时变时滞随机非线性系统的自适应神经网络跟踪控制

针对一类具有时变时滞的不确定随机非线性严格反馈系统的自适应跟踪问题,利用Razumikhin引理和backstepping方法,提出一种新的自适应神经网络跟踪控制器.该控制器可保证闭环系统的所有误差变量皆四阶矩半全局一致最终有界,并且跟踪误差可以稳定在原点附近的邻域内.仿真例子表明所提出控制方案的有效性.     

Adaptive neural control for uncertain stochastic nonlinear strict-feedback systems with time-varying delays: A Razumikhin functional method

This paper addresses the problem of adaptive neural control for a class of uncertain stochastic nonlinear strict-feedback systems with time-varying delays. A novel adaptive neural control scheme is presented for this class of systems, based on a combination of the Razumikhin functional approach, the backstepping technique and the neural network (NN) parameterization. The proposed adaptive controller guarantee that all the error variables are 4-Moment semi-globally uniformly ultimately bounded in a compact set while the system output converges to a small neighborhood of the reference signal. Two simulation examples are given to demonstrate the effectiveness of the proposed control schemes.     

Adaptive neural control of stochastic nonlinear systems with multiple time-varying delays and input saturation

This paper investigates the problem of adaptive neural control for a class of strict-feedback stochastic nonlinear systems with multiple time-varying delays, which is subject to input saturation. Via the backstepping technique and the minimal learning parameters algorithm, the problem is solved. Based on the Razumikhin lemma and neural networks’ approximation capability, a new adaptive neural control scheme is developed. The proposed control scheme can ensure that the error variables are semi-globally uniformly ultimately bounded in the sense of four-moment, while all the signals in the closed-loop system are bounded in probability. Two simulation examples are provided to demonstrate the effectiveness of the proposed control approach.     

基于神经网络的不确定随机非线性时滞系统自适应有界镇定

针对一类不确定严格反馈随机非线性时滞系统的自适应有界镇定问题,利用神经网络参数化和Backstepping方法,提出一种新的且含较少学习参数的神经网络自适应控制策略,以保证系统半全局随机有界.稳定性分析证明闭环系统的所有误差信号概率意义下有界.仿真结果表明所提出控制器设计方法的有效性.     

Adaptive Synchronization of Stochastic Memristor-Based Neural Networks with Mixed Delays

In this paper, adaptive synchronization of stochastic memristor-based neural networks with mixed delays is investigated. By using the differential inclusions theory, adaptive control technique and stochastic Lyapunov method, two adaptive updated laws are designed and two synchronization criteria are derived for stochastic memristor-based neural networks with mixed delays. The derived criteria complement and improve the previously known results since stochastic perturbations and mixed delays are considered. Finally, two numerical examples are provided to illustrate the effectiveness of the theoretical results.     

Observer-based Finite-time Control of Stochastic Non-strict-feedback Nonlinear Systems

This paper investigates the observer-based adaptive finite-time neural control issue of stochastic non-strict-feedback nonlinear systems. By establishing a state observer and utilizing the approximation property of the neural network, an adaptive neural network output-feedback controller is constructed. The controller solves the issue that the states of stochastic nonlinear system cannot be measured, and assures that all signals in the closed-loop system are bounded. Different from the existing adaptive control researches of stochastic nonlinear systems with unmeasured states, the proposed control scheme can guarantee the finite-time stability of the stochastic nonlinear systems. Furthermore, the effectiveness of the proposed control approach is verified by the simulation results.

     

Hybrid threshold strategy‐based adaptive tracking control for nonlinear stochastic systems with full‐state constraints

This article focuses on the adaptive tracking control problem for a class of interconnected nonlinear stochastic systems under full‐state constraints based on the hybrid threshold strategy. Different from the existing works, we propose a novel pre‐constrained tracking control algorithm to deal with the full‐state constraint problem. First, a novel nonlinear transformation function and a new coordinate transformation are developed to constrain state variables, which can directly cope with asymmetric state constraints. Second, the hybrid threshold strategy is constructed to provide a reasonable way in balancing system performance and communication constraints. By the use of dynamic surface control technique and neural network approximate technique, a smooth pre‐constrained tracking controller with adaptive laws is designed for the interconnected nonlinear stochastic systems. Moreover, based on the Lyapunov stability theory, it is proved that all state variables are successfully pre‐constrained within asymmetric boundaries. Finally, a simulation example is presented to verify the effectiveness of proposed control algorithm.     

