控制增益为未知函数的不确定系统预设性能反演控制

对一类控制增益为未知函数的不确定严格反馈系统的预设性能反演控制进行研究.首先,提出一种新的变参数约束方案,放宽了对初始跟踪误差已知的限制,并通过误差转化将不等 式约束的受限系统转化为非受限系统.随后,通过引入积分型Lyapunov函数,避免了因控制增益未知而引起的系统奇异问题.最后,综合应用自适应技术、径向基函数(Radial basis function,RBF)神经网络和反演控制技术完成了控制器的设计,系统中的未知函数利用RBF神经网络直接进行逼近.所设计的控制器能够满足预设性能的要求,且保证闭环系统所有的状态量有界.仿真研究证明了控制器设计方法的有效性.     

未知控制方向的迟滞非线性系统预设自适应控制

针对一类含有迟滞特性的未知控制方向严反馈非线性系统,设计了基于误差变换的反步自适应控制器.首先提出动态迟滞算子来扩展输入空间建立神经网络迟滞模型.然后利用径向基函数(RBF)神经网络逼近未知函数,并引入Nussbaum型函数来解决系统未知控制方向问题.最后采用误差变换将误差限定在预设的范围内,并利用反步法设计自适应控制器.该控制方案不仅能够保证跟踪精度,还可以提高系统暂态和稳态性能.仿真结果表明了控制方案的可行性.     

基于状态可行域约束的极值搜索系统预设性能控制

针对极值搜索系统在稳定状态存在可行域约束情况下的预设性能控制问题,首先利用罚函数构造新型目标函数并设计极值参考轨迹;然后,通过性能函数和误差转换函数构建系统等效模型,利用反演控制方法进行预设性能控制器设计;最后,设计不确定参数自适应估计律.系统在实现极值搜索的同时能够满足预先设定的性能指标.数值仿真验证了所提出方法的有效性.     

控制增益符号未知的不确定非线性系统鲁棒自适应控制

针对一类控制增益函数及符号均未知的不确定非线性系统,基于反推滑模设计方法,提出一种鲁棒自适应神经网络控制方案.结合Nussbaum增益设计技术和神经网络逼近能力,取消了控制增益函数及符号已知的条件,应用积分型Lyapunov函数避免了控制器奇异性问题,并通过引入神经网络逼近误差和不确定干扰上界的自适应补偿项消除了建模误差和不确定干扰的影响.理论分析证明了闭环系统所有信号半全局一致终结有界,仿真结果验证了该方法的有效性.     

输入受限的非仿射无人帆船航向系统自适应动态面控制

针对输入受限和控制方向未知的无人帆船航向控制问题,考虑系统模型存在动态不确定和未知外界扰动的情况,本文提出一种基于非仿射航向运动数学模型的最小参数自适应递归滑模动态面控制策略.该策略通过Taylor展开方法将非仿射模型转化为具有线性结构的仿射时变系统,采用最小参数学习(minimal learning parameter,MLP)神经网络逼近无人帆船模型不确定部分,并利用双曲正切函数处理控制输入饱和现象,引入Nussbaum函数处理系统中未知控制方向问题,同时综合考虑帆船艏摇角速度误差和航向误差之间关系设计递归滑模动态面舵角控制律,并设计参数自适应律对神经网络逼近误差与复合干扰总和的界进行估计.选取李雅普诺夫函数证明了所设计控制器能够保证航向闭环系统内所有信号的一致最终有界性.最后,基于一艘12 m无人帆船进行仿真验证,结果表明无人帆船航向控制响应速度快,所设计的控制器能有效地处理模型不确定项和风浪等外界扰动,具有较强的鲁棒性.     

