未知非线性系统的神经网络跟踪控制与仿真研究

应用输入／输出反馈线性化方法和李亚普诺夫方法,研究了一类具有未知非线性函数的非线性动态系统的自适应鲁棒输出跟踪控制问题。首先通过坐标变换和输入变换,将非线性系统变换为部分线性可控系统。接着采用多层前向神经网络来逼近未知非线性函数,网络的权值根据李亚普诺夫原则来在线修正,这样就克服了多神经网络控制系统中存在的稳定性问题。同时,为了减少权值学习时间,应用遗传算法预先离线训练网络权值。最后提出了一个基于神经网络建模的自适应鲁棒控制律,给出了李亚普诺夫意义下的稳定性证明。所提出的控制律可确保相应闭环系统的状态及跟踪误差一致最终有界。所给的Van der pol系统的例子说明了所提控制方案的有效性与鲁棒性。     

Formation Tracking for Nonlinear Multi-agent Systems with Input and Output Quantization via Adaptive Output Feedback Control

Signal quantization can reduce communication burden in multi-agent systems, whereas it brings control challenge to multi-agent formation tracking. This paper studies the output feedback control problem for formation tracking of multi-agent systems with both quantized input and output.The agents are described by a nonlinear dynamic model with unknown parameters and immeasurable states. To estimate immeasurable states and solve the uncertainties, state observers are developed by using dynamic high-gain tools. Through proper parameter designs, an output feedback quantized controller is established based on quantized output signals, and the quantization effect on the control system is eliminated. Stability analysis proves that, with the proposed control scheme, multi-agent systems can track the reference trajectory while forming and maintaining the desired formation shape.In addition, all the signals in the closed-loop systems are bounded. Finally, the numerical simulation and practical experiment are provided to verify the theoretical analysis.     

一类严格反馈时滞系统的自适应输出反馈控制

针对一类单输入单输出的严格反馈时滞系统研究跟踪控制问题。该控制系统包含不确定项、输出约束、未知死区特性和未知时间延迟。首先,设计一个状态观测器来估计无法测量的系统状态;其次,利用径向基函数(radial basis function,RBF)神经网络去逼近未知的系统内部动态;同时,利用障碍李雅普诺夫(Lyapunov)函数确保输出约束及Lyapunov-Krasovskii方法消除时滞项对系统的影响;最后,基于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,并且克服了过参数问题。结果显示,设计的神经网络输出反馈控制器可以保证闭环系统中的所有信号都是半全局最终一致有界的,跟踪误差能收敛到零值小的领域内。文中通过两个例子进一步验证了提出方法的有效性。     

基于状态观测器的非线性系统神经网络自适应控制

结合高增益观测器,针对相对阶为n的非线性系统,设计了神经网络自适应控制器。利用Lyapnov定理获得了神经网络权值的更新律和控制器的控制律,从而确保了整个闭环系统的稳定性和有界性。由于神经网络不需任何的离线训练,因而该控制器能够广泛应用于一大类非线性性系统的控制中。仿真结果验证了控制方案的有效性。     

Robust decentralized adaptive output feedback fuzzy controller design and application to AHS

A novel decentralized indirect adaptive output feedback fuzzy controller is developed for a class of large-scale uncertain nonlinear systems using error filtering. By the properly filtering of the observation error dynamics, the strictly positive-real condition is guaranteed to hold such that the proposed output feedback and adaptation mechanisms are practicable in practice owing to the fact that its implementation does not require the observation error vector itself any more, which corrects the impracticable schemes in the previous literature involved. The presented control algorithm can ensure that all the signals of the closed-loop large-scale system keep uniformly ultimately bounded and that the tracking error converges to zero asymptotically. The decentralized output feedback fuzzy controller can be applied to address the longitudinal control problem of a string of vehicles within an automated highway system (AHS) and the effectiveness of the design procedure is supported by simulation results.     

Output Tracking for One-Dimensional Wave Equation with Non-Collocated Control and Output Configuration

This paper considers output tracking for a one-dimensional wave equation with general disturbance which includes both internal nonlinear uncertainty and external disturbance. The performance output is non-collocated to the control. The disturbance is estimated by an essentially extended state observer from active disturbance rejection control and the difficulty caused by the non-collocated configuration of control and output is overcome by a proper trajectory planning. An output feedback law is proposed to make the tracking error be convergent to zero exponentially as time goes to infinity.At the same time, all states of the closed-loop system are shown to be uniformly bounded. Numerical simulation is also presented to validate the theoretical results.     

