Adaptive synchronization for two identical generalized Lorenz chaotic systems via a single controller

This paper presents a systematic design procedure to synchronize two identical generalized Lorenz chaotic systems based on a sliding mode control. In contrast to the previous works, this approach only needs a single controller to realize synchronization, which has considerable significance in reducing the cost and complexity for controller implementation. A switching surface only including partial states is adopted to ensure the stability of the error dynamics in the sliding mode. Then an adaptive sliding mode controller (ASMC) is derived to guarantee the occurrence of the sliding motion even when the parameters of the drive and response generalized Lorenz systems are unknown. Last, an example is included to illustrate the results developed in this paper.     

基于神经网络的一类非线性时滞系统自适应控制器设计

针对一类带有扰动和未知时滞的非线性系统,通过反步方法设计一种鲁棒自适应控制器.提出了一种新的Lyapunov-Krasovskii泛函,补偿了未知时滞项的不确定性.引入一种合适的偶函数,避免了控制器的奇异性问题.通过Lyapunov直接方法,证明了所设计的控制器能保证闭环系统所有信号全局一致最终有界.     

Adaptive synchronization of a modified and uncertain chaotic Van der Pol-Duffing oscillator based on parameter identification

This paper considers the problem of adaptive synchronization and parameter identification of an uncertain chaotic oscillator. Using recent results on adaptive control, we design a controller which enables both the synchronization of two unidirectionally coupled modified Van der Pol-Duffing oscillators and the estimation of unknown parameters of the drive oscillator.     

A novel adaptive controller for two-degree of freedom polar robot with unknown perturbations

In industrial applications, the performance of robot manipulators is always affected due to the presence of uncertainties and disturbances. This paper proposes a novel adaptive control scheme for robust control of robotic manipulators perturbed by unknown uncertainties and disturbances. First, an active sliding mode controller is designed and a sufficient condition is obtained guarantying reachability of the states to hit the sliding surface in finite time. Then, based on a Lyapunov function candidate an adaptive switching gain is derived which make the controller capable to bring the tracking error to zero without any disturbance exerted upon the stability. By virtue of this controller it can be shown that the controller can track the desired trajectories even in the presence of unknown perturbations. For the problem of determining the control parameters Particle Swarm Optimization (PSO) algorithm has been employed. Our theoretic achievements are verified by numerical simulations.     

Application of a rule self-regulating fuzzy controller for robotic deburring on unknown contours

Most metal parts made by machining operations contain burrs, which can be removed by robotic manipulators. Modeling a deburring robot on unknown contours is a relatively difficult task. In this study, we present a novel compliant motion controller that uses a modified on-line rule self-regulating fuzzy control (RSFC) and depends on no mathematical models. In the proposed controller, a Cartesian robot on which a grinding tool is mounted rigidly performs edge following (precision deburring) and chamfering on unknown contours. The manipulator is controlled along the tangential direction of a constrained surface and its cutting force is maintained at a desired level. Experimental results demonstrate the effectiveness of this control strategy in terms of automatically deburring the edges of parts with an unknown geometrical configuration.     

Adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts

This paper investigates the design of an output feedback adaptive stabilization controller for a nonholonomic chained system with strong nonlinear drifts, including modeled nonlinear dynamics, unmodeled dynamics, and dynamics modeled with unknown parameters. Also the virtual control directions of the system are unknown. The purpose is to design a nonlinear output feedback switching controller such that the closed loop system is globally asymptotically stable. A novel observer and estimator are introduced for states and parameter estimates, respectively. A constructive procedure of design for an output feedback adaptive controller is given, by using the integrator backstepping approach and based on the proposed observer and parameter estimator. An example is given to show the effectiveness of the proposed scheme.     

Stabilization of unknown nonlinear systems using a cognition-based framework

This paper considers an adaptive control method based on a cognition-based framework to stabilize unknown nonlinear systems. In order to fulfill the task of stabilization, neither the information about the systems dynamical structure nor the knowledge about system physical behaviors, but the system states, which are assumed as measurable, are required. The structure of the proposed controller consists of three parts. The first part is based on a recurrent neural network (RNN) to be used for local identification of the unknown nonlinear system in real time. The network can be utilized as system characteristics, which is further used to design the controller within the third part. In the second part, the set of the given input values leading to stable behavior of the closed-loop system will be calculated numerically with a geometrical criterion based on a suitable definition of quadratic stability. In the third part, a suitable control input value is chosen accordingly to a time-relevant criteria from the set of input values generated in the second part of the controller. These three parts and their internal connections are arranged within a so-called cognition framework. The proposed cognitive controller is able to gain useful knowledge (with local validity) and define autonomously a suitable control input with respect to the requirements of the time-relevant criteria. Numerical examples are shown to demonstrate the successful application and performance of the method. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adaptive fuzzy sliding-mode control for multi-input multi-output chaotic systems

