Design of an adaptive finite-time controller for synchronization of two identical/different non-autonomous chaotic flywheel governor systems

The centrifugal flywheel governor (CFG) is a mechanical device that automatically controls the speed of an engine and avoids the damage caused by sudden change of load torque. It has been shown that this system exhibits very rich and complex dynamics such as chaos. This paper investigates the problem of robust finite-time synchronization of non-autonomous chaotic CFGs. The effects of unknown parameters, model uncertainties and external disturbances are fully taken into account. First, it is assumed that the parameters of both master and slave CFGs have the same value and a suitable adaptive finite-time controller is designed. Second, two CFGs are synchronized with the parameters of different values via a robust adaptive finite-time control approach. Finally, some numerical simulations are used to demonstrate the effectiveness and robustness of the proposed finite-time controllers.     

Design of an adaptive finite-time controller for synchronization of two identical/different non-autonomous chaotic flywheel governor systems

The centrifugal flywheel governor(CFG) is a mechanical device that automatically controls the speed of an engine and avoids the damage caused by sudden change of load torque.It has been shown that this system exhibits very rich and complex dynamics such as chaos.This paper investigates the problem of robust finite-time synchronization of non-autonomous chaotic CFGs.The effects of unknown parameters,model uncertainties and external disturbances are fully taken into account.First,it is assumed that the parameters of both master and slave CFGs have the same value and a suitable adaptive finite-time controller is designed.Second,two CFGs are synchronized with the parameters of different values via a robust adaptive finite-time control approach.Finally,some numerical simulations are used to demonstrate the effectiveness and robustness of the proposed finite-time controllers.     

参数不确定永磁同步电机混沌系统的有限时间稳定控制

针对含有参数不确定性的永磁同步电机混沌系统, 结合主动控制与有限时间稳定控制理论, 提出一种改进的主动有限时间稳定控制器. 该控制器不仅具有较强的鲁棒性, 而且可以通过调整终端吸引子比例系数, 有效地缩短系统的响应时间, 以提高系统的响应能力. 通过仿真实验, 验证了该控制器比传统的控制器的具有更强的鲁棒性和响应能力. 关键词： 永磁同步电机 混沌控制 有限时间稳定 主动控制     

Chaos suppression of uncertain gyros in a given finite time

The gyro is one of the most interesting and everlasting nonlinear dynamical systems,which displays very rich and complex dynamics,such as sub-harmonic and chaotic behaviors.We study the chaos suppression of the chaotic gyros in a given finite time.Considering the effects of model uncertainties,external disturbances,and fully unknown parameters,we design a robust adaptive finite-time controller to suppress the chaotic vibration of the uncertain gyro as quickly as possible.Using the finite-time control technique,we give the exact value of the chaos suppression time.A mathematical theorem is presented to prove the finite-time stability of the proposed scheme.The numerical simulation shows the efficiency and usefulness of the proposed finite-time chaos suppression strategy.     

冠状动脉系统高阶滑模自适应混沌同步设计

针对冠状动脉系统混沌同步问题, 系统模型受到有界但未知的不确定干扰条件下, 利用几何齐次性理论和积分滑模面设计高阶滑模自适应控制器, 使响应系统在有限时间内跟踪驱动系统, 该方法无需提前预知扰动边界. 采用Lyapunov理论对闭环系统进行分析并证明该控制器保证该系统能够在有限时间内镇定, 从仿真实验结果可以看出所设计的控制器在不确定干扰的情况下系统具有良好鲁棒性和未知参数的自适应性, 为能够有效治疗心肌梗死等冠状动脉疾病提供了一定的理论依据.     

Finite-time synchronization of Markovian jumping complex dynamical networks and hybrid couplings

This paper of finite-time synchronization for Markovian jumping complex dynamical frameworks with hybrid couplings is studied. A state feedback control is planned for finite-time synchronization of complex frameworks is presented. Sufficient synchronization criteria are proposed in light of the Lyapunov stability theory. A sensible Lyapunov-Krasovskii functional (LKF) is worked with Kronecker products. The desired state feedback controller can be refined by comprehending a plan of linear matrix inequalities (LMIs). Numerical simulation of complex frameworks demonstrates the comprehensiveness and the ampleness of the proposed method.     

Controlling chaos in permanent magnet synchronous motor based on finite-time stability theory

This paper reports that the performance of permanent magnet synchronous motor (PMSM) degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in PMSM, a nonlinear controller, which is simple and easy to be constructed, is presented to achieve finite-time chaos control based on the finite-time stability theory. Computer simulation results show that the proposed controller is very effective. The obtained results may help to maintain the industrial servo driven system's security operation.     

