含有非线性参数化的非完整系统的鲁棒自适应控制

针对一类含有强非线性漂移项和未知非线性参数的非完整系统, 提出了一种全局自适应状态反馈控制策略. 首先通过引入参数分离技术, 将非线性参数化系统转换为似然线性参数化系统. 然后引入反馈支配方法设计全局自适应稳定控制器, 同时, 为了避免系统出现不可控性, 设计了一种开关策略. 所设计的控制器能保证系统状态全局收敛到原点, 且其它信号保持有界. 仿真例子验证了算法的有效性和鲁棒性.     

一类非齐次高阶非线性系统的连续反馈控制设计

研究了一类非齐次的高阶非线性系统的连续状态反馈控制设计问题. 通过定义一列适当的辅助函数,放宽了对非线性项的约束条件. 利用传统的积分反推技术,并增加一个积分项的方法,得到了这类系统的稳定性,给出了控制器的设计方法,并通过一个例子验证了本文的理论结果.     

有未知控制系数和零动态的高阶非线性系统的自适应控制设计

主要研究一类控制系数未知和有不可测零动态的高阶非线性系统的全局自适应镇定问题. 进一步放宽了对零动态的约束条件, 通过定义一个恰当的未知参数, 把连续自适应状态反馈控制器的动态阶数降到最低(仅一维). 通过结合增加幂次积分方法, 相关的自适应技术以及交换能量函数思想, 给出控制器的设计步骤. 所设计的控制器确保闭环系统的所有状态是全局一致有界的, 且原系统的状态收敛到零.     

一类控制系数未知但等同高阶非线性系统的稳定控制设计

本文研究了一类控制系数未知但等同高阶非线性系统的状态反馈稳定控制设计问题. 尽管该类系统具有不确定性, 即控制系数未知,但本文没有采用自适应技术, 而是通过选取适当的设计参数, 从而得到了设计该类非线性系统稳定控制器的新方法, 并基于反推技术, 给出了稳定控制器的设计步骤. 所设计的状态反馈控制器使得闭环系统全局渐近稳定, 并保持在原点的平衡性.     

一类高阶非线性不确定系统自适应稳定控制

研究了一类高阶非线性不确定性系统的自适应稳定控制设计问题.因该系统的非线性程度高,其控制系数不等同、符号已知、但数值未知,故在此之前其稳定控制设计问题没有得到解决.本文应用自适应技术,结合设计参数的适当选取,从而得到了设计该类非线性系统状态反馈稳定控制器的新方法,并基于反推技术,给出了稳定控制器的设计步骤.所设计的状态反馈控制器使得闭环系统的状态全局渐近收敛于零,其余闭环信号一致有界.最后通过一个仿真例子说明了控制设计方法的有效性.     

不确定高次随机非线性系统的自适应控制

针对一类含有噪声干扰和非线性参数的高次随机非线性系统,研究了依概率全局自适应稳定问题.在噪声的协方差未知的情况下,利用自适应增加幂积分方法和参数分离技术,提出了一种反馈占优设计方法并构造了一个光滑自适应控制器.该控制器能保证闭环系统依概率全局稳定,并且系统的状态几乎必然收敛到零.仿真例子验证了控制方案的有效性.     

不确定串联非线性系统H∞鲁棒自适应控制

针对一类含有未知参数和干扰的非最小相位串联非线性系统,结合H∞控制和自适应控制方法并利用李雅普诺夫函数递推设计方法设计了状态反馈H∞自适应控制器,避免了求解Hamilton-Jacobi-Isaacs不等式设计控制器的困难.该控制器不仅保证闭环系统ISS(input-to-state)稳定,而且使得系统对于所有允许的参数不确定从干扰输入到可控输出的 L 2增益不大于给定的值.最后,给出了一个仿真例子,仿真结果充分表明了所设计的控制器的可行性和有效性.     

