Adaptive tracking control of nonlinear systems with dynamic uncertainties using neural network

In this paper, an adaptive neural tracking control approach is proposed for a class of nonlinear systems with dynamic uncertainties. The radial basis function neural networks (RBFNNs) are used to estimate the unknown nonlinear uncertainties, and then a novel adaptive neural scheme is developed, via backstepping technique. In the controller design, instead of using RBFNN to approximate each unknown function, we lump all unknown functions into a suitable unknown function that is approximated by only a RBFNN in each step of the backstepping. It is shown that the designed controller can guarantee that all signals in the closed-loop system are semi-globally bounded and the tracking error finally converges to a small domain around the origin. Two examples are given to demonstrate the effectiveness of the proposed control scheme.     

神经网络非线性系统模型参考自适应控制器统一设计法

针对一类控制器无论是否具有可分离结构的非线性系统 ,利用内模控制的思想提出一种统一的神经网络模型参考自适应控制器设计方案 ,简化了基于神经网络的模型参考自适应控制系统的设计。给出了统一的设计步骤 ,它适用于任意非线性系统 ,更接近于工程实际。理论分析和仿真结果证明了该方案的合理性和有效性     

Decentralized filtering adaptive constrained tracking control for interconnected nonlinear systems

This paper presents a novel decentralized filtering adaptive constrained tracking control framework for uncertain interconnected nonlinear systems. Each subsystem has its own decentralized controller based on the established decentralized state predictor. For each subsystem, a piecewise constant adaptive law will generate total uncertainty estimates by solving the error dynamics between the host system and decentralized state predictor with the neglection of unknowns, whereas a decentralized filtering control law is designed to compensate both local and mismatched uncertainties from other subsystems, as well as achieve the local objective tracking of the host system. The achievement of global objective depends on the achievement of local objective for each subsystem. In the control scheme, the nonlinear uncertainties are compensated for within the bandwidth of low‐pass filters, while the trade‐off between tracking and constraints violation avoidance is formulated as a numerical constrained optimization problem which is solved periodically. Priority is given to constraints violation avoidance at the cost of deteriorated tracking performance. The uniform performance bounds are derived for the system states and control inputs as compared to the corresponding signals of a bounded closed‐loop reference system, which assumes partial cancelation of uncertainties within the bandwidth of the control signal. Compared with model predictive control (MPC) and unconstrained controller, the proposed control architecture is capable of solving the tracking control problems for interconnected nonlinear systems subject to constraints and uncertainties.     

Design of an adaptive terminal sliding‐function controller for nonlinear multivariable systems

This paper presents an adaptive terminal sliding‐function controller approach for controlling a class of nonlinear multivariable systems with uncertainty. An appropriate terminal sliding function (TSF) is designed and then applied to the control law. Based on the Lyapunov stability theory, the adaptive terminal sliding‐function controller for nonlinear multivariable systems guarantees that the TSF is asymptotically convergent. Different from classical terminal sliding mode control, which uses a discontinuous switching control law, the TSF control uses a continuous TSF and thus avoids the chattering problem. The simulation results demonstrate that the proposed method achieves satisfactory stability. Copyright © 2013 John Wiley & Sons, Ltd.     

有向图下非线性无人机群自适应合围控制

本文研究了有向图下具有非线性和干扰的无人机群的分布式合围控制问题. 其中仅部分跟随者是领导者的邻 居, 对于每一个跟随者, 至少存在一条从领导者到这个跟随者有向路径. 文中假设无人机的空气动力学特性是非线性不 确定的, 并且领导者的输出是时变的. 结合反推设计方法提出了仅利用邻居信息的分布式合围控制方法, 使得跟随者的 状态收敛于领导者状态所张成的凸包里. 利用神经网络函数逼近技术补偿无人机系统中的非线性不确定项, 通过李雅普 诺夫稳定性理论证明了合围误差可以以任意收敛速度收敛到原点任意小的邻域. 最后通过仿真结果验证了控制协议的 有效性.     

