正交回归神经网络及其在控制系统中的应用
摘要
现代社会的不断发展使控制理论面临的对象日益复杂化，传统的控制理论遇到巨大的挑战。神经网络、遗传算法和模糊逻辑等先进思想的出现并与控制理论相结合，无疑推动了控制理论的发展。为了克服现有的神经网络模型在动态非线性对象控制中的不足。本文提出了一种新型的动态正交基函数神经网络模型(DOPBNN)，并将该神经网络模型引入自动控制与建模领域，探讨和研究了基于该神经网络模型的模型辨识和控制问题，并做了大量的仿真工作。
本文的工作主要包括下面几个方面的内容：
1) 首先综述了神经网络及其在自动控制中的最新研究方法与成果以及目前存在的不足，为本文以后的工作构筑了一个较高的起点。
2) 在正交多项式理论基础上，结合了正交多项式基函数神经网络和高阶动态神经网络的长处，提出了一种新的神经网络结构—动态正交基神经网络。并从理论上证明了该网络结构具有良好的近似任何非线性动态特性的能力。这为非线性动态系统的辨识和控制提供了一种新的神经网络类工具。
3) 提出并证明了一些关于Legendre多项式的重要的不等式并在此基础上研究了使网络全局指数稳定的充分条件。
4) 详细研究了DOPBNN在非线性动态系统模型辨识中的应用。基于Lyapunov稳定性理论的网络权值学习规则保证了在无建模误差情况下辨识误差收敛至零，并使网络参数收敛。通过引入奇异摄动理论的有关方法，在存在渐近稳定的未建模动态情况下，证明了当奇异摄动满足一定的条件时，前述训练规则同样能够有效地使辨识误差收敛至零，并使网络参数收敛。通过引入在学习规则中加鲁棒项的方法，使得存在有界建模误差时，确保辨识误差和动态神经网络的参数能一致最终有界(UUB)稳定。
5) 针对一类反馈可线性化非线性系统，以基于Legendre多项式的动态正交基神经网络作为的辨识模型，运用等价原理和Lyapunov稳定性理论，
提出一种有效的稳定自适应间接控制算法以确保整个闭环控制系统误差和参数的UUB稳定性。
Society developments are increasing the complexity of many real tasks, which makes the traditional control theories limited. It is no doubt that more and more appearances of advanced tools such as neural networks, genetic algorithm and fuzzy logic can cause development of control theories. To overcome the drawback of existing neural network models in control and modeling of dynamic nonlinear systems, a novel neural network model known as Dynamic Orthogonal Polynomial Basis Neural Network (DOPBNN) is presented in this thesis. The modeling and control strategies and methodologies based on the DOPBNN are discussed in this thesis.
The main contributions of this thesis are as follows:
1) Up to date methods, applications, researches and drawbacks of existing neural networks in the cybernetics are summarized firstly. It becomes a good starting point of following research work.
2) Based on the combination of orthogonal polynomial theory and the existent recurrent neural network structure, a novel neural network model DOPBNN is proposed. It is proved that given enough number of neuron in the middle layer, a DOPBNN can approximate any dynamical system to any degree of accuracy.
3) Some important inequalities about Legendre polynomial are proposed and proved. Based on these inequalities, the sufficient
conditions of globally exponential stability criteria is proposed
4) The application of DOPBNN to modeling dynamic nonlinear systems is researched in detail. The update laws of weights of DOPBNN derived from the Lyapunov method ensure the convergency of the identification error and weights. By using the singular perturbation method, it is proved that if singular perturbation satisfies some conditions the convergency is ensured even there exist
本文的工作主要包括下面几个方面的内容：
1) 首先综述了神经网络及其在自动控制中的最新研究方法与成果以及目前存在的不足，为本文以后的工作构筑了一个较高的起点。
2) 在正交多项式理论基础上，结合了正交多项式基函数神经网络和高阶动态神经网络的长处，提出了一种新的神经网络结构—动态正交基神经网络。并从理论上证明了该网络结构具有良好的近似任何非线性动态特性的能力。这为非线性动态系统的辨识和控制提供了一种新的神经网络类工具。
3) 提出并证明了一些关于Legendre多项式的重要的不等式并在此基础上研究了使网络全局指数稳定的充分条件。
4) 详细研究了DOPBNN在非线性动态系统模型辨识中的应用。基于Lyapunov稳定性理论的网络权值学习规则保证了在无建模误差情况下辨识误差收敛至零，并使网络参数收敛。通过引入奇异摄动理论的有关方法，在存在渐近稳定的未建模动态情况下，证明了当奇异摄动满足一定的条件时，前述训练规则同样能够有效地使辨识误差收敛至零，并使网络参数收敛。通过引入在学习规则中加鲁棒项的方法，使得存在有界建模误差时，确保辨识误差和动态神经网络的参数能一致最终有界(UUB)稳定。
5) 针对一类反馈可线性化非线性系统，以基于Legendre多项式的动态正交基神经网络作为的辨识模型，运用等价原理和Lyapunov稳定性理论，
提出一种有效的稳定自适应间接控制算法以确保整个闭环控制系统误差和参数的UUB稳定性。
Society developments are increasing the complexity of many real tasks, which makes the traditional control theories limited. It is no doubt that more and more appearances of advanced tools such as neural networks, genetic algorithm and fuzzy logic can cause development of control theories. To overcome the drawback of existing neural network models in control and modeling of dynamic nonlinear systems, a novel neural network model known as Dynamic Orthogonal Polynomial Basis Neural Network (DOPBNN) is presented in this thesis. The modeling and control strategies and methodologies based on the DOPBNN are discussed in this thesis.
The main contributions of this thesis are as follows:
1) Up to date methods, applications, researches and drawbacks of existing neural networks in the cybernetics are summarized firstly. It becomes a good starting point of following research work.
2) Based on the combination of orthogonal polynomial theory and the existent recurrent neural network structure, a novel neural network model DOPBNN is proposed. It is proved that given enough number of neuron in the middle layer, a DOPBNN can approximate any dynamical system to any degree of accuracy.
3) Some important inequalities about Legendre polynomial are proposed and proved. Based on these inequalities, the sufficient
conditions of globally exponential stability criteria is proposed
4) The application of DOPBNN to modeling dynamic nonlinear systems is researched in detail. The update laws of weights of DOPBNN derived from the Lyapunov method ensure the convergency of the identification error and weights. By using the singular perturbation method, it is proved that if singular perturbation satisfies some conditions the convergency is ensured even there exist
引文
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