Design of adaptive block backstepping controllers for uncertain nonlinear dynamic systems with n blocks

Based on the Lyapunov stability theorem, a design methodology of adaptive block backstepping control is proposed in this article for a class of multi-input systems with matched and mismatched perturbations to solve regulation problems. The systems to be controlled contain n blocks' dynamic equations, hence n???1 virtual input controllers are firstly designed so that the state variables of first n???1 blocks are asymptotically stable if each virtual control input is equal to the state variable of next block. Then the control input is designed in the last nth block to ensure asymptotic stability for the whole state variables even if the perturbations exist. In addition, adaptive mechanisms are embedded in each virtual input function and control input, so that the upper bound of perturbations is not required to be known beforehand. Finally, a numerical example is given for demonstrating the feasibility of the proposed control scheme.     

动态不确定非线性系统直接自适应模糊backstepping控制

对一类单输入单输出动态不确定非线性系统,提出一种直接自适应模糊backstepping和小增益相结合的控制方法.设计中,首先用模糊逻辑系统逼近虚拟控制器:其次把自适应模糊控制和backstepping控制设计技术相结合.给出了直接自适应模糊控制设计方法.最后基于Lyapunov函数和小增益方法证明了整个闭环系统的稳定性.仿真实例进一步验证了所提方法的有效性.     

一类不确定非线性系统反步自适应神经网络控制研究

针对合有高阶不确定扰动项且不可参数线性化的一类非线性系统，采用反步递推方法设计基于多层神经网络的自适应控制器，多层神经网络可较好地逼近非线性系统，其权值能在系统先验知识不多的情况下在线调整，给出了神经网络Lyapunov意义下稳定的在线自适应律，在设计控制器的过程中，采用类加权形式Lyapunov函数，使得控制器能有效处理自适应控制奇异性问题，仿真结果表明，该控制器对系统参数的不确定性和有界干扰具有一定的鲁棒性，并能保证闭环系统全局稳定。     

Design of a simplified adaptive fuzzy backstepping control for uncertain discrete-time nonlinear systems

This paper presents a simplified adaptive fuzzy backstepping control for uncertain discrete-time nonlinear systems. It is assumed that the systems are described by a discrete-time equation with nonlinear uncertainties to be viewed as the modelling errors and the unknown external disturbances, and the states are observed with measurement noises. To design the simplified adaptive fuzzy backstepping control, the modelling errors are approximated by using the fuzzy inference approach based on the extended single-input rule modules, and the estimates for the unmeasurable states and the adjustable parameters are derived by using the weighted and its simplified weighted least squares estimators. It is proved that the states are ultimately bounded, and the estimation errors remain in the vicinity of zero. The effectiveness of the proposed approach is indicated through the simulation experiment of a simple numerical system.     

Robust adaptive tracking control for a class of mechanical systems with unknown disturbances under actuator saturation

A robust adaptive tracking control scheme is presented for a class of multiple‐input and multiple‐output mechanical systems with unknown disturbances under actuator saturation. The unknown disturbances are expressed as the outputs of a linear exogenous system with unknown coefficient matrices. An adaptive disturbance observer is constructed for the online disturbance estimation. An actuator saturation compensator is introduced to attenuate the adverse effects of actuator saturation. The adaptive backstepping method is then applied to design the robust adaptive tracking control law. It is proved that the designed control law makes the system outputs track the desired trajectories and guarantees the global uniform ultimate stability of the closed‐loop control system. Simulations on a two‐link robotic manipulator verify the effectiveness of the proposed control scheme.     

Robust adaptive backstepping control for a class of uncertain nonlinear systems based on disturbance observers

In this paper, a novel robust adaptive control scheme for a class of uncertain nonlinear systems is proposed using disturbance observer and backstepping method.Firstly, a disturbance observer is developed using radial basis function(RBF) neural network.The parameter updated law of the RBF neural network is given for monitoring subsystem disturbance well.The robust adaptive control scheme is then presented with backstepping method based on the designed disturbance observer.Semiglobal uniform ultimate bounded...     

一类不确定分数阶混沌系统同步的自适应滑模控制方法

针对一类系统不确定及受外界干扰的分数阶混沌系统,本文首先将分数阶微积分应用到滑模控制中,构造了一个具有分数阶积分项的滑模面.针对系统不确定及外界干扰项,基于分数阶Lyapunov稳定性理论与自适应控制方法,设计了一种滑模控制器以及分数阶次的参数自适应律,实现了两不确定分数阶混沌系统的同步控制,并辨识出相应误差系统中不确定项及外界干扰项的边界.在分数阶系统稳定性分析中使用的分数阶Lyapunov稳定性理论及相关函数都可以很好地运用到其它分数阶系统同步控制方法中.最后数值仿真验证了所提控制方法的可行性与有效性.     

