Adaptive Neural Network-Based Control for a Class of Nonlinear Pure-Feedback Systems With Time-Varying Full State Constraints

Abstract--In this paper, an adaptive neural network （NN） control approach is proposed for nonlinear pure-feedback sys- tems with time-varying full state constraints. The pure-feedback systems of this paper are assumed to possess nonlinear function uncertainties. By using the mean value theorem, pure-feedback systems can be transformed into strict feedback forms. For the newly generated systems, NNs are employed to approximate unknown items. Based on the adaptive control scheme and backstepping algorithm, an intelligent controller is designed. At the same time, time-varying Barrier Lyapunov functions （BLFs） with error variables are adopted to avoid violating full state constraints in every step of the backstepping design. All closed- loop signals are uniformly ultimately bounded and the output tracking error converges to the neighborhood of zero, which can be verified by using the Lyapunov stability theorem. Two simulation examples reveal the performance of the adaptive NN control approach. Index TermsmAdaptive control, neural networks （NNs）, non- linear pure-feedback systems, time-varying constraints.

Robust adaptive fuzzy control for a class of perturbed pure-feedback nonlinear systems

A new design scheme of direct adaptive fuzzy controller for a class of perturbed pure-feedback nonlinear systems is proposed. The design is based on backstepping and the approximation capability of the first type fuzzy systems. A continuous robust term is adopted to minify the influence of modeling errors or disturbances. By introducing the modified integral-type Lyapunov function, the approach is able to avoid the requirement of the upper bound of the first time derivation of the high frequency control gain. Through theoretical analysis, the closed-loop control system is proven to be semi-globally uniformly ultimately bounded, with tracking error converging to a residual set.

Adaptive Barrier-Lyapunov-Functions Based Control Scheme of Nonlinear Pure-Feedback Systems with Full State Constraints and Asymptotic Tracking Performance

In this paper,the authors propose an adaptive Barrier-Lyapunov-Functions(BLFs)based control scheme for nonlinear pure-feedback systems with full state constraints.Due to the coexist of the non-affine structure and full state constraints,it is very difficult to construct a desired controller for the considered system.According to the mean value theorem,the authors transform the pure-feedback system into a system with strict-feedback structure,so that the well-known backstepping method can be applied.Then,in the backstepping design process,the BLFs are employed to avoid the violation of the state constraints,and neural networks(NNs)are directly used to online approximate the unknown packaged nonlinear terms.The presented controller ensures that all the signals in the closed-loop system are bounded and the tracking error asymptotically converges to zero.Meanwhile,it is shown that the constraint requirement on the system will not be violated during the operation.Finally,two simulation examples are provided to show the effectiveness of the proposed control scheme.

Adaptive Tracking Control for Output-Constrained Switched MIMO Pure-Feedback Nonlinear Systems with Input Saturation

In this paper,an adaptive neural tracking control scheme for a class of uncertain switched multi-input multi-output(MIMO)pure-feedback nonlinear systems is proposed.The considered MIMO pure-feedback nonlinear system contains input and output constraints,completely unknown nonlinear functions and time-varying external disturbances.The unknown nonlinear functions representing system uncertainties are identified via radial basis function neural networks(RBFNNs).Then,the Nussbaum function is utilized to deal with the nonlinearity issue caused by the input saturation.To prevent system outputs from violating prescribed constraints,the barrier Lyapunov functions(BLFs)are introduced.Also,a switched disturbance observer is designed to make the time-varying external disturbances estimable.Based on the backstepping recursive design technique and the Lyapunov stability theory,the developed control method is verified applicable to ensure the boundedness of all signals in the closed-loop system and make the system output track given reference signals well.Finally,a numerical simulation is given to demonstrate the effectiveness of the proposed control method.