带有死区输入的非线性系统的自适应控制

针对一类具有死区非线性输入的非线性系统,同时考虑系统中存在未建模不确定项,设计了自适应控制器及未知参数的自适应估计率.该控制器使得闭环系统全局稳定且实现了输出信号对参考信号的精确跟踪.仿真结果进一步证实了该控制器能对未知死区及未建模动态进行有效的补偿。     

一种新的数据驱动的非线性自适应切换控制方法

针对一类非线性离散时间动态系统, 提出了一种新的非线性自适应切换控制方法. 该方法首先把非线性项分解为前一拍可测部分与未知增量和的形式, 并充分利用被控对象的大数据信息和知识, 把非线性项前一拍可测数据与未知增量都用于控制器设计, 分别设计了线性自适应控制器, 带有非线性项前一拍可测数据补偿的非线性自适应控制器以及带有非线性项未知增量估计与补偿的非线性自适应控制器. 三个自适应控制器通过切换函数和切换规则来协调控制被控对象. 既保证了闭环系统的稳定性, 同时又提高了闭环系统的性能. 分析了闭环切换系统的稳定性和收敛性. 最后, 通过水箱液位系统的物理实验, 实验结果验证了所提算法的有效性.     

基于S类函数的严格反馈非线性周期系统的自适应控制

针对一类严格反馈非线性周期系统, 在周期非线性可时变参数化的条件下设计自适应控制器. 通过将周期时变参数展开成傅里叶级数, 并采用微分自适应律估计未知系数, 进行控制器反推设计. 引入S类函数, 并在控制器设计中应用S类函数处理截断误差项对系统跟踪性能的影响, 同时, S类函数能确保虚拟控制的可微. 给出几种不同的S类函数设计, 分析比较将其应用于控制器设计时产生的不同效果. 理论分析与仿真结果表明, 提出的控制方法能够实现系统输出跟踪期望轨迹, 且闭环系统所有信号有界.     

Globally Stable Adaptive Tracking Control for Uncertain Strict‐Feedback Systems Based on Neural Network Approximation

This paper addresses the problem of globally stable adaptive neural tracking control for a class of strict‐feedback nonlinear systems. Compared with the existing works, the salient properties of the proposed scheme are given as follows. First, a novel switching controller is developed, which consists of a traditional adaptive neural controller and an extra robust controller to pull back the transient outside of the approximation domain. Second, only two adaptive parameters need to be tuned online, and the computational burden is considerably alleviated in practice. Third, to design the desired switching controller via the backstepping technique, a novel switching function, which has continuous derivatives up to the nth order, is constructed. It is shown that the system output converges to a small neighborhood of the reference signal and the closed‐loop system is globally stable. Finally, an example is provided to verify the effectiveness of the proposed control method.     

An adaptive homogeneous domination method to time-varying control of nonlinear systems

The adaptive control issue of uncertain nonlinear system which has complicated polynomial growing condition is studied. Utilizing the dynamic-gain transformation, we transform the considered system into the time-varying system. By using a recursively design for its nominal system, a controller is skillfully constructed first. Subsequently, for the original system, by flexibly utilizing the dynamic gain and presenting an adaptive homogeneous domination method, a new time-varying adaptive controller is successfully obtained to ensure that the equilibrium point is globally asymptotically stable. An extended robust adaptive controller is also provided. Finally, we discuss two examples to verify the proposed approach.     

Adaptive state-feedback stabilization for high-order stochastic non-linear systems with uncertain control coefficients

This paper investigates the adaptive state-feedback stabilization problem for a class of high-order stochastic non-linear systems with unknown lower and supper bounds for uncertain control coefficients. Under some weaker and reasonable assumptions, a smooth adaptive state-feedback controller is designed, which guarantees that the closed-loop system has an almost surely unique solution on [0,∞, the equilibrium of interest is globally stable in probability and the states can be regulated to the origin almost surely. A simulation example is given to show the systematic design and effectiveness of the controller.     