Observer-based adaptive fuzzy backstepping control of uncertain nonlinear pure-feedback systems

In this paper,a new fuzzy adaptive control approach is developed for a class of SISO uncertain pure-feedback nonlinear systems with immeasurable states.Fuzzy logic systems are utilized to approximate the unknown nonlinear functions;and the filtered signals are introduced to circumvent algebraic loop systems encountered in the implementation of the controller,and a fuzzy state adaptive observer is designed to estimate the immeasurable states.By combining the adaptive backstepping technique,an adaptive fuzzy output feedback control scheme is developed.It is proven that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded(SGUUB),and the observer and tracking errors converge to a small neighborhood of the origin by appropriate choice of the design parameters.Simulation studies are included to illustrate the efectiveness of the proposed approach.     

Adaptive backstepping controller design for nonlinear uncertain systems using fuzzy neural systems

In this article, we propose an adaptive backstepping control scheme using fuzzy neural networks (FNNs), ABC_FNN, for a class of nonlinear non-affine systems in non-triangular form. The nonlinear non-affine system contains the uncertainty, external disturbance or parameters variations. Two kinds of FNN systems are used to estimate the unknown system functions. According to the FNN estimations, the adaptive backstepping control (ABC_FNN) signal can be generated by backstepping design procedure such that the system output follows the desired trajectory. To ensure robustness and performance, a proportional-integral-surface function and robust controller are designed to improve the control performance. Based on the Lyapunov stability theory, the stability of a closed-loop system is guaranteed and the adaptive laws of the FNN parameters are obtained. This approach is also valid for nonlinear affine system with uncertainty or disturbance. The uncertainty and disturbance terms are estimated by FNNs and treated by the ABC_FNN scheme. Finally, the effectiveness of the proposed ABC_FNN is demonstrated through the simulation of controlling a nonlinear non-affine system and the continuously stirred tank reactor plant to demonstrate the performances of our approach.     

An adaptive control with optimal disturbances rejection

This paper provides a way to optimize the overall disturbances rejection performance of the adaptive control system in the presence of unknown external disturbances.Especially,the updatable non-empty admissible model set,which is consistent to the a priori knowledge of the plant parameter and the online measurements,is computed.With the overall system performance as the criteria,the nominal model is optimally chosen within the admissible model set.The optimal nominal model is subsequently used to synthesize the optimal closed-loop controller based on the 1 design methodology.Combining the above two aspects,an optimal adaptive control scheme is proposed.Because of the consistency of the identification criteria and control object,the adaptive control scheme proposed in this paper can achieve the overall optimal disturbances rejection performance,and the effect of the interplay between the identification and control of the adaptive system can be handled effectively.In addition,the computable optimal performance is also provided.     

一类非参数不确定系统的自适应重复学习控制

本文针对一类非参数不确定系统提出一种全限幅自适应重复学习控制方法.利用期望轨迹的周期特性,构造周期性期望控制输入,并基于Lyapunov方法设计自适应重复学习控制器,实现系统对周期性期望轨迹的高精度跟踪,且无需已知非参数不确定性的上界.设计全限幅学习律估计未知的期望控制输入,保证估计值被限制在指定的界内.同时,通过构造完全平方式消除部分误差相关项,控制器设计中可避免使用符号函数,从而抑制控制器抖振问题.最后,基于Lyapunov方法对误差收敛性进行了分析,并通过仿真对比验证本文所提方法的有效性.     

Adaptive fuzzy observer backstepping control for a class of uncertain nonlinear systems with unknown time-delay

In this paper, a new adaptive fuzzy backstepping control approach is developed for a class of nonlinear systems with unknown time-delay and unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the state observer and applying the backstepping technique, an adaptive fuzzy observer control approach is developed. The main features of the proposed adaptive fuzzy control approach not only guarantees that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded, but also contain less adaptation parameters to be updated on-line. Finally, simulation results are provided to show the effectiveness of the proposed approach.     

Output‐feedback robust adaptive backstepping control for a class of multivariable nonlinear systems with guaranteed tracking performance

This paper is devoted to output‐feedback adaptive control for a class of multivariable nonlinear systems with both unknown parameters and unknown nonlinear functions. Under the Hurwitz condition for the high‐frequency gain matrix, a robust adaptive backstepping control scheme is proposed, which is able to guarantee the tracking performance and needs only one parameter to be updated online regardless of the system order and input–output dimension. To cope with the unknown nonlinear functions and improve the tracking performance, a kind of high‐gain K‐filters is introduced. It is proved that all signals of the closed‐loop system are globally uniformly bounded. Simulation results on coupled inverted double pendulums are presented to illustrate the effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

一类不确定非线性系统的预定性能自适应控制

本文研究了一类不确定严格反馈非线性系统的预定性能控制问题.为保证系统预定性能,引入了一个简单的障碍型Lyapunov函数.结合反推设计法,给出了一种新的自适应控制算法.理论与实验结果表明,所得控制器不仅保证了系统预定性能,且使得闭环系统所有信号有界.     