Adaptive neural control for pure-feedback nonlinear time-delay systems with unknown dead-zone: a Lyapunov-Razumikhin method

This paper addresses the problem of adaptive neural control for a class of uncertain pure-feedback nonlinear systems with multiple unknown state time-varying delays and unknown dead-zone. Based on a novel combination of the Razumikhin functional method, the backstepping technique and the neural network parameterization, an adaptive neural control scheme is developed for such systems. All closed-loop signals are shown to be semiglobally uniformly ultimately bounded, and the tracking error remains in a small neighborhood of the origin. Finally, a simulation example is given to demonstrate the effectiveness of the proposed control schemes.

Adaptive NN Dynamic Surface Control for a Class of Uncertain Non-affine Pure-feedback Systems with Unknown Time-delay

Adaptive neural network （NN） dynamic surface control （DSC） is developed for a class of non-affine pure-feedback systems with unknown time-delay. The problems of ＂explosion of complexity＂ and circular construction of the practical controller in the traditional backstepping algorithm are avoided by using this controller design method. For removing the requirements on the sign of the derivative of function f~, Nussbaum control gain technique is used in control design procedure. The effects of unknown time-delays are eliminated by using appropriate Lyapunov-Krasovskii functionals. Proposed control scheme guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Two simulation examples are presented to demonstrate the method.

考虑时变时滞特性的船舶航向自适应控制

针对一类带有时变参数和时滞性质的船舶航向控制系统,提出一种基于后推技术的神经网络自适应控制器。将较高精度的3自由度分离型船舶运动模型(MMG)等价变换为具有时变参数和时滞性质的非仿射非线性船舶航向控制系统。结合动态面控制(DSC)技术、径向基(RBF)神经网络,利用后推技术进行自适应控制器设计。通过对复杂目标信号的跟踪,验证神经网络自适应控制器的有效性。提出的控制方法在对船舶航向实现有效控制的同时,能避免复杂度爆炸等问题,并具有结构简单易于工程实现等优点。稳定性分析结果表明闭环内的所有信号一致最终有界。

非仿射纯反馈非线性系统的自抗扰控制

针对一类具有外部扰动的不确定非仿射纯反馈非线性系统,结合反演和自抗扰技术,提出了一种新的控制设计方案,该方案中反演设计的每一步引入了自抗扰设计,同时采用微分器和扩展状态观测器分别估计虚拟控制的导数和系统的未知部分.与现有设计方法不同,它不是直接利用逼近定理来构建理想的控制器.该方案设计过程简单,并且通过输入状态稳定性分析证明了系统状态能渐近收敛到原点的任意小邻域内.仿真结果证实了该方法的有效性.

输入受限的非仿射纯反馈不确定系统自适应动态面容错控制

针对存在执行器故障和输入饱和受限的非仿射纯反馈不确定动态系统,提出了一种自适应动态面容错控制策略.在不损失模型精度和考虑系统输入饱和受限的前提下,基于中值定理将非仿射系统转化为具有线性结构的时变不确定系统,在此基础上,再利用参数自适应投影技术对有界不确定时变参数进行在线估计,参数估计误差和外界扰动采用非线性动态阻尼技术进行补偿,并利用双曲正切函数和Nussbaum函数处理系统输入饱和受限和控制增益函数方向未知的问题,同时将反演法和动态面法相结合设计鲁棒自适应控制器,消除了反演法的计算膨胀问题,并且在系统出现执行器失效故障的情况下可确保稳定跟踪.最后,根据解耦反推法,基于Lyapunov稳定性定理证明了闭环系统的半全局一致最终有界.仿真结果验证了所设计控制方案的可行性与有效性.

