用线性多步法训练神经网络

研究用微分方程数值解法－－线性多步法替代神经网络的学习算法,指出在一定条件下神经网络的BP学习问题与求解一个相应的微分系统在渐近意义下是等价的,从而求解微分动力系统的数值解法也可用于神经网络的学习,给出了训练神经网络的Milne方法和BP－Milne结合算法以及Hamming方法和BP－Hamming结合算法,并以9点两类模式、随机模式识别和石油地质中沉积微相模式识别等3个问题为例进行了实验,实验结果表明利用微分动力系统的数值解法进行神经网络的学习是可行的。     

光滑神经网络解决一类线性约束的非Lipschitz优化问题

带有线性不等式约束的非光滑非优化问题被广泛应用于稀疏优化，具有重要的研究价值.为了解决这类问题，提出了一种基于光滑化和微分包含理论的神经网络模型.通过理论分析，证明了所提神经网络的状态解全局存在，轨迹能够在有限时间进入可行域并永驻其中，且任何聚点都是目标优化问题的广义稳定点.最后给出数值实验和图像复原实验验证神经网络在理论和应用中的有效性.与现有神经网络相比，它具有以下优势：初始点可以任意选取；避免计算精确罚因子；无需求解复杂的投影算子.     

模糊协商微分对策及其折中解

对于协商问题，为避免非线性问题带来求解上的困难并且使其能够处理不确定信息，基于T-S模糊微分对策的思想，构造出协商微分对策的模糊线性化模型．进一步探讨了在模糊线性协商微分对策系统下相应于折中解的控制器的设计方法．对一个2∶2对策问题做了仿真，其效果说明了解决问题方法的可行性．     

神经网络求解图最短路径问题的一种新方法

本文给出一种求解图最短路径问题的实用反馈式神经网络，并证明这两种网络的求解稳定性，这种网络基于最小值选择网而构成，对任意有向图和无向图均能收敛到其唯一的稳定点，由此求得图所有顶点对间的最短路径及最短路径长度，本文结果是神经网络求解非ＮＰ－骓难解类优化问题的一种新尝试。     

非线性零和微分对策的事件触发自适应动态规划算法

针对一类非线性零和微分对策问题,本文提出了一种事件触发自适应动态规划(event-triggered adaptive dynamic programming,ET--ADP)算法在线求解其鞍点.首先,提出一个新的自适应事件触发条件.然后,利用一个输入为采样数据的神经网络(评价网络)近似最优值函数,并设计了新型的神经网络权值更新律使得值函数、控制策略及扰动策略仅在事件触发时刻同步更新.进一步地,利用Lyapunov稳定性理论证明了所提出的算法能够在线获得非线性零和微分对策的鞍点且不会引起Zeno行为.所提出的ET--ADP算法仅在事件触发条件满足时才更新值函数、控制策略和扰动策略,因而可有效减少计算量和降低网络负荷.最后,两个仿真例子验证了所提出的ET--ADP算法的有效性.     

基于微分器与神经网络的PID控制算法研究

在工控系统微分器设计优化问题的研究中,由于在工业生产实践中,传统PID参数整定方法难以得到合理优化的PID参数,传统增量式PID控制存在抗干扰性较差、控制精度不高的问题.针对上述问题,提出了基于跟踪微分器与神经网络的PID控制算法.对跟踪微分器的原理进行了阐述,通过跟踪微分器实现位置信号滤波与速度信号求解;对增量式自适应PID控制算法进行了改进.在上述基础上,构建了基于微分跟踪器与神经网络的PID控制器.对控制算法进行了仿真,仿真结果表明,提出的控制算法具有抗扰动能力强、控制精度高等优点.     