This paper describes an adaptive fuzzy sliding-mode control algorithm for controlling unknown or uncertain, multi-input multi-output (MIMO), possibly chaotic, dynamical systems. The control approach encompasses a fuzzy system and a robust controller. The fuzzy system is designed to mimic an ideal sliding-mode controller, and the robust controller compensates the difference between the fuzzy controller and the ideal one. The parameters of the fuzzy system, as well as the uncertainty bound of the robust controller, are tuned adaptively. The adaptive laws are derived in the Lyapunov sense to guarantee the asymptotic stability and tracking of the controlled system. The effectiveness of the proposed method is shown by applying it to some well-known chaotic systems.     

Adaptive feedback control for a class of chaotic systems

In this paper, the problem of control for a class of chaotic systems is considered. The nonlinear functions of chaotic systems are not necessarily to satisfy the Lipsichtz conditions, but bounded by a polynomial with the gains unknown. Employing adaptive method, the corresponding controller which renders the closed-loop system asymptotically stable is constructed. The designed controller is robust with respect to certain class of disturbances in the chaotic systems. Simulations on unified chaotic systems and Arneodo chaotic system are performed and the results verify the validity of the proposed techniques.     

Synchronizing chaotic systems using control based on a special matrix structure and extending to fractional chaotic systems

This work presents a direct approach to design stabilizing controller based on a special matrix structure to synchronize chaotic systems and extends the approach to synchronize fractional chaotic systems. With this method, chaos synchronization is implemented in Lorenz chaotic systems with known parameters and the same to Lorenz chaotic systems with unknown parameters. Especially, fractional Lorenz chaotic system with unknown parameters is synchronized by fractional Chen chaotic system too. Numerical simulations confirm the effectiveness of the method proposed.     

Design of a nonsingular adaptive fuzzy backstepping controller for electrostatically actuated microplates

This paper adopts some alternative strategies to design a nonlinear controller for double electrostatically actuated microplates. The novel design is carried out to solve the singularity problem reported in many articles due to the use of the Taylor expansion to simplify the electrostatic force. The nonlinear governing partial differential equation is converted to the modal equation using the Galerkin method. Then, based on the Lyapunov stability criterion, a fuzzy backstepping controller facilitated by prescribed performance functions is applied to the non-affine system to extend the travel range beyond the pull-in region and capture the structural and nonstructural uncertainties that exist in the practical systems. The present work also aims to bring satisfactory transient and steady-state performance indices to the system. Moreover, unknown time-varying delays as the indispensable part of practical systems are considered in the proposed control scheme to suppress the delays occurring in the measurement of the states by constructing Lyapunov–Krasovskii function. The accuracy of the modal equation in both the static and dynamic analysis is verified through a meshless method as a direct solution of the partial differential equation. The proposed controller guarantees that all the closed-loop signals are semi-globally, uniformly ultimately bounded, and the error evolves within the decaying prescribed bounds. Finally, the proposed controller demonstrates its feasibility to extend the travel range within and beyond the pull-in range despite the unknown uncertainties and time-varying delays which exist in the system.     

不确定关联时滞大系统的自适应分散镇定控制

针对时变的满足一定匹配条件的不确定关联时滞大系统,利用自适应界化技术,给出了设计分散镇定控制器的自适应的方法.其特点是在假设中系统不确定项是有界的,但界是未知的,且在关联项存在时变时滞的情况下证明了闭环自适应系统的渐近稳定性.最后举例说明了该方法的有效性.     

Nonlinear control of a variable displacement axial piston pump

In this contribution a mathematical model of a variable displacement axial piston pump controlled by a solenoid valve is derived. For the purpose of a controller design the mathematical model is simplified using singular perturbation arguments. The goal of the controller design is to track prescribed trajectories in the load pressure for arbitrary unknown load conditions. The control concept being proposed comprises a feedforward controller and a nonlinear backstepping controller combined with a load estimator for the trajectory error system. The feasibility of this control concept is shown by means of measurements on a test-stand. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

具有未知增长率的非线性系统的一般适应控制

阐明对于一类不确定系统在适当的条件下如何设计适应输出反馈控制器.这个不确定性来源于系统的未知参数.设计了一般输出反馈控制器结合Barbalat's引理从而证明系统的所有状态全局稳定.     

