic-type constraint condition. A novel finite-time boundedness(FTB) based sliding mode controller design theory is proposed. And then a sufficient condition is obtained in terms of linear matrix inequalities(LMIs), which guarantees the resulted sliding mode dynamics to be FTB wrt some predefined scalars. Thereafter, a FTB-based sliding mode control(SMC) law is synthesized to ensure the state of the controlled system is driven into a novel desired switching surface s(t) = c(c is a constant) in a finite time. Simulation results illustrate the validity of the proposed FTB-based SMC design theory.

Time-Delayed Feedback Control in a Single-Mode Laser System

The effects of time-delayed feedback control in a single-mode laser system is investigated.Using the smalltime delay approximation,the analytic expression of the stationary probability distribution function of the laser field isobtained.The mean,normalized variance and skewness of the steady-state laser intensity are calculated.It is found thatthe time-delayed feedback control can suppress the intensity fluctuation of the laser system.The numerical simulationsare in good agreement with the approximate analytic results.

Finite-Time Normal Mode Disturbances and Error Growth During Southern Hemisphere Blocking

The structural organization of initially random errors evolving in abarotropic tangent linear model, with time-dependent basic states taken from analyses, is examinedfor cases of block development, maturation and decay in the Southern Hemisphere atmosphere duringApril, November, and December 1989. The statistics of 100 evolved errors are studied for six-dayperiods and compared with the growth and structures of fast growing normal modes and finite-timenormal modes (FTNMs). The amplification factors of most initially random errors are slightly lessthan those of the fastest growing FTNM for the same time interval. During their evolution, thestandard deviations of the error fields become concentrated in the regions of rapid dynamicaldevelopment, particularly associated with developing and decaying blocks. We have calculatedprobability distributions and the mean and standard deviations of pattern correlations between eachof the 100 evolved error fields and the five fastest growing FTNMs for the same time interval. Themean of the largest pattern correlation, taken over the five fastest growing FTNMs, increases withincreasing time interval to a value close to 0.6 or larger after six days. FTNM 1 generally, but notalways, gives the largest mean pattern correlation with error fields. Corresponding patterncorrelations with the fast growing normal modes of the instantaneous basic state flow aresignificant' but lower than with FTNMs. Mean pattern correlations with fast growing FTNMs increasefurther when the time interval is increased beyond six days.

Time delay control of hydraulic manipulators with continuous nonsingular terminal sliding mode

For the position tracking control of hydraulic manipulators,a novel method of time delay control(TDC) with continuous nonsingular terminal sliding mode(CNTSM) was proposed in this work.Complex dynamics of the hydraulic manipulator is approximately canceled by time delay estimation(TDE),which means the proposed method is model-free and no prior knowledge of the dynamics is required.Moreover,the CNTSM term with a fast-TSM-type reaching law ensures fast convergence and high-precision tracking control performance under heavy lumped uncertainties.Despite its considerable robustness against lumped uncertainties,the proposed control scheme is continuous and chattering-free and no pressure sensors are required in practical applications.Theoretical analysis and experimental results show that faster and higher-precision position tracking performance is achieved compared with the traditional CNTSM-based TDC method using boundary layers.

Fixed time integral sliding mode controller and its application to the suppression of chaotic oscillation in power system

Chattering phenomenon and singularity are still the main problems that hinder the practical application of sliding mode control. In this paper, a fixed time integral sliding mode controller is designed based on fixed time stability theory, which ensures precise convergence of the state variables of controlled system, and overcomes the drawback of convergence time growing unboundedly as the initial value increases in finite time controller. It makes the controlled system converge to the control objective within a fixed time bounded by a constant as the initial value grows, and convergence time can be changed by adjusting parameters of controllers properly. Compared with other fixed time controllers, the fixed time integral sliding mode controller proposed in this paper achieves chattering-free control, and integral expression is used to avoid singularity generated by derivation. Finally, the controller is used to stabilize four-order chaotic power system. The results demonstrate that the controller realizes the non-singular chattering-free control of chaotic oscillation in the power system and guarantees the fixed time convergence of state variables, which shows its higher superiority than other finite time controllers.

Variable structure control with sliding mode prediction for discrete-time nonlinear systems

A new variable structure control algorithm based on sliding mode prediction for a class of discrete-time nonlinear systems is presented. By employing a special model to predict future sliding mode value, and combining feedback correction and receding horizon optimization methods which are extensively applied on predictive control strategy, a discrete-time variable structure control law is constructed. The closed-loop systems are proved to have robustness to uncertainties with unspecified boundaries. Numerical simulation and pendulum experiment results illustrate that the closed-loop systems possess desired performance, such as strong robustness, fast convergence and chattering elimination.

Sliding mode control and Lyapunov based guidance law with impact time constraints

This paper analyses the issue of impact time control of super-cavitation weapons impact fixed targets which mainly refer to the ships or submarines who lost power, but still have combat capability. Control over impact time constraints of guidance law(ITCG) is derived by using sliding mode control(SMC) and Lyapunov stability theorem. The expected impact time is realized by using the notion of attack process and estimated time-to-go to design sliding mode surface(SMS). ITCG contains equivalent and discontinuous guidance laws, once state variables arrive at SMS,the equivalent guidance law keeps the state variables on SMS,then the discontinuous guidance law enforces state variables to move and reach SMS. The singularity problem of ITCG is also analyzed. Theoretical analysis and numerical simulation results are given to test the effectiveness of ITCG designed in this paper.

Robust pre-specified time synchronization of chaotic systems by employing time-varying switching surfaces in the sliding mode control scheme

In the conventional chaos synchronization methods, the time at which two chaotic systems are synchronized, is usually unknown and depends on initial conditions. In this work based on Lyapunov stability theory a sliding mode controller with time-varying switching surfaces is proposed to achieve chaos synchronization at a pre-specified time for the first time. The proposed controller is able to synchronize chaotic systems precisely at any time when we want. Moreover, by choosing the time-varying switching surfaces in a way that the reaching phase is eliminated, the synchronization becomes robust to uncertainties and exogenous disturbances. Simulation results are presented to show the effectiveness of the proposed method of stabilizing and synchronizing chaotic systems with complete robustness to uncertainty and disturbances exactly at a pre-specified time.

Exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and mode-dependent probabilistic time-varying delays

In this paper, the problem of exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and Mode-dependent probabilistic time-varying coupling delays is investigated. The sam- pling period is assumed to be time-varying and bounded. The information of probability distribution of the time-varying delay is considered and transformed into parameter matrices of the transferred complex dynamical network model. Based on the condition, the design method of the desired sampled data controller is proposed. By constructing a new Lyapunov functional with triple integral terms, delay-distribution-dependent exponential synchronization criteria are derived in the form of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

Robust Sliding-mode Filtering for a Class of Uncertain Nonlinear Discrete-time State-delayed Systems

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.