一类非匹配不确定纯反馈非线性系统新型变幂次趋近律滑模控制

针对以熔化极气体保护焊(gas metal arc welding,GMAW)为代表的一类非匹配不确定纯反馈非线性系统的输出问题,提出一种基于变幂次趋近律的滑模控制方法。首先,采用滑模微分器得到含系统非匹配不确定性干扰的输出一阶导数。得益于终端滑模有限时间稳定的性能,该方法具有估计精度高、估计误差收敛速度快的优点。然后,提出一种新型的变幂次趋近律,并证明在相同增益下,其趋近速度均快于现有各种趋近律,且具有自适应调节趋近速度的能力,既保证了在全局范围内系统轨迹有限时间趋近滑模面,又避免了在滑模面附近出现抖振。最后,采用变幂次趋近律滑模变结构控制方法和传统趋近律滑模变结构控制方法分别对带有非匹配干扰的GMAW中的弧长进行控制仿真,并对比弧长跟踪效果,分析稳态误差。结果表明,变幂次趋近律滑模变结构方法能够有效的提高系统收敛的快速性,滑模控制方法对于非匹配不确定非线性系具有强鲁棒性。

一类非线性系统的自适应模糊反推近似滑模控制

针对一类含有未知非线性函数项和外界干扰的不确定纯反馈非线性系统,提出了一种自适应模糊反推近似滑模变结构控制方法。采用中值定理和隐函数定理使未知非仿射输入函数拥有显式的控制输入,利用模糊系统逼近未知非线性函数,动态面控制技术解决了反推设计中出现的"微分爆炸"问题。所提出的自适应近似滑模控制方案削弱了传统滑模控制中的抖振现象。从理论上证明了所设计的控制器能够保证闭环系统所有信号半全局一致终结有界。仿真算例验证了算法的有效性。

一类纯反馈非线性系统的反推近似滑模控制

在非线性控制系统的优化过程中,针对一类含有未知函数项和外界干扰的不确定纯反馈非线性系统,提出了一种自适应反推近似滑模变结构控制方法。基于中值定理和隐函数定理将未知非仿射输入函数进行分解,使其含有显式的控制输入,利用神经网络逼近未知非线性函数,动态面控制技术解决了反推设计中对虚拟控制反复求导而导致的"微分爆炸"问题。提出的自适应近似滑模控制方案削弱了传统滑模控制中的抖振现象,取消了不确定干扰上界先验已知条件。最后,从理论上证明了所设计的控制器能够保证闭环系统所有信号半全局一致终结有界,为控制系统性能优化提供了有效方法。

非仿射纯反馈不确定系统预设性能鲁棒自适应控制

针对一类结构和参数及控制方向均未知的非仿射纯反馈非线性不确定系统,提出了一种保预设性能鲁棒自适应控制方案。首先引入性能函数和误差转换函数,通过误差转换将原始的输出误差存在性能约束的受限系统转换为等价的非受限系统;其次,基于中值定理将非仿射型系统转化为具有线性结构形式的时变系统,并同时利用自适应投影算法对有界时变参数进行辨识,参数辨识误差和外界干扰采用非线性阻技术项进行补偿;随后综合运用反演技术和Nussbaum函数设计控制器并进行稳定性分析。所设计的控制器不仅能够保证闭环系统所有信号有界且输出误差满足预设的瞬态及稳态性能要求;最后,仿真结果验证了所设计控制方案的可行性与有效性。

一类不确定非线性纯反馈系统的自适应鲁棒模糊控制

针对一类带有不确定性的非线性MIMO纯反馈系统,提出一种自适应鲁棒模糊控制方法.该方法放宽了已有文献对系统模型的限制条件,基于李雅普诺夫分析方法获得了控制输入和自适应律.在控制输入设计中,鲁棒控制项用于补偿逼近误差向量.通过选择适当的设计参数,提出的控制方法使得闭环系统的所有信号是一致有界的和跟踪误差向量的范数收敛到小的零邻域内.仿真结果表明了所提出方法的有效性.