Design,modelling and simulation of a new nonlinear and full adaptive backstepping speed tracking controller for uncertain PMSM

In this study, a new nonlinear and full adaptive backstepping speed tracking control scheme is developed for an uncertain permanent magnet synchronous motor (PMSM). Except for the number of pole pairs, all the other parameters in both PMSM and load dynamics are assumed unknown. Three phase currents and rotor speed are supposed to be measurable and available for feedback in the controller design. By designing virtual control inputs and choosing appropriate Lyapunov functions, the final control and parameter estimation laws are derived. The overall control system possesses global asymptotic stability; all the signals in the closed loop system remain bounded, according to stability analysis results based on Lyapunov stability theory. Further, the proposed controller does not require computation of regression matrices, with the result that take the nonlinearities in quite general. Simulation results clearly exhibit that the controller guarantees tracking of a time varying desired reference speed trajectory under all the uncertainties in both PMSM and load dynamics without singularity and overparameterization. The results also show that all the parameter estimates converge to their true values on account of the fact that reference speed signal chosen to be sufficiently rich ensures persistency of excitation condition. Consequently, the proposed controller ensures strong robustness against all the parameter uncertainties and unknown bounded load torque disturbance in the PMSM drive system. Numerical simulations demonstrate the performance and feasibility of the proposed controller.     

Finite time control of a class of nonlinear switched systems in spite of unknown parameters and input saturation

This article is devoted to the problem of robust stabilization of uncertain nonlinear switched systems with canonical structure. It is assumed that the constant parameters of the subsystems are unknown and cannot be adopted in the controller design. In addition, the dynamics of the subsystems are perturbed via modeling errors and external disturbances. The effects of unknown actuator saturation are compensated via proper adaptive control signals. The derived controller is based on the terminal sliding mode theory and does not need any prior knowledge about the bounds of the lumped uncertain terms. It is proved that once the system states reach the prescribed sliding manifold in a finite time interval, the whole system becomes insensitive to both the lumped uncertainties and the switching dynamics of the system. The common assumption of having known quadratic Lyapunov functions for the subsystems is relaxed and the derived adaptive approach does not force any limitation on the switching signal of the system. Subsequently, non-conservative conditions are provided to guarantee the global finite time bounded stability of the equilibrium state for the overall uncertain nonlinear switched system under arbitrary switching signals. A numerical computer simulation demonstrates the robust performance of the proposed controller.     

一类参数不确定系统的输出反馈自适应稳定控制设计

研究一类n阶、相对阶为n-m(n为任意自然数,m≤n为非负整数)参数不确定系统的输出反馈自适应镇定控制设计问题.所给出的控制器适用于相对阶为n-m的n阶系统.通过引入一个新型的3n+2m阶动态补偿器,构造性地给出了输出反馈自适应镇定控制器的显式表达.所设计的控制器使得闭环系统所有信号有界或渐近稳定.     

Speed and current regulation of a permanent magnet synchronous motor via nonlinear and adaptive backstepping control

This paper proposes a new speed and current control scheme for a Permanent Magnet Synchronous Motor (PMSM) by means of a nonlinear and adaptive backstepping design. All the parameters in both PMSM and load dynamics are considered unknown. It is assumed that all state variables are measurable and available for feedback in the controller design. The final control and parameter estimation laws are derived by the design of the virtual control inputs and the Lyapunov function candidate. The overall control system is asymptotically stable according to stability analysis results based on Lyapunov stability theory. Simulation results clearly show that the controller guarantees tracking of a time varying reference speed owing to the fact that the speed and current tracking errors asymptotically converge to zero despite all the parameter uncertainties/perturbations and load torque disturbance variation. Numerical simulations reveal the performance and feasibility of the proposed controller.     

Adaptive synchronization for a unified chaotic system with uncertainty

A new adaptive controller is designed to synchronize of a unified chaotic system with uncertainty (unknown parameter, noise perturbation, etc.). It is implemented by using variable structure control. The controller designed here only uses the derivative information of the uncertainty. Even if the uncertainty is time-varying or unbounded, as long as its derivative is bounded, the adaptive controller can guarantee the synchronization of the unified chaotic system with uncertainty. Finally, digital simulation is carried out for Lorenz system, and the results verify the effectiveness of the proposed method.     

受扰不确定混沌系统的双路组合函数投影同步

研究了具有未知参数和外界扰动的多个混沌系统之间的双路组合函数投影同步问题.首先给出了由四个混沌驱动系统和两个混沌响应系统组成的双路组合函数投影同步系统的定义,然后以Lyapunov稳定性理论和不等式变换方法为分析依据,设计了鲁棒自适应控制器和参数自适应律,使得两路同步系统中的响应系统和驱动系统按照相应的函数比例因子矩阵实现同步,并有效克服未知有界干扰和未知参数的影响.相应的理论分析和数值仿真证明了该同步方案的可行性和有效性.