带非线性观测器的欠驱动船舶自适应动态面输出反馈轨迹跟踪控制

针对船速与艏摇角速度均不可测的三自由度欠驱动船舶轨迹跟踪问题,考虑在海洋环境扰动未知,提出一种带非线性观测器的动态面自适应输出反馈控制方法。该方法通过对系统模型进行坐标变换,设计非线性观测器估计船舶的速度向量;采用动态面技术可处理反演法对虚拟控制量求导导致的“微分膨胀”问题,减少计算量;同时采用自适应律估计海洋环境干扰的界值,从而防止参数漂移。利用Lyapunov函数证明该控制律可保证船舶轨迹跟踪误差的一致最终有界性,仿真结果证明了所提出控制方法的有效性。     

机械手鲁棒输出跟踪控制与仿真

研究了两自由度机械手终端夹持不定载荷时的输出跟踪问题。应用输入 /输出反馈线性化法和李亚普诺夫方法 ,提出了一种基于不确定项上界的机械手鲁棒输出跟踪控制器设计算法。所述控制器可确保系统输出按指数规律跟踪期望输出 ,同时相应闭环系统的状态一致最终有界。该方法计算简单 ,容易实现。仿真结果证明了其可行性及有效性。     

高阶非线性时滞系统的神经网络动态面控制

针对一类具有未知时变时滞的不确定高阶非线性系统,基于增加幂次积分方法,提出了一种非光滑状态反馈自适应神经网络动态面控制设计方案。通过构造适当的Lyapunov Krasovskii泛函处理了未知时变时滞不确定项;通过利用神经网络权值范数的适当形式幂次函数,将神经网络用于对在单步递推中所构造的未知函数进行建模;采用动态面技术,解决了“微分爆炸”问题。所提控制方案能够保证闭环控制系统的状态量和跟踪误差半全局一致终结有界。最后,仿真算例结果表明了该方案的有效性。     

二阶输出反馈滑模极值搜索控制方法

针对一类单输入单输出(single input single output,SISO)非线性极值系统的控制问题,提出了一种二阶输出反馈滑模极值搜索控制方法。考虑到此系统的状态量不可测,利用斜坡函数作为输出量的参考跟踪信号,以系统的输出跟踪误差及其微分信号构建切换函数,设计出二阶滑模极值搜索控制律。稳定性分析证明了在任意初始条件下,该方法可使系统的输出量全局收敛至其期望极值的任意小邻域内且所有状态量均是一致范数有界。仿真结果验证了该方法的有效性。     

Combined indirect and direct method for adaptive fuzzy output feedback control of nonlinear system

A novel control method for a general class of nonlinear systems using fuzzy logic systems (FLSs) is presertted. Indirect and direct methods are combined to design the adaptive fuzzy output feedback controller and a high-gain observer is used to estimate the derivatives of the system output. The closed-loop system is proven to be semiglobally uniformly ultimately bounded. In addition, it is shown that if the approximation accuracy of the fuzzy logic system is high enough and the observer gain is chosen sufficiently large, an arbitrarily small tracking error can be achieved. Simulation results verify the effectiveness of the newly designed scheme and the theoretical discussion.     

非线性时滞系统自适应输出反馈跟踪控制

针对一类参数化非线性时滞输出反馈系统,提出了一种自适应输出跟踪控制器的设计方案。引入时滞滤波器估计未知系统状态,采用backstepping技术设计控制律和参数自适应律,运用占优方法处理非线性时滞项,从而放宽了对非线性时滞函数的要求,实现了对给定目标轨线的全局渐近跟踪,同时保证闭环系统所有信号一致有界。基于Lyapunov-Krasoviskii泛函方法证明了整个闭环系统的稳定性。实例仿真说明了该方案的可行性。     

Sampled-Data Semi-Global Robust Output Regulation for a Class of Nonlinear Systems

This paper investigates the semi-global robust output regulation problem for a class of uncertain nonlinear systems via a sampled-data output feedback control law. What makes the results interesting is that the nonlinearities of the proposed system do not have to satisfy linear growth condition and the uncertain parameters of our system are allowed to belong to some arbitrarily large prescribed compact subset. Two cases are considered. The first case is that the exogenous signal is constant. The second case is that the exogenous signal is time-varying and bounded. For the first case,the authors solve the problem exactly in the sense that the tracking error approaches zero asymptotically. For the second case, the authors solve the problem practically in the sense that the steady-state tracking error can be made arbitrarily small. Finally, an example is given to illustrate the effectiveness of our approach.     

基于神经网络的机械臂分散自适应跟踪控制

提出了一种适用于机械臂的基于神经网络的分散自适应轨迹跟踪控制方法。将机械臂的轨迹跟踪控制系统考虑为由多个非线性关联组成的不确定性复杂系统,采用分散控制方法进行控制器设计。在对每一子系统设计控制器时,采用直接反馈线性化,利用控制器构建伪线性系统,并引入神经网络自适应环节消除干扰、关联及逼近误差,从而使所提出的控制方法能够保证系统状态有较高的跟踪精度,且算法简单,易于实现。仿真表明,该算法能保证较高的跟踪效果。     