Asymptotical synchronization for delayed stochastic neural networks with uncertainty via adaptive control

In this paper, the problem of the adaptive synchronization control is considered for neural networks with uncertainty and stochastic noise. Via utilizing stochastic analysis method and linear matrix inequality (LMI) approach, several sufficient conditions to ensure the adaptive synchronization for neural networks are derived. By the adaptive feedback methods, some suitable parameters update laws are found. Finally, a simulation result is provided to substantiate the effectiveness of the proposed approach.     

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.     

随机非线性系统基于事件触发机制的自适应神经网络控制

针对一类具有严格反馈结构且控制方向未知的随机非线性系统,提出了基于事件触发机制的自适应神经网络（Adaptive neural network,ANN）输出反馈控制方法.利用径向基神经网络逼近系统中未知的非线性函数.通过引入Nussbaum增益函数并设计滤波器,解决了系统控制方向未知的问题.通过设计具有相对阈值的事件触发机制,保证了闭环随机非线性系统的有界性.最后给出数值仿真例子验证所提控制方法的有效性.     

ANASA-a stochastic reinforcement algorithm for real-valued neuralcomputation

This paper introduces ANASA (adaptive neural algorithm of stochastic activation), a new, efficient, reinforcement learning algorithm for training neural units and networks with continuous output. The proposed method employs concepts, found in self-organizing neural networks theory and in reinforcement estimator learning algorithms, to extract and exploit information relative to previous input pattern presentations. In addition, it uses an adaptive learning rate function and a self-adjusting stochastic activation to accelerate the learning process. A form of optimal performance of the ANASA algorithm is proved (under a set of assumptions) via strong convergence theorems and concepts. Experimentally, the new algorithm yields results, which are superior compared to existing associative reinforcement learning methods in terms of accuracy and convergence rates. The rapid convergence rate of ANASA is demonstrated in a simple learning task, when it is used as a single neural unit, and in mathematical function modeling problems, when it is used to train various multilayered neural networks.     

具有输入和输出约束的高阶随机系统神经网络控制

针对高阶非线性系统,开展自适应神经网络跟踪控制器设计,系统受到随机扰动的影响.首次把输入和输出约束问题引入到高阶系统的跟踪控制中,并假定系统动态是未知.首先借用高斯误差函数表达连续可微的非对称饱和模型以实现输入约束,和障碍Lyapunov函数保证系统输出受限;其次,针对高阶非线性系统,径向基函数(RBF)神经网络用来克服未知系统动态和随机扰动.在每一步的backstepping计算中,仅用到单一的自适应更新参数,从而克服了过参数问题;最后,基于Lyapunov稳定性理论提出自适应神经网络控制策略,并减少了学习参数.最终结果表明设计的控制器能保证所有闭环信号半全局最终一致有界,并能使跟踪误差收敛到零值小的邻域内.仿真研究进一步验证了提出方法的有效性.     

Targeting and synchronization at tokamak with recurrent artificial neural networks

In this study, we propose an adaptive recurrent neural networks synchronization of H-mode and edge localized modes that is important for obtaining a long-pulse tokamak without disruption regime. The deterministic part of the plasma behavior should be synchronized with stochastic part by introducing stochastic artificial neural network.     

Adaptive finite-time neural network control for nonlinear stochastic systems with state constraints

This paper focuses on the adaptive finite-time neural network control problem for nonlinear stochastic systems with full state constraints. Adaptive controller and adaptive law are designed by backstepping design with log-type barrier Lyapunov function. Radial basis function neural networks are employed to approximate unknown system parameters. It is proved that the tracking error can achieve finite-time convergence to a small region of the origin in probability and the state constraints are confirmed in probability. Different from deterministic nonlinear systems, here the stochastic system is affected by two random terms including continuous Brownian motion and discontinuous Poisson jump process. Therefore, it will bring difficulties to the controller design and the estimations of unknown parameters. A simulation example is given to illustrate the effectiveness of the designed control method.     

