H∞ synchronization of chaotic systems using output feedback control design

This article investigates the H_∞ synchronization problem for a general class of chaotic systems. Based on Lyapunov theory, linear matrix inequality (LMI) and linear matrix equality (LME) formulation, the output feedback controller is established to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance to an H_∞-norm constraint. Two illustrative examples are provided to demonstrate the effectiveness of the developed theoretical results.     

A theoretical and experimental study of advanced control methods to suppress vibrations in a small square plate subject to temperature variations

In this paper, we seek to develop an efficient controller for vibration reduction in a small square plate clamped on all edges. The plate mimics a piece of an aircraft's skin. Small plate size results in higher natural frequencies than normally investigated in literature. Such high-frequency systems are more susceptible to time delays. In addition, the control system must be able to operate over a wide range of temperatures, a requirement for in-flight vibration suppression systems. We investigate two methodologies (sliding mode control, and an adaptive H_∞ control) for control over a wide range of temperatures. Theoretical and experimental studies are conducted and produced varying results. The best theoretical and experimental results are obtained with the adaptive H_∞ controller.     

Optimal tracking control with zero steady-state error for time-delay systems with sinusoidal disturbances

The problem of optimal tracking control with zero steady-state error for linear time-delay systems with sinusoidal disturbances is considered. Based on the internal model principle, a disturbance compensator is constructed such that the system with external sinusoidal disturbances is transformed into an augmented system without disturbances. By introducing a sensitivity parameter and expanding power series around it, the optimal tracking control problem can be simplified into the problem of solving an infinite sum of linear optimal control series without time-delay and disturbance. The obtained optimal tracking control law with zero steady-state error consists of accurate linear state feedback terms and a time-delay compensating term, which is an infinite sum of an adjoint vector series. The accurate linear terms can be obtained by solving a Riccati matrix equation and a Sylvester equation, respectively. The compensation term can be approximately obtained through a recursive algorithm. A numerical simulation shows that the algorithm is effective and easily implemented, and the designed tracking controller is robust with respect to the sinusoidal disturbances.     

ROBUST VIBRATION CONTROL OF A BEAM USING THE H∞-BASED CONTROLLER WITH MODEL ERROR COMPENSATOR

The vibration control of a flexible beam subjected to arbitrary, unmeasurable disturbance forces is investigated in this paper. The beam is analyzed by using modal expansion theorem. The independent modal space control is adopted for the active vibration control. Discrete sensors and actuators are used here. The modal filters are used as the state estimator to obtain the modal co-ordinates and modal velocities for the state feedback control. Because of the existence of the disturbance forces, the vibration control only with the state feedback control law cannot suppress the vibration well. The method of disturbance forces cancellation is then added in the feedback loop. In order to implement the disturbance forces cancellation, the unknown disturbance forces must be observed. The model error compensator is employed to observe the unknown disturbance modal forces for the direct cancellation. After the implementation of the disturbance modal forces cancellation, there are still some residual disturbance modal forces which excite the beam. The disturbance attenuation problem is of concern in the design of the state feedback control law. For ensuring that influence of the residual disturbance modal forces is reduced to an acceptable level, the robust static H_∞ state feedback controller is designed. The vibration control performances of the feedback control with the H_∞ controller and the disturbance forces cancellation are discussed.     

Robust chaos synchronization of noise-perturbed chaotic systems with multiple time-delays

The aim of this paper is to propose an output coupling and feedback scheme, which is not only to guarantee the asymptotic synchronization between the master and the slave chaotic systems with multiple time-delays but also to attenuate the effects of noise perturbation on the overall error system to a prescribed level in terms of the performance index H_∞-norm. The output coupling and feedback gain is derived on the basis of the Lyapunov theory and the linear matrix inequality (LMI) technique. Some numerical examples are given to demonstrate the effectiveness of the main results.     

Energy-to-peak control for seismic-excited buildings with actuator faults and parameter uncertainties

This paper deals with the problem of robust reliable energy-to-peak controller design for seismic-excited buildings with actuator faults and parameter uncertainties. It is assumed that uncertainties mainly exist in damping and stiffness of the buildings because they are difficult to be measured precisely. The objective of designing controllers is to guarantee the asymptotic stability of closed-loop systems and attenuate disturbance from earthquake excitation. Energy-to-peak performance is believed to be of great significance when conditions and requirements of active building vibration control are carefully considered. Based on energy-to-peak control theory and linear matrix inequality techniques, a new approach for reliable building vibration control with satisfactory energy-to-peak performance is presented. An n-degree-of-freedom linear building structure under earthquake excitation is analyzed and simulations are employed to validate the effectiveness of the proposed approach in reducing seismic-excited building vibration. Some comparisons are also made between energy-to-peak control systems and H_∞ control systems to further prove the importance of the method raised in this paper.     

