一类非线性时变系统基于观测器的反馈稳定化

1　引言目前,有关非线性系统的状态反馈控制已取得了许多引人注目的研究结果,其中状态可测是此控制方法中的一个必不可少的假设.在实际中,许多系统的状态是部分可测或不完全可测,故构造观测器,并用估计状态实现反馈控制是一个非常有意义的研究工作.本文研究了一类仿射非线性时变系统基于状态观测器的输出反馈稳定控制问题.首先设计了系统的状态观测器,然后综合控制器和观测器得到了非线性输出反馈控制器,并证明了反馈后闭环系统的指数稳定性.研究结果表明,系统的控制器与观测器可以分离独立进行设计.2　系统的描述及预备知识考虑下列非线性…     

一类不确定模糊模型的输出反馈鲁棒预测控制

针对一类满足扇形界条件的不确定模糊模型描述的非线性系统,提出一种输出反馈鲁棒预测控制方法．该方法将鲁棒预测控制的Min-Max优化问题转化为具有LMI约束的线性目标最小化问题,并且不需系统状态完全可测,仅仅利用系统测量输出和不可测状态的界限值来确定保证闭环系统鲁棒稳定的输出反馈控制器．仿真实验证明了该方法的有效性．     

三相电压型逆变器的一种非线性复合控制策略研究

为了减少在三相电压型逆变器系统中应用精确线性化时选择反馈增益矩阵参数的随机性,提出将精确线性化方法和反步法结合起来应用于此系统中.首先根据非线性微分几何理论,验证了该系统仿射非线性模型满足2输入2输出系统精确线性化的条件.经过非线性坐标变换得到系统的参数严格反馈形式模型,再根据反步法的设计步骤,逐步设计虚拟控制相量和中间控制相量,使系统的状态分量具有渐近稳定性,从而得到原非线性系统的控制模型.最后通过实验验证了该复合控制策略的可行性.     

非线性系统的直接自适应输出反馈监督模糊控制

针对一类单输入单输出非线性不确定系统，提出一种稳定的直接自适应模糊输出反馈监督控制算法，该算法不需要系统的状态完全可测的假设条件，监督控制不仅迫使系统的状态在指定的集合内，而且当模糊自适应控制处于良好的工作状态时，监督控制可以关闭，证明了整个模糊自适应输出反馈控制算法可以保证闭环系统稳定。     

基于神经网络的一类非线性系统自适应输出跟踪

针对一类未知非线性系统,提出了一种输出反馈控制方法.首先,在假设系统状态已 知情况下设计状态反馈控制器,实现跟踪性能;然后,在系统状态不完全可测的情况下,通过 设计高增益观测器对系统的状态进行估计,实现输出反馈控制器设计,证明了所设计的输出 反馈控制器可以获得状态反馈控制器的性能.     

一类非线性系统的扩展状态空间预测控制

针对一类具有输出反馈耦合的离散非线性系统，将过程模型表示为扩展状态空间模型，并利用反馈回路非线性函数在参考轨迹附近的局部线性表示，导出一种具有类似离散PI最优调节器结构并具有未来P步设定值前馈控制的新型预测控制器．因其目标函数中考虑了系统状态的变化，所以控制效果要优于仅考虑预测输出误差的情况．仿真结果表明了它的有效性．     

无未知参数先验信息的非线性自适应观测器设计

研究了一类具有未知参数的非线性系统自适应观测器设计问题．不同于现有结果,本文所研究的非线性系统更为。一般,已知的系统信息更少：1）系统未知参数的范数的上界未知;2）具有关于可测输出非Lipschitz连续的非线性动态;3）系统输出显式地依赖于控制输入．通过设计自适应调节器来估计未知参数范数,从而给出了不基于未知参数先验信息的非线性自适应观测器设计的新方法．所设计的观测器为令局渐近收敛的,即实现了系统状态的渐近重构,确保了未知参数估计的一致有界性．此外,在系统输出不显式地依赖于控制输入的条件下,研究了降维观测器的设计问题．仿真例子验证了本文理论结果的正确性．     