两个优化问题的神经网络计算

本文采用推广的Ｈｏｐｈｆｉｅｌｄ神经网络模型求解ＮＰ完备的箱问题和背包问题，取得了较好的效果，为这两个问题的解决提供了一条新的途径。同时，对用推广的Ｈｏｐｆｉｅｌｄ神经网络模型解决优化问题的方法进行了探讨。     

基于T—S模糊建模思想的多人非合作微分对策

多人微分对策的研究是微分对策研究领域的难点.如果微分对策的状态方程和支付函数是非线性的,研究的方法有双边极值原理和变分法,那么就不可避免的要求解Hamilton-Jacobi偏微分方程组,这样的求解是比较困难的.针对非线性系统的多人微分对策,利用T-S模糊思想方法将非线性系统转化成若干个线性子系统,并对多个局中人进行分组,从而建立了多人非合作微分对策模型,最后举出一个4人非合作的实例进行仿真试验,效果说明了解决问题方法的可行性.     

基于暂态混沌神经网在非平衡B指派问题的应用

讨论了非平衡B指派问题的求解算法，给出了暂态混沌神经网络模型，并描述了非平衡B指派问题，提出了基于暂态混沌神经网络的非平衡B指派问题的求解算法。仿真结果表明，该网络可以通过混沌机制来避免陷入局部极小点，从而能够保证快速有效地求解该指派问题。该文还用这种方法求解了属于NP难题的文件分配问题(FAP)。     

神经网络求解图最短路径问题的一种新方法*

本文给出一种求解图最短路径问题的实用反馈式神经网络，并证明这种网络的求解稳定性．这种网络基于最小值选择网而构成，对任意有向图和无向图均能收敛到其唯一的稳定点．由此求得图所有顶点对阃的最短路径及最短路径长度．本文结果是神经网络求解非NP—难解类优化问题的一种新尝试．     

Impulsive Control and Synchronization for Delayed Neural Networks With Reaction–Diffusion Terms

This paper discuss the global exponential stability and synchronization of the delayed reaction–diffusion neural networks with Dirichlet boundary conditions under the impulsive control in terms of $p$-norm and point out the fact that there is no constant equilibrium point other than the origin for the reaction–diffusion neural networks with Dirichlet boundary conditions. Some new and useful conditions dependent on the diffusion coefficients are obtained to guarantee the global exponential stability and synchronization of the addressed neural networks under the impulsive controllers we assumed. Finally, some numerical examples are given to demonstrate the effectiveness of the proposed control methods.      

A robust Markov game controller for nonlinear systems

This paper proposes a reinforcement learning (RL)-based game-theoretic formulation for designing robust controllers for nonlinear systems affected by bounded external disturbances and parametric uncertainties. Based on the theory of Markov games, we consider a differential game in which a ‘disturbing’ agent tries to make worst possible disturbance while a ‘control’ agent tries to make best control input. The problem is formulated as finding a min–max solution of a value function. We propose an online procedure for learning optimal value function and for calculating a robust control policy. Proposed game-theoretic paradigm has been tested on the control task of a highly nonlinear two-link robot system. We compare the performance of proposed Markov game controller with a standard RL-based robust controller, and an H_∞ theory-based robust game controller. For the robot control task, the proposed controller achieved superior robustness to changes in payload mass and external disturbances, over other control schemes. Results also validate the effectiveness of neural networks in extending the Markov game framework to problems with continuous state–action spaces.     

Optimal Process Control Using Neural Networks

Infinite time optimal controllers have been designed for a dispersion type tubular reactor model by using the framework of adaptive critic optimal control design. For the reactor control problem, which is governed by two coupled nonlinear partial differential equations, an optimal controller synthesis is presented through two sets of neural networks. One set of neural networks captures the relationship between the states and the control, whereas the other set of networks captures the relationship between the states and the costates. This innovative approach embeds the solutions to the optimal control problem for a large number of initial conditions in the domain of interest. Although the main aim of this paper is to solve a process control problem, the methodology presented here can be viewed as a practical computational tool for many problems associated with nonlinear distributed parameter systems. Numerical results demonstrate the viability of the proposed method.     