Finite-time complex projective synchronization of fractional-order complex-valued uncertain multi-link network and its image encryption application

Multi-link networks are universal in the real world such as relationship networks, transportation networks, and communication networks. It is significant to investigate the synchronization of the network with multi-link. In this paper, considering the complex network with uncertain parameters, new adaptive controller and update laws are proposed to ensure that complex-valued multilink network realizes finite-time complex projective synchronization (FTCPS). In addition, based on fractional-order Lyapunov functional method and finite-time stability theory, the criteria of FTCPS are derived and synchronization time is given which is associated with fractional order and control parameters. Meanwhile, numerical example is given to verify the validity of proposed finite-time complex projection strategy and analyze the relationship between synchronization time and fractional order and control parameters. Finally, the network is applied to image encryption, and the security analysis is carried out to verify the correctness of this method.     

Finite-time control of chaotic systems with nonlinear inputs

A finite-time controller is designed for a class of nonlinear systems subject to sector nonlinear inputs. A novel and simple approach is suggested based on the finite-time control principle. The designed sliding-mode controller can drive a chaotic system to track a smooth target signal in a finite time. The chaotic Duffing--Holmes oscillator is used for verification and demonstration.     

Multi-rate sensor fusion-based adaptive discrete finite-time synergetic control for flexible-joint mechanical systems

This paper proposes an adaptive discrete finite-time synergetic control （ADFTSC） scheme based on a multi-rate sensor fusion estimator for flexible-joint mechanical systems in the presence of unmeasured states and dynamic uncertainties. Multi-rate sensors are employed to observe the system states which cannot be directly obtained by encoders due to the existence of joint flexibilities. By using an extended Kalman filter （EKF）, the finite-time synergetic controller is designed based on a sensor fusion estimator which estimates states and parameters of the mechanical system with multi-rate measurements. The proposed controller can guarantee the finite-time convergence of tracking errors by the theoretical derivation. Simulation and experimental studies are included to validate the effectiveness of the proposed approach.     

Dynamic modeling and aperiodically intermittent strategy for adaptive finite-time synchronization control of the multi-weighted complex transportation networks with multiple delays

The idea of network splitting according to time delay and weight is introduced. Based on the cyber physical systems(CPS), a class of multi-weighted complex transportation networks with multiple delays is modeled. The finite-time synchronization of the proposed complex transportation networks model is studied systematically. On the basis of the theory of stability, the technique of adaptive control, aperiodically intermittent control and finite-time control, the aperiodically intermittent adaptive finite-time synchronization controller is designed. The controller designed in this paper is beneficial for understanding the synchronization in multi-weighted complex transportation networks with multiple delays. In addition,the conditions for the existence of finite time synchronization have been discussed in detail. And the specific value of the settling finite time for synchronization is obtained. Moreover, the outer coupling configuration matrices are not required to be irreducible or symmetric. Finally, simulation results of the finite-time synchronization problem are given to illustrate the correctness of the results obtained.     

Control of a unique active vibration isolator with a phase compensation technique and automatic on/off switching

This work examines the characteristics of a unique active vibration isolator and develops a control strategy for it. The proposed active vibration isolator is introduced and its dynamic model is presented. A characterization study is conducted to identify system parameters. It is shown that with a simple proportional feedback the closed-loop system has a very narrow stability margin due to the inherent dynamics of the actuator. To improve the stability of the closed-loop system and enhance the performance of vibration isolation, a phase compensator is incorporated in the control scheme. An optimization problem is formulated to determine the optimum controller parameters by minimizing the 2nd norm of the displacement transmissibility. Both absolute position feedback and relative position feedback are considered. In real time implementation, an automatic on/off switching strategy is devised to take full advantage of both the active isolator and passive isolator. The experimental results show that with the proposed control scheme, the isolator is capable of suppressing base excitations effectively.     

Memory feedback finite-time control for memristive neutral-type neural networks with quantization

The drive-response of memory feedback control design for memristor neural networks of neutral type over finite-time domain is scrutinized in this paper. Notably, the main purpose of this work is to synthesize memory feedback controller in the presence of logarithmic quantizer and actuator saturation to guarantee the finite-time boundedness of the resulting memristive neural networks. On basis of proper Lyapunov–Krasovskii-functional and linear matrix inequalities, new sufficient criterian is established to assure the delay-dependent finite-time stabilization criteria for the addressed network model. Also, by solving the developed linear matrix inequalities, the finite-time memory feedback control law gain matrices could be attained. Eventually, the validations of the proposed mechanism are ultimately explored through two numerical examples.     

A novel adaptive finite-time controller for synchronizing chaotic gyros with nonlinear inputs

In this paper, the problem of the finite-time synchronization of two uncertain chaotic gyros is discussed. The parameters of both the master and the slave gyros are assumed to be unknown in advance. The effects of model uncertainties and input nonlinearities are also taken into account. An appropriate adaptation law is proposed to tackle the gyros' unknown parameters. Based on the adaptation law and the finite-time control technique, proper control laws are introduced to ensure that the trajectories of the slave gyro converge to the trajectories of the master gyro in a given finite time. Simulation results show the applicability and the efficiency of the proposed finite-time controller.     