Prescribed performance global stable adaptive neural dynamic surface consensus tracking control of stochastic multi-agent systems with hysteresis inputs and nonlinear dynamics

This paper focuses on the leader-following consensus control problem of stochastic multi-agent systems with hysteresis inputs and nonlinear dynamics. A leader-following consensus scheme is presented for stochastic multi-agent systems directions under directed graphs, which can achieve predefined synchronisation error bounds. By mainly activating an auxiliary robust control component for pulling back the transient escaped from the neural active region, a multi-switching robust neuro adaptive controller in the neural approximation domain, which can achieve globally uniformly ultimately bounded tracking stability of multi-agent systems recently. A specific Nussbaum-type function is introduced to solve the problem of unknown control directions. Using a dynamic surface control technique, distributed consensus controllers are developed to guarantee that the outputs of all followers synchronise with that of the leader with prescribed performance. Based on Lyapunov stability theory, it is proved that all signals in closed-loop systems are uniformly ultimately bounded and all the follower agents can keep consensus with the leader. Two simulation examples are provided to illustrate the effectiveness and advantage of the proposed control scheme.     

Adaptive output feedback control of a class of uncertain nonlinear systems with unknown time delays

This article studies the adaptive output feedback control problem of a class of uncertain nonlinear systems with unknown time delays. The systems considered are dominated by a triangular system without zero dynamics satisfying linear growth in the unmeasurable states. The novelty of this article is that a universal-type adaptive output feedback controller is presented to time-delay systems, which can globally regulate all the states of the uncertain systems without knowing the growth rate. An illustrative example is provided to show the applicability of the developed control strategy.     

Adaptive tracking control for a class of random pure‐feedback nonlinear systems with Markovian switching

This note studies the tracking control problem for a class of random pure‐feedback nonlinear systems with Markovian switching and unknown parameters. An adaptive tracking controller is constructed by introducing an auxiliary integrator subsystem and using the improved backstepping method such that the closed‐loop system has a unique solution that is globally bounded in probability. Meanwhile, the tracking error can converge to an arbitrarily small neighborhood of zero via the parameter regulation technique. The efficiency of the tracking controller designed in this paper is demonstrated by simulation examples.     

Multiple model-based event-triggered adaptive control of a class of discrete-time nonlinear systems

In this study, the problem of event-triggered-based adaptive control (ETAC) for a class of discrete-time nonlinear systems with unknown parameters and nonlinear uncertainties is considered. Both neural network (NN) based and linear identifiers are used to approximate the unknown system dynamics. The feedback output signals are transmitted, and the parameters and the NN weights of the identifiers are tuned in an aperiodic manner at the event sample instants. A switching mechanism is provided to evaluate the approximate performance of each identifier and decide which estimated output is utilised for the event-triggered controller design, during any two events. The linear identifier with an auxiliary output and an improved adaptive law is introduced so that the nonlinear uncertainties are no longer assumed to be Lipschitz. The number of transmission times are significantly reduced by incorporating multiple model schemes into ETAC. The boundedness of both the parameters of identifiers and the system outputs is demonstrated though the Lyapunov approach. Simulation results demonstrate the effectiveness of the proposed method.     

Global adaptive stabilization for high‐order uncertain time‐varying nonlinear systems with time‐delays

This paper focuses on the adaptive stabilization problem for a class of high‐order nonlinear systems with time‐varying uncertainties and unknown time‐delays. Time‐varying uncertain parameters are compensated by combining a function gain with traditional adaptive technique, and unknown multiple time‐delays are manipulated by the delicate choice of an appropriate Lyapunov function. With the help of homogeneous domination idea and recursive design, a continuous adaptive state‐feedback controller is designed to guarantee that resulting closed‐loop systems are globally uniformly stable and original system states converge to zero. The effectiveness of the proposed control scheme is illustrated by the stabilization of delayed neural network systems. Copyright © 2016 John Wiley & Sons, Ltd.