Differential games,finite-time partial-state stabilisation of nonlinear dynamical systems,and optimal robust control

Two-player zero-sum differential games are addressed within the framework of state-feedback finite-time partial-state stabilisation of nonlinear dynamical systems. Specifically, finite-time partial-state stability of the closed-loop system is guaranteed by means of a Lyapunov function, which we prove to be the value of the game. This Lyapunov function verifies a partial differential equation that corresponds to a steady-state form of the Hamilton–Jacobi–Isaacs equation, and hence guarantees both finite-time stability with respect to part of the system state and the existence of a saddle point for the system's performance measure. Connections to optimal regulation for nonlinear dynamical systems with nonlinear-nonquadratic cost functionals in the presence of exogenous disturbances and parameter uncertainties are also provided. Furthermore, we develop feedback controllers for affine nonlinear systems extending an inverse optimality framework tailored to the finite-time partial-state stabilisation problem. Finally, two illustrative numerical examples show the applicability of the results proven.     

Intelligent computing to solve fifth-order boundary value problem arising in induction motor models

In this study, biologically inspired intelligent computing approached based on artificial neural networks (ANN) models optimized with efficient local search methods like sequential quadratic programming (SQP), interior point technique (IPT) and active set technique (AST) is designed to solve the higher order nonlinear boundary value problems arise in studies of induction motor. The mathematical modeling of the problem is formulated in an unsupervised manner with ANNs by using transfer function based on log-sigmoid, and the learning of parameters of ANNs is carried out with SQP, IPT and ASTs. The solutions obtained by proposed methods are compared with the reference state-of-the-art numerical results. Simulation studies show that the proposed methods are useful and effective for solving higher order stiff problem with boundary conditions. The strong motivation of this research work is to find the reliable approximate solution of fifth-order differential equation problems which are validated through strong statistical analysis.

     

Control of nonlinear dynamical systems using neural networks:controllability and stabilization

An attempt is made to indicate how practically viable controllers can be designed using neural networks, based on results in nonlinear control theory. The problem of stabilization of a dynamical system around an equilibrium point when the state of the system is accessible is considered. Simulation results are included to complement the theoretical discussions.     

Pinning Exponential Synchronization of Nonlinearly Coupled Neural Networks with Mixed Delays via Intermittent Control

This paper is concerned with the exponential synchronization problem of nonlinearly coupled neural networks with mixed delays. By employing the intermittent control strategy, several appropriate linear and adaptive pinning controllers are designed in each control period. With the help of a new differential inequality, some conditions are proposed to guarantee that the coupled networks can realize pinning synchronization exponentially. The minimum number of pinned nodes is determined by using high-degree pinning scheme. Two numerical examples are provided finally to demonstrate the effectiveness of the theoretical results.     

Artificial neural networks for solving ordinary and partialdifferential equations

We present a method to solve initial and boundary value problems using artificial neural networks. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the initial/boundary conditions and contains no adjustable parameters. The second part is constructed so as not to affect the initial/boundary conditions. This part involves a feedforward neural network containing adjustable parameters (the weights). Hence by construction the initial/boundary conditions are satisfied and the network is trained to satisfy the differential equation. The applicability of this approach ranges from single ordinary differential equations (ODE), to systems of coupled ODE and also to partial differential equations (PDE). In this article, we illustrate the method by solving a variety of model problems and present comparisons with solutions obtained using the Galerkin finite element method for several cases of partial differential equations. With the advent of neuroprocessors and digital signal processors the method becomes particularly interesting due to the expected essential gains in the execution speed.     

Using direct competition to select for competent controllers in evolutionary robotics

Evolutionary robotics (ER) is a field of research that applies artificial evolution toward the automatic design and synthesis of intelligent robot controllers. The preceding decade saw numerous advances in evolutionary robotics hardware and software systems. However, the sophistication of resulting robot controllers has remained nearly static over this period of time. Here, we make the case that current methods of controller fitness evaluation are primary factors limiting the further development of ER. To address this, we define a form of fitness evaluation that relies on intra-population competition. In this research, complex neural networks were trained to control robots playing a competitive team game. To limit the amount of human bias or know-how injected into the evolving controllers, selection was based on whether controllers won or lost games. The robots relied on video sensing of their environment, and the neural networks required on the order of 150 inputs. This represents an order of magnitude increase in sensor complexity compared to other research in this field. Evolved controllers were tested extensively in real fully-autonomous robots and in simulation. Results and experiments are presented to characterize the training process and the acquisition of controller competency under different evolutionary conditions.