Direct adaptive neural network controller for a class of nonlinear systems based on fuzzy estimator of the control error

A new approach of direct adaptive control of single input single output nonlinear systems in affine form using single-hidden layer neural network (NN) is introduced. In contrast to the algorithms in the literature, the weights adaptation laws are based on the control error and not on the tracking error or its filtered version. Since the control error is being expressed in terms of the NN controller, hence its weights updating laws are obtained via back-propagation concept. A fuzzy inference system (FIS) with heuristically defined rules is introduced to provide an estimate of this error based on the past history of the system behaviour. The stability of the closed loop is studied using Lyapunov theory. A fixed structure is then proposed for the FIS and the design parameters reduce to the parameters of the NN. The method is reproducible and does not require any pre-training of the network weights.     

一类非线性多变量系统的多模型自适应控制

针对一类不确定的非线性多变量离散时间动态系统,提出了一种基于切换的多模型自适应控制方法.该控制方法的特点在于以下两个方面:首先,引入一个高阶差分算子使得非线性系统的非线性项的限制条件不再要求全局有界;其次,提出的控制方法由线性自适应控制器、神经网络非线性自适应控制器以及切换机构组成:线性控制器用来保证闭环系统的输入输出信号有界,神经网络非线性控制器用来改善闭环系统的性能,基于性能指标的切换机构在每一时刻选择性能指标较好的控制器对系统进行控制.理论分析和仿真实验说明了提出的多模型自适应控制方法的有效性.     

Experimental evaluation of a multivariable adaptive nonlinear predictive controller

A new multivariable adaptive nonlinear predictive controller is designed using a general nonlinear input-output model and variable transformations. The controller is similar in form to typical linear predictive controllers can be tuned analogously or by specifying a single parameters for each controlled variable. In addition, the design procedure is computationally efficient. The new controller is compared to a multi-loop proportional-integral (PI) controller with one-way static decoupling and to an adaptive linear predictive controller through tests on a simulated nonlinear distillation column. The new controller performed well in an experimental application to a multicomponent distillation column.     

不确定非线性系统全局渐近自适应神经网络控制

针对一类控制增益为一般函数形式的不确定仿射非线性系统,提出一种能够确保全局渐近稳定的自适应神经控制(adaptiveneural control,ANC)方法.为了保证神经网络逼近的适用性,设计一种可变控增益的比例微分(proportionaldifferential,PD)控制器以全局镇定被控对象.利用状态变换解决由未知控制增益函数导致的控制奇异问题.提出一种连续的自适应鲁棒控制项实现闭环系统的渐近跟踪.与现有的全局渐近跟踪ANC方法相比较,本文方法不仅简化了PD增益的选择,而且减轻了控制输入的颤振问题.仿真结果表明了本文方法的有效性.     

一类含不匹配干扰的非线性系统非递归鲁棒/自适应一体化控制律设计

针对一类含不匹配干扰的非线性系统的控制问题, 基于递归化方案得到鲁棒或自适应控制律是常见的设计思路, 如反步法及其衍生控制策略等. 然而, 递归设计的控制律通常由含多偏微分项的多个虚拟控制器组成, 形式复杂的同时, 控制参数选取也较为困难, 易出现“复杂性爆炸”的问题, 因此较难得到广泛的工程应用. 同时, 因递归设计处理系统的非线性与不确定性的差异较大, 难以实现鲁棒/自适应控制的本质性融合. 本文从一个新颖的非递归控制角度出发, 提出了一个能够融合鲁棒/自适应控制策略的设计框架, 实现系统在不匹配受扰情形下的无静差跟踪. 仅通过一步坐标变换, 在等价的可镇定系统框架下, 根据实际工况来灵活切换合适的控制增益, 为工程师同时提供了两个可供选择的控制方案. 相较于已有算法, 本文所提控制器形式简洁易实现, 参数易调节, 适用范围广. 案例分析与实例仿真验证阐明了所提方法的简洁性及有效性, 并给出了一体化控制器工作模式的选取原则.     

块控非线性系统自适应神经网络控制

针对一类含有非匹配不确定性的块控型多输入多输出非线性系统,提出一种基于反演技术和RBF神经网络的控制系统设计方案.通过引入一种改进型的Lyapunov函数,避免了控制矩阵未知情况下可能出现的奇异问题.在控制系统设计过程中,充分应用鲁棒自适应控制技术,解决了多输入多输出结构不确定性所带来的设计难题,得到了系统所有状态量将全局指数收敛至原点附近一个邻域的结论.最后的仿真结果表明了设计方案的正确性.     