Passive control of chaotic system with multiple strange attractors

In this paper we present a new simple controller for a chaotic system, that is, the Newton--Leipnik equation with two strange attractors: the upper attractor (UA) and the lower attractor (LA). The controller design is based on the passive technique. The final structure of this controller for original stabilization has a simple nonlinear feedback form. Using a passive method, we prove the stability of a closed-loop system. Based on the controller derived from the passive principle, we investigate three different kinds of chaotic control of the system, separately: the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one, and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the suggested method.     

Base impedance of velocity feedback control units with proof-mass electrodynamic actuators

Control units comprising a proof-mass electrodynamic actuator and accelerometer-sensor pair with a time integrator and fixed gain controller are an effective way to implement velocity feedback control on thin flexible structures. These control units produce active damping provided the fundamental resonance frequency of the actuators is well below that of the structure under control. Control stability limits arise from the actuators fundamental resonances which introduce a 180° phase lag in the sensor-actuator frequency response functions, thus causing the feedback loops to be only conditionally stable. In contrast to previous studies, this paper discusses the response of a control unit with electrodynamic proof-mass actuator in terms of the open- and closed-loop base impedance that it exerts on the structure. This allows for a straight-forward physical interpretation of both stability and control performance. Experimental and simulation results show that the base impedance can be described as the sum of passive and active frequency response functions, where the active part of the control unit response depends on the actuator electromechanical response and also on the response function of the analogue controller circuit. The results show that the base impedance formulation can be effectively used to investigate new designs of both the actuator and electronic controller in order to optimise the stability and performance properties of the control unit.     

考虑运动受限的履带式移动机器人轨迹跟踪控制

针对履带式移动机器人的轨迹跟踪控制问题进行研究,首先,建立了履带式移动机器人的运动学模型和跟踪误差模型；其次,设计了转速有限时间控制和线速度滑模控制的轨迹跟踪控制律,并给出了考虑运动受限作用下的控制律修正表达式；最后,基于MATLAB对所提控制律进行仿真,对比分析了不考虑运动受限情况下跟踪控制效果;结果表明,设计的跟踪控制律能够实现履带式移动机器人对圆轨迹的有效跟踪,且考虑运动受限作用的控制律更加符合实际;文章研究分析了运动受限作用对于移动机器人轨迹跟踪控制的影响,分析结果对其他移动机器人的运动控制研究具有参考价值。     

Finite-time modified combination synchronization of memristive FitzHugh–Nagumo circuit with unknown disturbances

The memristor-based FitzHugh-Nagumo neuron system shows special dynamical behaviors, which make it have a good application in the fields of image processing and signal transmission. The accurate dimensionality reduction model of the system is established, which facilitates the internal interpretation and physical control of the multistability that depends on the initial values. The dynamical behavior analyses of the dimensionality reduction memristive system with different original initial states are developed through bifurcation diagram and Lyapunov index spectrum. Multistability and antimonotonicity with periodic-chaotic bubbles are investigated. The sliding mode control method with a smooth function is designed to achieve the finite-time synchronization of the multistable memristive neuron systems, which make three different behaviors of systems synchronized. The sliding mode controller can enable the system to quickly and smoothly implement combination synchronization within finite time. Numerical simulations show the effectiveness of the sliding mode controller designed.     

Nonsingular terminal sliding mode approach applied to synchronize chaotic systems with unknown parameters and nonlinear inputs

This paper deals with the design of a novel nonsingular terminal sliding mode controller for finite-time synchronization of two different chaotic systems with fully unknown parameters and nonlinear inputs.We propose a novel nonsingular terminal sliding surface and prove its finite-time convergence to zero.We assume that both the master’s and the slave’s system parameters are unknown in advance.Proper adaptation laws are derived to tackle the unknown parameters.An adaptive sliding mode control law is designed to ensure the existence of the sliding mode in finite time.We prove that both reaching and sliding mode phases are stable in finite time.An estimation of convergence time is given.Two illustrative examples show the effectiveness and usefulness of the proposed technique.It is worthwhile noticing that the introduced nonsingular terminal sliding mode can be applied to a wide variety of nonlinear control problems.     

基于Terminal滑模的有限时间混沌同步实现

提出了混沌同步有限时间实现问题，将Terminal滑模控制技术与混沌同步问题相结合，把同步问题视为响应系统的跟踪问题，给出了由线性滑模函数引入非线性项构造Terminal滑模面的充分条件，以及相应Terminal滑模控制器.以主从Duffing系统为例研究验证同步策略的可行性和有效性. 关键词： Terminal滑模 混沌同步 Duffing系统