基于广义无源的输入非仿射系统的H∞控制律设计

基于动态耗散的一般理论,提出了具有任意非线性输入端的非线性系统的一种新的控制器设计方法。该方法解决了以下两个问题：１）当系统严格广义无源时,设计非线性输出反馈使闭环系统稳定;２）当系统非广义严格无源时,设计同时具有状态反馈和输出反馈的双闭环控制器,使得闭环系统的内稳且具有Ｈ＾∞干扰衰减。对于线性系统,所设计的问题转化为对ＬＭＩ和ＡＲＥ的求解问题。     

基于遗传算法的输出反馈动态面优化控制

针对一类只有输出信号可测且非线性项含不可测状态的不确定系统,基于输入信号置换思想构建了神经网络状态观测器,结合动态面理论设计了输出反馈自适应控制方案。通过理论分析确定了控制律参数选取范围,保证了闭环控制系统所有信号半全局一致终结有界; 利用遗传算法提出一种参数寻优策略,选取了最优的输入初始值和控制律参数,解决了控制冲击问题,提高了跟踪精度。     

机器人系统输出反馈重复学习轨迹跟踪控制

针对高度非线性多关节机器人的轨迹跟踪问题,提出一类输出反馈重复学习控制算法,使得在只有位置信息可测以及模型信息不确定的条件下即能获得良好的控制品质.非线性滤波器的引入解决了现实中速度信号较难获得的问题,重复学习控制策略实现了对周期性参考输入的渐近稳定跟踪.应用Lyapunov直接稳定性理论证明了闭环系统的全局渐近稳定性.三自由度机器人系统数值仿真结果表明了所提出的输出反馈重复学习控制的有效性.     

Recursive Back‐Stepping Design of An Adaptive Fuzzy Controller for Strict Output Feedback Nonlinear Systems

In this paper, a back‐stepping adaptive fuzzy controller is proposed for strict output feedback nonlinear systems. The unknown nonlinearity and external disturbances of such systems are considered. We assume that only the output of the system is available for measurement. As a result, two filters are constructed to estimate the states of strict output feedback systems. Since fuzzy systems can uniformly approximate nonlinear continuous functions to arbitrary accuracy, the adaptive fuzzy control theory combined with a tuning function scheme is developed to derive the control laws of strict output feedback systems that possess unknown functions. Moreover, the H∞ performance condition is introduced to attenuate the effect of the modeling error and external disturbances. Finally, an example is simulated in order to confirm the applicability of the proposed method.     

Decentralized adaptive control of a class of large-scaleinterconnected nonlinear systems

Decentralized adaptive control design for a class of large-scale interconnected nonlinear systems with unknown interconnections is considered. The motivation behind this work is to develop decentralized control for a class of large-scale systems which do not satisfy the matching condition requirement. To this end, large-scale nonlinear systems transformable to the decentralized strict feedback form are considered. Coordinate-free geometric conditions under which any general interconnected nonlinear system can be transformed to this form are obtained. The interconnections are assumed to be bounded by polynomial-type nonlinearities. Global stability and asymptotic regulation are established using classical Lyapunov techniques. The controller is shown to maintain robustness for a wide class of systems obtained by perturbation in the dynamics of the original system. Furthermore, appending additional subsystems does not require controller redesign for the original subsystems. Finally, the scheme is extended to the model reference tracking problem when global uniform boundedness of the tracking error to a compact set is established     

Adaptive output control of uncertain nonlinear systems with non-symmetric dead-zone input

This paper deals with the adaptive output feedback control problem of a class of uncertain nonlinear systems with an unknown non-symmetric dead-zone nonlinearity. The nonlinear system considered here is dominated by a triangular system without zero dynamics satisfying polynomial growth in the unmeasurable states. An adaptive control scheme is developed without constructing the dead-zone inverse. The proposed adaptive control scheme requires only the information of bounds of the slopes and the breakpoint of dead-zone nonlinearity. The novelty of this paper is that a universal-type adaptive output feedback controller is numerically constructed by using a sum of squares (SOS) optimization algorithm, which ensures the boundedness of all the signals in the adaptive closed-loop without knowing the growth rate of the uncertainties. An example is presented to show the effectiveness of the proposed approach.     

Adaptive practical preassigned finite‐time stability for a class of pure‐feedback systems with full state constraints

This paper focuses on an adaptive practical preassigned finite‐time control problem for a class of unknown pure‐feedback nonlinear systems with full state constraints. Two new concepts, called preassigned finite‐time function and practical preassigned finite‐time stability, are defined. In order to achieve the main result, the pure‐feedback system is first transformed into an affine strict‐feedback nonlinear system based on the mean value theorem. Then, an adaptive preassigned finite‐time controller is obtained based on a modified barrier Lyapunov function and backstepping technique. Finally, simulation examples are exhibited to demonstrate the effectiveness of the proposed scheme.     