Adaptive backstepping sliding mode control for feedforward uncertain systems

Output tracking backstepping sliding mode control for feedforward uncertain systems is considered in this article. Feedforward systems are not usually transformable to the parametric semi-strict feedback form, and they may include unmatched uncertainties consisting of disturbances and unmodelled dynamics terms. The backstepping method presented in this article, even without uncertainties differs from that of Ríos-Bolívar and Zinober [Ríos-Bolívar, M. and Zinober, A.S.I. (1999), ‘Dynamical Adaptive Sliding Mode Control of Observable Minimum Phase Uncertain Nonlinear Systems’, in Variable Structure Systems: Variable Structure Systems, Sliding Mode and Nonlinear Control, eds., K.D. Young and Ü. Özgüner. Ozguner, London, Springer-Verlag, pp. 211–236; Ríos-Bolívar, M., and Zinober, A.S.I. (1997a), ‘Dynamical Adaptive Backstepping Control Design via Symbolic Computation’, in Proceedings of the 3rd European Control Conference, Brussels]. In this article, the backstepping is not a dynamical method as in Ríos-Bolívar and Zinober (1997a Ríos-Bolívar, M and Zinober, ASI. 1997a. Dynamical Adaptive Sliding Mode Output Tracking Control of a Class of Nonlinear Systems. International Journal of Robust and Nonlinear Control, 7: 387–405.  [Google Scholar], 1999), since at each step, the control and map input remain intact, and the differentiations of the control are not used. Therefore, the method can be introduced as static backstepping. Two different controllers are designed based upon the backstepping approach with and without sliding mode. The dynamic and static backstepping methods are applied to a gravity-flow/pipeline system to compare two methods.     

基于后推设计的直接自适应模糊控制

针对一类严格反馈不确定非线性动态系统，提出一种直接鲁棒自适应模糊控制新方案．利用模糊系统的逼近能力、后推设计方法和积分型李亚普诺夫函数，依次确定各虚拟控制及模糊系统中可调参数的自适应律，并最终确定出控制律．为改善控制系统的性能，引入逼近误差的自适应补偿项．通过李亚普诺夫方法，证明了闭环系统是一致终结有界的．仿真结果表明了该方法的有效性。     

一类非线性系统基于Backstepping的自适应鲁棒神经网络控制

针对一类未知非线性系统提出了一种基于Backstepping的自适应神经网络控制方法, 放松了满足匹配条件, 要求神经网络逼近误差的边界已知等一些限制性的假设. 扩展了自适应backstepping和自适应神经控制的适用范围, 整个闭环系统表明是最终一致有界的, 跟踪误差收敛于原点的一个大小可调的邻域.     

风浪流干扰及参数不确定欠驱动船舶航迹跟踪的滑模鲁棒控制

针对欠驱动船舶的模型参数不确定和外界风浪流干扰问题,为实现水平面的航迹跟踪控制,提出了一种基于上下界的滑模控制方法.首先利用反步法将控制器的设计分解为运动学回路和动力学回路.其次,在运动学回路中为实现位置跟踪误差的收敛,根据期望航迹与当前位置信息,设计船舶的纵向与侧移参考速度,并视为镇定位置误差的虚拟控制律;在动力学回路中,将虚拟控制律作为新的跟踪目标,利用滑模方法设计实际控制律实现对参考速度的跟踪控制,最终实现了欠驱动船舶的跟踪控制.最后对有无干扰下的欠驱动船模分别进行了仿真实验,仿真结果证明了控制律的有效性.     

严格反馈互联系统分散式backstepping自适应迭代学习控制

基于Lyapunov分析方法,针对具有严格反馈形式的非线性互联系统,本文设计了一种分散式backstepping自适应迭代学习控制器.子系统之间的互联项为所有子系统输出项线性有界,为每个子系统设计的控制器仅采用该子系统的信息,不需要子系统之间相互传递信息.在控制器中,引入在时间轴和迭代轴上同时更新的自适应参数,以补偿子系统之间的互联项影响.通过采用本文给出的控制器,可使得每个子系统的输出跟踪相应的参考模型输出,仿真结果验证了本文算法的有效性.