基于EKF滤波的倒立摆神经网络控制研究

为解决一类带干扰的模型不确定倒立摆系统中存在的两类未知项——未知函数和外界干扰,采用了基于Lyapunov函数稳定性的神经网络控制方法设计控制器。控制器设计中利用扩展卡尔曼滤波(EKF)消除系统观测噪声,获取系统状态的估计值,进而利用径向基函数(RBF)神经网络良好的逼近性来近似设计的控制律中的未知项。最后在倒立摆系统中对设计的神经网络控制器进行了仿真研究,仿真结果表明所设计的控制器能有效抑制外界干扰,在精确控制倒立摆的同时可以保证控制系统的稳定性和快速性。     

随机时滞系统的神经网络输出反馈动态面控制

针对一类具有未知控制方向的随机时滞系统设计自适应神经输出反馈控制器.首先,利用状态观测器估计不可测量的系统状态;其次,选择合适的Lyapunov-Krasovskii函数消除未知延迟项对系统的影响,利用Nussbaum-type函数处理系统的未知控制方向问题,通过神经网络逼近未知的非线性函数,以及用动态表面控制(DSC)解决控制器设计中出现的复杂性问题;最后,通过Lyapunov稳定性理论,构造一个鲁棒自适应神经网络输出反馈控制器,可以保证闭环系统中所有信号在二阶或四阶矩意义下一致最终有界,跟踪误差能收敛到零值小的领域内.仿真实例验证了所提出方法的有效性.     

时变时滞非线性系统自适应神经网络控制

对于一类具有未知时变时滞和虚拟控制系数的不确定严格反馈非线性系统,基于后推设计提出一种自适应神经网络控制方案.选取适当的Lyapunov-Krasovskii泛函补偿未知时变时滞不确定项.通过构造连续的待逼近函数来解决利用神经网络对未知非线性函数进行逼近时出现的奇异问题.通过引入一个新的中间变量,保证了虚拟控制求导的正确性.仿真算例表明,所设计的控制器能保证闭环系统所有信号是半全局一致终结有界的,且跟踪误差收敛到零的一个邻域内.     

基于DSC后推法的非线性系统的鲁棒自适应NN控制

针对一类具有不确定系统函数和方向未知的不确定增益函数的非线性系统, 提出了一种鲁棒自适应神经网络控制算法. 本算法采用RBF神经网络(Radial based function neural network, RBF NN)逼近模型不确定性, 外界干扰和建模误差采用非线性阻尼项进行补偿, 将动态面控制(Dynamic surface control, DSC)与后推方法结合, 消除了反推法的计算膨胀问题, 降低了控制器的复杂性; 尤其是采用Nussbaum函数处理系统中方向未知的不确定虚拟控制增益函数, 不仅可以避免可能存在的控制器奇异值问题, 而且还能使得整个系统的在线学习参数显著减少, 与DSC方法优点结合, 使得控制算法的计算量大为减少, 便于计算机实现. 稳定性分析证明了所得闭环系统是半全局一致最终有界(Semi-global uniformly ultimately bounded, SGUUB)的, 并且跟踪误差可以收敛到原点的一个较小邻域. 最后, 计算机仿真结果表明了本文所提出控制器的有效性.     

控制方向未知的二阶时变非线性系统自适应迭代学习控制

对一类二阶严格反馈时变非线性系统的自适应迭代学习控制问题进行了研究.系统中含有非周期时变参数化不确定性且控制方向未知.首先,提出了一种神经网络估计器,实现了对未知非周期时变非线性函数的逼近.随后,用Nussbaum函数对未知控制方向进行了自适应估计,并综合应用baCkstcpping技术和自适应迭代学习控制技术设计了控制器.所设计的控制器能保证系统所有状态量在Lpe-范数意义下有界,且系统的输出量在LT2-范数意义下收敛到期望轨迹.最后的仿真研究证明了控制器设计方法的有效性.     

Adaptive neural prescribed performance control for a class of strict-feedback stochastic nonlinear systems under arbitrary switchings

This paper presents an adaptive neural tracking control scheme for strict-feedback stochastic nonlinear systems with guaranteed transient and steady-state performance under arbitrary switchings. First, by utilising the prescribed performance control, the prescribed tracking control performance can be ensured, while the requirement for the initial error is removed. Second, radial basis function neural networks approximation are used to handle unknown nonlinear functions and stochastic disturbances. At last, by using the common Lyapunov function method and the backstepping technique, a common adaptive neural controller is constructed. The designed controller overcomes the problem of the over-parameterisation, and further alleviates the computational burden. Under the proposed common adaptive controller, all the signals in the closed-loop system are 4-Moment (or 2 Moment) semi-globally uniformly ultimately bounded, and the prescribed tracking control performance are guaranteed under arbitrary switchings. Three examples are presented to further illustrate the effectiveness of the proposed approach.     