考虑齿隙的多约束导引控制一体化设计方法

在舰炮制导炮弹进行远程对岸火力支援的末段,考虑舵机齿隙、限定攻击角以及测量视线角速率受限,提出了一种基于动态面滑模与扩张状态观测器的多约束导引控制一体化设计方法。构建了制导炮弹的导引控制一体化的严反馈串级模型,将舵机视为更符合实际的含齿隙双惯量子系统。针对视线角速率和风等未知干扰,设计扩张状态观测器对其实施迅速而准确的估计。设计具备自适应指数趋近律的非奇异终端滑模,致使视线角速率与视线角跟踪误差在有限时间内零化。在高阶串级系统中合理运用动态面滑模,有效改善微分膨胀问题。运用Lyapunov理论证明了系统一致最终有界性以及重要状态的有限时间收敛性。通过对比仿真实验,在所提方法的调控下,含有舵机齿隙的制导炮弹在打击固定与蛇形机动目标时,均具有良好的制导性能。     

Global Output-Feedback Tracking for Nonlinear Cascade Systems with Unknown Growth Rate and Control Coefficients

This paper deals with the global practical tracking problem by output-feedback for a class of uncertain cascade systems with zero-dynamics and unmeasured states dependent growth.The systems investigated are substantially different from the closely related works,and have zero-dynamics,unknown growth rate,and unknown time-varying control coefficients.This makes the problem much more difficult to solve.Motivated by the authors' recent works,this paper proposes a new adaptive control scheme to achieve the global practical tracking.It is shown that the designed controller guarantees that the state of the resulting closed-loop system is globally bounded and the tracking error converges to a prescribed arbitrarily small neighborhood of the origin after a finite time.This is achieved by combining the methods of universal control and dead zone with backstepping technique,and using the framework of performance analysis in the closely related works.A numerical example demonstrates the effectiveness of the theoretical results.     

Model Reference Adaptive Control for Networked Distributed Systems with Strong Interconnections and Communication Delays

In recent years, networked distributed control systems (NDCS) have received research attention. Two of the main challenges that such systems face are possible delays in the communication network and the effect of strong interconnections between agents. This paper considers an NDCS that has delays in the communication network, as well as strong interconnections between its agents. The control objective is to make each agent track efficiently a reference model by attenuating the effect of strong interconnections via feedback based on the delayed information. First, the authors assume that each agent knows its own dynamics, as well as the interconnection parameters, but receives information about the states of its neighbors with some communication delay. The authors propose a distributed control scheme and prove that if the interconnections can be weakened and if the communication delays are small enough, then the proposed scheme guarantees that the tracking error of each agent is bounded with a bound that depends on the size of the weakened interconnections and delays, and reduces to zero as these uncertainties reduce to zero. The authors then consider a more realistic situation where the interconnections between agents are unknown despite the cooperation and sharing of state information. For this case the authors propose a distributed adaptive control scheme and prove that the proposed scheme guarantees that the tracking errors are bounded and small in the mean square sense with respect to the size of the weakened interconnections and delays, provided the weakened interconnections and time delays are small enough. The authors then consider the case that each agent knows neither its dynamics nor the interconnection matrices. For this case the authors propose a distributed adaptive control scheme and prove that the proposed scheme guarantees that the tracking errors are bounded and small in the mean square sense provided the weakened interconnections and time delays are small enough. Finally, the authors present an illustrative example to present the applicability and effectiveness of the proposed schemes.     

非仿射非线性系统的自适应模糊输出反馈控制

针对一类单输入单输出非仿射非线性系统,提出了基于观测器的自适应模糊输出反馈控制。该算法通过构造线性误差观测器估计系统输出误差和系统状态,利用估计状态变量和估计输出误差变量设计自适应控制律,采用模糊逻辑系统在线消除非线性系统中的不确定模型,引入监督控制消除系统逼近误差和外界干扰,并利用Lyapunov方法严格证明了在该控制律作用下闭环系统所有信号一致最终有解,闭环系统的输出能最终跟踪期望输出。仿真结果表明了该方法的有效性。     

The further result on global practical tracking for high-order uncertain nonlinear systems

This paper extends the unknown control coefficients with lower and upper constant bounds to the ones which may take arbitrarily large and /or small values.Since the existing methods are no longer applicable and the technical obstacles caused by the extensions are essential,new control design scheme should be exploited to the global practical tracking.By the approaches of Nussbaum-gain and adding a power integrator,the authors successfully propose the design scheme of the adaptive practical tracking controller for the systems.It is shown that the designed controller guarantees that all the closed-loop system states are bounded and the tracking error becomes prescribed arbitrarily small after a finite time.     

高超飞行器自适应动态规划的控制系统设计

针对高超声速飞行器的控制问题, 提出一种基于自适应动态规划的非线性优化学习控制方法, 设计了速度和高度自适应控制系统。首先, 将控制器分解为稳态控制项和最优反馈控制项, 同时借助反步法, 将原高超声速动力学模型转化为兼顾速度跟踪误差和高度跟踪误差的统一的误差控制模型。其次, 利用自适应动态规划法, 通过自适应调节评价网络的权值, 设计最优反馈学习控制律, 并通过Lyapunov稳定性理论严格证明了跟踪误差的一致最终有界性。最后, 数学仿真结果验证了所提方法的有效性。