基于自适应事件触发牵制控制的多时滞随机耦合神经网络簇同步

本文通过自适应事件触发牵制控制策略,研究了多时滞的随机耦合神经网络在均方意义下以指数速率进行簇同步的问题.在耦合神经网络中,同一簇中的节点只需与相应的孤立节点同步,而对于不同簇中节点之间的同步状态没有要求.首先,本文提出了一种事件触发牵制控制方法来解决耦合神经网络中节点数量众多、通讯复杂的问题.该方法不仅能减少耦合神经网络中控制器的数量,还可以减少控制信号的传输次数、减轻网络传输压力.然后根据M矩阵方法,建立了随机耦合神经网络均方指数稳定的充分条件.同时,利用自适应控制策略,给出了反馈增益的更新规律.最后,通过一个数值例子验证了所提出的自适应事件触发牵制控制策略的有效性和适用性.     

Compound binomial processes in neural integration

Explores some of the properties of stochastic digital signal processing in which the input signals are represented as sequences of Bernoulli events. The event statistics of the resulting stochastic process may be governed by compound binomial processes, depending upon how the individual input variables to a neural network are stochastically multiplexed. Similar doubly stochastic statistics can also result from datasets which are Bernoulli mixtures, depending upon the temporal persistence of the mixture components at the input terminals to the network. The principal contribution of these results is in determining the required integration period of the stochastic signals for a given precision in pulsed digital neural networks.     

Adaptive event-triggered tracking control for a class of stochastic nonlinear systems with full-state constraints

This paper proposes an adaptive event trigger-based sample-and-hold tracking control scheme for a class of strict-feedback nonlinear stochastic systems with full-state constraints. By introducing a tan-type stochastic Barrier Lyapunov function (SBLF) combined with radial basis function neural networks (RBFNNs), which is used to approximate the nonlinear functions in backstepping procedures, an adaptive event-triggered controller is designed. It is shown with stochastic stability theory that all the states cannot violate their constraints, and Zeno behavior is excluded almost surely. Meanwhile, all the signals of the closed-loop systems are bounded almost surely and the tracking error converges to an arbitrary small compact set in the fourth-moment sense. A simulation example is given to show the effectiveness of the control scheme.     

On adaptive boundary control for stochastic parabolic systems withunknown potential coefficient

An adaptive boundary control problem for a stochastic heat diffusion equation is studied. The considered system contains an unknown potential coefficient which is a function of the spatial variables. The estimation algorithm for the unknown potential coefficient is proposed by using the stochastic approximation technique. After showing the strong consistency of the estimated parameter, the cost for the adaptive control scheme presented here is shown to converge to the optimal ergodic cost. Finally some numerical examples are shown     

一种神经网络学习过程的数学描述

本文试图用神经网络学习的数学理论，以一个统一的方式看待，处理不同神经网络结构的学习过程。根据该理论，学习过程就是由随机信息源产生的输入信号驱动神经网络参数不断修改的过程，神经系统的自适应和自组织就是神经系统不断修改其行为以适应外部环境的变化。     

Controller design for synchronization of an array of delayed neural networks using a controllable probabilistic PSO

In this paper, a controllable probabilistic particle swarm optimization (CPPSO) algorithm is introduced based on Bernoulli stochastic variables and a competitive penalized method. The CPPSO algorithm is proposed to solve optimization problems and is then applied to design the memoryless feedback controller, which is used in the synchronization of an array of delayed neural networks (DNNs). The learning strategies occur in a random way governed by Bernoulli stochastic variables. The expectations of Bernoulli stochastic variables are automatically updated by the search environment. The proposed method not only keeps the diversity of the swarm, but also maintains the rapid convergence of the CPPSO algorithm according to the competitive penalized mechanism. In addition, the convergence rate is improved because the inertia weight of each particle is automatically computed according to the feedback of fitness value. The efficiency of the proposed CPPSO algorithm is demonstrated by comparing it with some well-known PSO algorithms on benchmark test functions with and without rotations. In the end, the proposed CPPSO algorithm is used to design the controller for the synchronization of an array of continuous-time delayed neural networks.