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.     

Prescribed performance adaptive neural tracking control for strict-feedback Markovian jump nonlinear systems with time-varying delay

A prescribed performance adaptive neural tracking control problem is investigated for strict-feedback Markovian jump nonlinear systems with time-varying delay. First, a new prescribed performance constraint variable is proposed to generate the virtual control that forces the tracking error to fall within prescribed boundaries. Combining with the approximation capability of neural networks and backstepping design, the adaptive tracking controller is designed. The designed controller is independent on time delay by constructing appropriate Lyapunov functions to offset the unknown time-varying delays. It is proved that the closed-loop system is uniformly ultimately bounded in probability, and that both steady-state and transient-state performances are guaranteed. Finally, simulation results are given to illustrate the effectiveness of the proposed approach.     

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.     

Adaptive neural output feedback tracking control for a class of nonlinear systems

In this paper, an adaptive neural output feedback control scheme based on backstepping technique and dynamic surface control (DSC) approach is developed to solve the tracking control problem for a class of nonlinear systems with unmeasurable states. Firstly, a nonlinear state observer is designed to estimate the unmeasurable states. Secondly, in the controller design process, radial basis function neural networks (RBFNNs) are utilised to approximate the unknown nonlinear functions, and then a novel adaptive neural output feedback tracking control scheme is developed via backstepping technique and DSC approach. It is shown that the proposed controller ensures that all signals of the closed-loop system remain bounded and the tracking error converges to a small neighbourhood around the origin. Finally, two numerical examples and one realistic example are given to illustrate the effectiveness of the proposed design approach.     

倒立摆的自适应积分反步控制策略

针对直线单级倒立摆在模型参数不确定和外部扰动情况下的稳定控制问题,提出一种自适应积分反步控制策略。采用拉格朗日方程建立倒立摆系统的运动学模型,为减少稳态误差,将误差积分项引入反步法,设计了倒立摆的控制器;对含有未知参数的系统非线性状态微分方程,设计适当的Lyapunov函数推导出系统未知参数的自适应更新律,削弱了参数不确定性的影响。将自适应积分反步控制与一般的反步法控制、模糊控制及神经网络控制的仿真结果进行了对比,并在LabVIEW开发环境下进行了实物实验。结果表明,自适应积分反步法可以较为迅速且精确地完成稳定控制,较好地克服系统参数不确定及外部扰动的影响,具有较强的鲁棒性。     

随机激励下板球系统建模与有限时间全状态预设性能跟踪控制

研究板球系统受到随机激励时的数学建模与轨迹跟踪控制问题. 首次建立了板球系统的随机数学模型, 并 结合backstepping方法、有限时间预设性能函数、全状态约束及新的预设性能推导方法设计了具有未知输入饱和的 随机板球系统实际有限时间全状态预设性能跟踪控制器, 实现了随机激励下板球系统的有限时间预设性能轨迹跟 踪控制. 所设计的控制器保证了系统跟踪误差能够被预先给定的有限时间性能函数约束, 并且能在任意给定的停息 时间内收敛到预先给定的邻域内. 最后通过仿真实验验证了所设计控制器具有更好的控制效果.     

Adaptive neural network control of nonlinear systems with unknown time delays

In this note, adaptive neural control is presented for a class of strict-feedback nonlinear systems with unknown time delays. Using appropriate Lyapunov-Krasovskii functionals, the uncertainties of unknown time delays are compensated for such that iterative backstepping design can be carried out. In addition, controller singularity problems are solved by using the integral Lyapunov function and employing practical robust neural network control. The feasibility of neural network approximation of unknown system functions is guaranteed over practical compact sets. It is proved that the proposed systematic backstepping design method is able to guarantee semiglobally uniformly ultimate boundedness of all the signals in the closed-loop system and the tracking error is proven to converge to a small neighborhood of the origin.