Robust adaptive fuzzy neural tracking control for a class of unknown chaotic systems

In this paper, an adaptive fuzzy neural controller (AFNC) for a class of unknown chaotic systems is proposed. The proposed AFNC is comprised of a fuzzy neural controller and a robust controller. The fuzzy neural controller including a fuzzy neural network identifier (FNNI) is the principal controller. The FNNI is used for online estimation of the controlled system dynamics by tuning the parameters of fuzzy neural network (FNN). The Gaussian function, a specific example of radial basis function, is adopted here as a membership function. So, the tuning parameters include the weighting factors in the consequent part and the means and variances of the Gaussian membership functions in the antecedent part of fuzzy implications. To tune the parameters online, the back-propagation (BP) algorithm is developed. The robust controller is used to guarantee the stability and to control the performance of the closed-loop adaptive system, which is achieved always. Finally, simulation results show that the AFNC can achieve favourable tracking performances.     

Robust chaos synchronization based on adaptive fuzzy delayed feedback ${\bf{\mathcal{H}}}_{\bf{\infty}}$ control

In this paper, we propose a new adaptive H_￥\mathcal H_\infty synchronization strategy, called an adaptive fuzzy delayed feedback H_￥\mathcal H_\infty synchronization (AFDFHS) strategy, for chaotic systems with uncertain parameters and external disturbances. Based on Lyapunov–Krasovskii theory, Takagi–Sugeno (T–S) fuzzy model and adaptive delayed feedback H_￥\mathcal H_\infty control scheme, the AFDFHS controller is presented such that the synchronization error system is asymptotically stable with a guaranteed H_￥\mathcal{H}_{\infty } performance. It is shown that the design of the AFDFHS controller with adaptive law can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed AFDFHS approach.     

混沌系统自适应追踪控制新方法

提出一种混沌系统自适应追踪控制任意参考信号的新方法.该方法是通过预先设计出补偿控制器将混沌系统状态变量对参考信号的追踪控制问题转化为同结构混沌系统状态变量的自适应同步问题,再通过设计出自适应控制器,使同结构混沌系统全局渐近达到同步,追踪控制器为补偿控制器和自适应控制器的代数和.基于Lyapunov稳定性原理,理论上严格证明了利用本方法所设计追踪控制器的正确性.最后,以超混沌Chen系统为控制对象,利用本方法设计出追踪控制器完成了对不动点,正、余弦信号,同结构混沌系统状态变量,异结构混沌系统状态变量的追踪控 关键词： 自适应追踪控制 补偿控制器 自适应控制器 追踪控制器     

基于Hamilton模型的永磁同步风力发电系统中混沌运动的H∞控制

针对永磁同步风力发电系统的混沌运动现象, 提出了基于系统Hamilton模型的H_∞控制方案, 使得系统脱离混沌, 运行稳定. 首先将永磁同步风力发电系统模型经过一系列状态变换, 转化为类Lorenz经典数学模型, 并验证了系统在一定参数区域内存在混沌现象. 随后基于Hamilton系统充分利用系统物理结构和无需补偿“无功力”的优点, 建立了混沌系统的Hamilton模型, 并考虑了系统存在外扰情况下的H_∞控制方法. 本文所设计的控制器不仅简单易实现而且反映了系统内部结构以及动态特性的信息. 仿真实验证明了控制器的有效性.     

Robust control synthesis for seat suspension systems with actuator saturation and time-varying input delay

The control synthesis problem is investigated in this paper for a class of semi-active seat suspension systems with norm-bounded parameter uncertainties, time-varying input delay and actuator saturation. A vertical vibration model of human body is introduced in order to make the modeling of seat suspension systems more precise. By employing a delay-range-dependent Lyapunov function and exploring the property of the saturation nonlinearity, the existence conditions of the desired state-feedback controller are derived in terms of linear matrix inequalities (LMIs). The controller is derived by solving the LMIs and the corresponding closed-loop system is asymptotically stable with a guaranteed H_∞ performance. A design example is presented to show the usefulness and advantages of the developed theoretical results.     

Adaptive synchronization of chaos in permanent magnet synchronous motors based on passivity theory

An adaptive synchronization control method is proposed for chaotic permanent magnet synchronous motors based on the property of a passive system.We prove that the controller makes the synchronization error system between the driving and the response systems not only passive but also asymptotically stable.The simulation results show that the proposed method is effective and robust against uncertainties in the systemic parameters.     