非匹配不确定高阶非线性系统的滑模控制新方法

对具有非匹配不确定的高阶非线性系统,采用改进的高阶滑模微分器获取已知状态的任意阶微分估计值,再以恰当阶次的状态微分估计值之差,得到非匹配不确定项及其微分的估计值,证明了其误差任意小.为避免奇异性和抖振,采用两种方案设计了滑模控制器,并设计鲁棒项提高系统鲁棒性.基于Lyapunov~论证明了系统稳定性.同现有其他方法相比,该方法具有适用范围更广、收敛速度快、控制精度高、运算量小、保守性低等优点.最后仿真证明了本文所有结论.     

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.     

不确定非线性系统的直接自适应神经网络控制

为解决一类带干扰的不确定非线性系统中存在的两类未知项——未知函数和外界干扰,采用了直接自适应神经网络控制方法设计控制器。控制器设计中利用径向基函数神经网络良好的逼近性来近似未知函数,利用非线性衰减项来抑制干扰。所用方法结构简单、算法简洁,在一定条件下稳定性和收敛性能定性地得到保证。最后,仿真结果证明了该方法是正确的。     

Robust adaptive fault‐tolerant tracking control of multiple time‐delays systems with mismatched parameter uncertainties and actuator failures

This study deals with the problem of robust adaptive fault‐tolerant tracking for uncertain systems with multiple delayed state perturbations, mismatched parameter uncertainties, external disturbances, and actuator faults including loss of effectiveness, outage, and stuck. It is assumed that the upper bounds of the delayed state perturbations, the external disturbances and the unparameterizable time‐varying stuck faults are unknown. Then, by estimating online such unknown bounds and on the basis of the updated values of these unknown bounds from the adaptive mechanism, a class of memoryless state feedback fault‐tolerant controller with switching signal function is constructed for robust tracking of dynamical signals. Furthermore, by making use of the proposed adaptive robust tracking controller, the tracking error can be guaranteed to be asymptotically zero in spite of multiple delayed state perturbations, mismatched parameter uncertainties, external disturbances, and actuator faults. In addition, it is also proved that the solutions with tracking error of resulting adaptive closed‐loop system are uniformly bounded. Finally, a simulation example for B747‐100/200 aircraft system is provided to illustrate the efficiency of the proposed fault‐tolerant design approach. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Robust adaptive neural control of uncertain pure-feedback nonlinear systems

In this paper, a robust adaptive neural control design approach is presented for a class of uncertain pure-feedback nonlinear systems. To reduce the complexity of the both controller structure and computation, only one neural network is used to approximate the lumped unknown function of the system at the last step of the recursive design process. By this approach, the complexity growing problem existing in conventional methods can be eliminated completely. Stability analysis shows that all the closed-loop system signals are uniformly ultimately bounded, and the steady state tracking error can be made arbitrarily small by appropriately choosing control parameters. Simulation results demonstrate the effectiveness and merits of the proposed approach.     

控制增益未知的多变量极值搜索系统神经网络自适应协同控制

针对一类控制增益未知的多变量极值搜索系统,提出了一种神经网络自适应协同控制方法.该方法利用协同控制实现状态变量之间的协同收敛,并确保对系统内部参数扰动和外界干扰具有不变性;以极值搜索控制方法得到的搜寻变量作为输入量,设计多层神经网络逼近状态变量的极值变化率和未知的变量与函数;采用Nussbaum函数解决系统控制增益未知的问题;同时运用自适应参数抵消神经网络逼近误差的影响.稳定性分析证明了系统的状态跟踪误差、输出量与其极值之间的误差、极值搜索变量的跟踪误差以及神经网络各参数的估计误差均指数收敛至原点的一个有界邻域.理论分析与仿真结果验证了该方法的有效性.     

基于动态结构自适应神经网络的不确定时滞系统跟踪控制

针对一类不确定时滞非线性系统,提出一种自适应跟踪控制器.首先采用Lyapunov-Krasovskii函数设计时滞补偿器,并构造其中的参数调节规律.再针对建模误筹及小确定非线性,引入动态结构自适应神经网络,其隐层神经元个数可以随着跟踪误差的增大而在线增加,以提高逼近精度.最后,用仿真示例表明本文所提方法是有效的.