Neural networks stabilization and disturbance attenuation for nonlinear switched impulsive systems

In this paper, we address the problem of neural networks (NNs) stabilization and disturbance rejection for a class of nonlinear switched impulsive systems. An adaptive NN feedback control scheme and an impulsive controller for output tracking error disturbance attenuation of nonlinear switched impulsive systems are given under all admissible switched strategy based on NN. The NN is used to compensate for the nonlinear uncertainties of switched impulsive systems, and the approximation error of NN is introduced to the adaptive law in order to improve the tracking attenuation quality of the switched impulsive systems. Impulsive controller is designed to attenuate effect of switching impulse. Under all admissible switching law, impulsive controller and adaptive NN feedback controller can guarantee asymptotic stability of tracking error and improve disturbance attenuation level of tracking error for the overall nonlinear switched impulsive system. Finally, a numerical example is given to demonstrate the effectiveness of the proposed control and stabilization methods.     

Adaptive optimal dynamic surface control of strict‐feedback nonlinear systems with output constraints

In this paper, an adaptive optimal control strategy is proposed for a class of strict‐feedback nonlinear systems with output constraints by using dynamic surface control. The controller design procedure is divided into two parts. One is the design of feedforward controller and the other is the design of optimal controller. To guarantee the satisfaction of output constraints in feedforward controller, nonlinear mapping is utilized to transform the constrained system into an unconstrained system. Neural‐network based adaptive dynamic programming algorithm is employed to approximate the optimal cost function and the optimal control law. By theoretical analysis, all the signals in the closed‐loop system are proved to be semi‐globally uniformly ultimately bounded and the output constraints are not violated. A numerical example illustrates the effectiveness of the proposed scheme.     

Backstepping sliding mode control with FWNN for strict output feedback non-smooth nonlinear dynamic system

An output feedback backstepping sliding mode control scheme was developed for precision positioning of a strict single-input and single-output (SISO) non-smooth nonlinear dynamic system that could compensate for deadzone, dynamic friction, uncertainty and estimations of immeasurable states. An adaptive fuzzy wavelet neural networks (FWNNs) technique was used to provide improved approximation ability to the system uncertainty. The adaptive laws were derived for application to estimate the deadzone and friction parameters using recursive backstepping controller design procedures. In addition, the sliding mode control method was also combined to enforce the robustness of the output feedback backstepping controller against disturbance. The Lyapunov stability theorem was used to prove stability of the proposed control system. The usefulness of the proposed control system was verified by simulations and experiments on a robot manipulator in the presence of a deadzone and friction in the actuator.     

Adaptive neural decentralized control for strict feedback nonlinear interconnected systems via backstepping

An approximation based adaptive neural decentralized output tracking control scheme for a class of large-scale unknown nonlinear systems with strict-feedback interconnected subsystems with unknown nonlinear interconnections is developed in this paper. Within this scheme, radial basis function RBF neural networks are used to approximate the unknown nonlinear functions of the subsystems. An adaptive neural controller is designed based on the recursive backstepping procedure and the minimal learning parameter technique. The proposed decentralized control scheme has the following features. First, the controller singularity problem in some of the existing adaptive control schemes with feedback linearization is avoided. Second, the numbers of adaptive parameters required for each subsystem are not more than the order of this subsystem. Lyapunov stability method is used to prove that the proposed adaptive neural control scheme guarantees that all signals in the closed-loop system are uniformly ultimately bounded, while tracking errors converge to a small neighborhood of the origin. The simulation example of a two-spring interconnected inverted pendulum is presented to verify the effectiveness of the proposed scheme.     

Prescribed performance adaptive neural output feedback dynamic surface control for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics

This paper studies the output feedback tracking control problem for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics using a prescribed performance adaptive neural dynamic surface control design approach. A nonlinear mapping technique is employed to address the state constraints. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. The unmodeled dynamics is addressed by introducing an available dynamic signal. Subsequently, we construct the controller and parameter adaptive laws using a backstepping technique. Based on Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobally uniformly ultimately bounded and that the tracking error always remains within the prescribed performance bound. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.