Adaptive synchronization of chaos in permanent magnet synchronous motors based on passivity theory

An adaptive synchronization control method is proposed for chaotic permanent magnet synchronous motors based on the property of a passive system. We prove that the controller makes the synchronization error system between the driving and the response systems not only passive but also asymptotically stable. The simulation results show that the proposed method is effective and robust against uncertainties in the systemic parameters.     

Adaptive fuzzy nonlinear inversion-based control for uncertain chaotic systems

<正>This paper presents a robust output feedback control method for uncertain chaotic systems,which comprises a nonlinear inversion-based controller with a fuzzy robust compensator.The proposed controller eliminates the unknown nonlinear function by using a fuzzy system,whose inputs are not the state variables but feedback error signals.The underlying stability analysis as well as parameter update law design are carried out by using the Lyapunov-based technique.The proposed method indicates that the nonlinear inversion-based control approach can also be applied to uncertain chaotic systems.Theoretical results are illustrated through two simulation examples.     

Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control

Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated.The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach.Based on Lyapunov’s stability theory,linear and nonlinear feedback control of adaptive H∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an H∞-norm constraint.Adaptive H∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems.Numerical simulations are also given to identify theeffectiveness of the theoretical analysis.     

Robust synchronization of a class of uncertain chaotic systems based on quadratic optimal theory and adaptive strategy

This paper presents a chaos synchronization method for a class of uncertain chaotic systems using the combination of an optimal control theory and an adaptive strategy. A quadratic optimal regulator and an adaptive control are used to represent the controller's structure. The asymptotic stability of the corresponding error dynamical system is guaranteed through Lyapunov stability analysis. The proposed controller is employed in two uncertain chaotic Lu systems, and their promising performances are illustrated.     

基于自适应滑模控制的不同维分数阶混沌系统的同步

针对异结构不同维分数阶混沌系统的广义同步问题进行研究, 设计了一种将滑模变结构理论和自适应控制理论相结合的方法.通过设计一种对外界干扰具有强鲁棒性的分数阶滑模面, 以及构造合适的自适应滑模控制器, 该控制器将系统的运动控制到滑模面上, 使系统轨道沿滑动模运动到所需的控制状态, 最终实现了两个不同维异结构混沌系统之间的广义同步.以四维超混沌Chen系统和三维Chen混沌系统为例, 对这两个系统分别进行升维和降维的同步仿真. 仿真模拟结果表明, 运用本文设计的控制器, 经过短暂的时间, 两系统的广义误差变量始终平稳地趋于零, 即证明了这种控制器的有效性. 关键词： 分数阶混沌系统 异结构 自适应滑模控制 混沌同步     

ADAPTIVE NONLINEAR FEEDBACK CONTROL OF CHAOTIC SYSTEMS BASED ON REDUCED PARAMETER QUADRATIC PREDICTORS

An adaptive nonlinear feedback-control method is proposed to control continuous-time chaotic dynamical systems, where the adaptive nonlinear controller acts on only one-dimensional error signal between the desired state and the observed chaotic state of a system. The reduced parameter adaptive quadratic predictor used in adaptive feedback cancellation of the nonlinear terms can control the system to any desired state. Computer simulation results on the Lorenz system are shown to demonstrate the effectiveness of this feedback-control method.     

Design of a broadband active silencer using μ-synthesis

A robust spatially feedforward controller is developed for broadband attenuation of noise in ducts. To meet the requirements of robust performance and robust stability in the presence of plant uncertainties, a μ-synthesis procedure via D–K iteration is exploited to obtain the optimal controller. This approach considers uncertainties as modelling errors of the nominal plant in high frequency and is implemented using a floating point digital signal processor (DSP). Experimental investigation was undertaken on a finite-length duct to justify the proposed controller. The μ- controller is compared to other control algorithms such as the H₂ method, the H_∞ method and the filtered-U least mean square (FULMS) algorithm. Experimental results indicate that the proposed system has attained 25.8 dB maximal attenuation in the band 250–650 Hz.     

H∞ Feedback control and Fx-LMS feedforward control for car engine vibration attenuation

The attenuation of the low frequency noise produced by the car engine vibration has been the major concern of the automotive community with the objective to increase the comfort of the driver and the passengers. The chassis subframe is the part responsible for transmission of the engine vibration to the car body through the engine mounts. At the beginning of this paper, we briefly describe the test rig we used and which has been experimentally investigated by using system identification. Then the experimental results of the feedforward control strategy and the achieved performance are briefly presented. These results are then compared to the feedback control method utilizing H_∞ strategy which allows us to design a robust controller requiring less sensors. Furthermore, a broadband noise attenuation could be achieved by using a robust feedback controller in the real time test.