一类纯反馈非仿射非线性系统的自适应神经网络变结构控制

研究了一类非仿射的纯反馈单输入单输出非线性系统。针对此系统,在中值定理、神经网络参数化和解耦Backstepping的基础上,提出了一种自适应变结构神经网络控制策略,而且所给出的定理证明闭环系统的所有信号在平衡点上是半全局一致有界的。通过对一个非仿射CSTR对象的仿真验证了该方法的有效性。

纯增益反馈控制律在MF模型中的应用研究

给出蒙代尔—弗莱明模型的动态表述,并证明蒙代尔—弗莱明模型的动态系统具有能控性、能达性、能观性等结构特征.在蒙代尔—弗莱明模型动态系统的基础上对开放经济条件下宏观经济模型的供需均衡问题转化为宏观经济政策的控制律设计问题,得出开放经济条件下宏观经济政策的纯增益反馈控制律的解析解并且对控制律的解析解的政策含义作出阐述.本文提出的方法对开放经济条件下的宏观经济系统具有较大的应用价值,并且能为有关决策层制定宏观经济调控政策和进行宏观经济系统的分析提供了新的方法与思路.

Neural Network Based Adaptive Tracking Control for a Class of Pure Feedback Nonlinear Systems With Input Saturation

In this paper, an adaptive neural networks(NNs)tracking controller is proposed for a class of single-input/singleoutput(SISO) non-affine pure-feedback non-linear systems with input saturation. In the proposed approach, the original input saturated nonlinear system is augmented by a low pass filter.Then, new system states are introduced to implement states transformation of the augmented model. The resulting new model in affine Brunovsky form permits direct and simpler controller design by avoiding back-stepping technique and its complexity growing as done in existing methods in the literature.In controller design of the proposed approach, a state observer,based on the strictly positive real(SPR) theory, is introduced and designed to estimate the new system states, and only two neural networks are used to approximate the uncertain nonlinearities and compensate for the saturation nonlinearity of actuator. The proposed approach can not only provide a simple and effective way for construction of the controller in adaptive neural networks control of non-affine systems with input saturation, but also guarantee the tracking performance and the boundedness of all the signals in the closed-loop system. The stability of the control system is investigated by using the Lyapunov theory. Simulation examples are presented to show the effectiveness of the proposed controller.

一类纯反馈非线性系统的反推控制

研究了一类纯反馈非线性系统的输出跟踪问题.通过引入一个新的坐标变换,提出了一种基于反推设计的状态反馈控制算法.所得控制算法不仅保证了系统跟踪误差全局渐近稳定,同时使得闭环系统所有信号有界.最后,一个仿真实例验证了本文控制算法的有效性.

非仿射纯反馈非线性切换系统自适应控制

针对一类单输入单输出的非仿射纯反馈非线性切换系统,研究了一种在任意切换下的自适应控制策略.首先,引入中值定理处理系统的非仿射特性问题,并利用径向基函数神经网络逼近系统的未知非线性动态.然后,采用Nussbaum函数处理系统控制增益未知的问题,且在反演设计的每一步引入低通滤波器以解决"微分爆炸"问题.最后,基于共同Lyapunov函数设计状态反馈控制器,并分析闭环系统的稳定性.所设计的控制器避免了切换发生时控制参数跳变和调节参数过多的问题,减少了计算负荷,可以保证闭环系统所有信号半全局一致有界,且跟踪误差可收敛到原点的一个较小邻域.仿真结果验证了控制策略的有效性.

一种改进的非线性纯反馈系统的自适应动态面控制

研究了一类带有未知扰动的非线性纯反馈系统的控制问题.通过引入动态面技术,结合神经网络逼近方法,并利用积分型Lyapunov函数,提出了一种改进的自适应动态面控制方案.在传统后推设计方法的每一步中引入一阶滤波器进行设计,避免了对一些非线性函数,如虚拟控制,反复求导而造成的计算复杂性问题.与现有研究结果相比,该方案放宽了对于控制系统的要求,有效地减少了可调参数的数目,无需虚拟控制增益系数导数的信息.理论分析证明了闭环控制系统是半全局一致终结有界的,且跟踪误差收敛到一个小的邻域内.