基于动态神经网络的非线性自适应逆控制研究
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摘要
自适应逆控制用数字信号处理的理论和方法解决自适应控制的问题，为控制系统设计和研究开辟了一个新颖的途径。自适应滤波技术是自适应逆控制系统设计和实现的基础，现代神经网络技术的发展为非线性自适应逆控制的研究和实现创造了条件。探索和设计合适的动态神经网络结构和算法，构建更加丰富的系统结构等已成为非线性自适应逆控制研究的重点，尤其对动态神经网络的研究为非线性自适应逆控制研究和实现奠定了必要的基础。本文研究了动态神经网络的结构和算法，及基于动态神经网络的非线性自适应逆控制系统，主要研究内容如下：
一、在分析研究生物神经元及人工神经元模型结构及功能的基础上，提出了一种新的动态人工神经元模型(DAF神经元)，它是一类自适应IIR突触时空神经元模型，它在简化动态神经元模型结构的同时提高了神经元的动态性能和自适应能力。基于DAF神经元模型可以构建一种新的动态神经网络(DAFNN)，DAFNN是一种局部反馈动态神经网络，其总体结构仍为前馈神经网络结构。与非线性自适应逆控制系统中常用的反馈神经网络相比，DAFNN的结构和算法都更加简单，而且具有可自适应调节的时间深度和时间分辨率。因此，DAFNN在非线性自适应逆控制中更具应用优势。
二、通过对PSO算法结构、稳定性及收敛性的研究，提出了一种以概率1全局收敛PSO算法，并进一步推广为神经网络离线学习算法。该算法通过加强对微粒群最优位置的局部搜索能力，提高了收敛的速度和精度；同时缩小了粒子群规模，提高了运行效率。与传统的BPTT算法相比，该算法无论是收敛速度、精度还是泛化能力，都有明显提高。
三、根据信号流图理论，设计并推导了一种神经网络的在线学习算法，并利用Lyapunov稳定性定理分析了算法的稳定性，提出了可以保证算法收敛的自适应学习速率。对于动态神经网络在线学习而言，该算法避免了传统梯度计算中复杂的链式求导过程，利用神经网络的信号流图及其线性的伴随流图，可以直接计算任何变量的梯度信息。并且，自适应的学习速率确保了动态神经网络稳定和算法的收敛。
四、结合两种现有非线性自适应逆控制系统的结构特点，提出了一种改进的非线性自适应逆控制系统扰动消除结构，在自适应过程收敛后，该系统能迅速消除输出扰动，且不影响系统自适应过程。最后，提出了一种用于非线性对象控制的近似线性自适应逆控制系统，它利用一组线性自适应LMS滤波器构建系统辨识器、控制器及对象逆模型，从而简化了非线性自适应逆控制系统结构和算法。
Adaptive inverse control (AIC) is a new method for the control problems. Itsrealization is based on adaptive filtering technology. Dynamical neural networks areimportant tools for design and control of nonlinear adaptive inverse control systems(NAICSs). In this dissertation, the architecture and learning algorithms of a certaindynamical neural networks and NAICSs based on that are studied. The main contents andresults are concluded as follow:
A novel dynamical neuron model is proposed for deal with temproal and spatialsignals. It is a kind of IIR filter synapses neuron, but the weights of the filters are adaptiveand the architecture is simpler than traditional ones. Feedforward neural networks based onsuch neurons, called DAFNNs, are locally recurrent neural networks, a kind of dynamicalneural networks. Compared with traditional recurrent neural networks, DAFNNs haveadaptive temporal depth and resolution. So they are good solutions for NAICSs.
A modified PSO (Particle Swarm Optimization) algorithm is proposed for nonlinearfuntions optimization. It has high convergence velocity and great convergence precision byimprove the locally searcher ability on best position of the swarm. Such PSO algorithm isused as a off-line training algorithm for neural networks. It can converge to global bestsolution in theory. Simulation results also show the neural networks trained with it havebetter generalization ability than that of BPTT algorithm.
A kind of on-line gradient learning algorithms based on signal flow graphs isproposed for neural networks on-line training. The signal flow graph and adjoint one of aneural network are used to compute the its gradients. The adaptive learning rate is designedby Lypunov theory for such on-line training algorithms.
A modified NAICS is proposed for improve the output disturbance cancellationability of the system. Such systems can cancel the disturbance immediately withoutaffecting other adaptive processings. Another NAICS is proposed in the paper. A set ofadaptive LMS filters are used as identifiers and controllers in the systems. The architectureof the systems is similar to a linear AIC. So the adaptive algorithms of the systems aresimpler than that of typical NAICSs.
一、在分析研究生物神经元及人工神经元模型结构及功能的基础上，提出了一种新的动态人工神经元模型(DAF神经元)，它是一类自适应IIR突触时空神经元模型，它在简化动态神经元模型结构的同时提高了神经元的动态性能和自适应能力。基于DAF神经元模型可以构建一种新的动态神经网络(DAFNN)，DAFNN是一种局部反馈动态神经网络，其总体结构仍为前馈神经网络结构。与非线性自适应逆控制系统中常用的反馈神经网络相比，DAFNN的结构和算法都更加简单，而且具有可自适应调节的时间深度和时间分辨率。因此，DAFNN在非线性自适应逆控制中更具应用优势。
二、通过对PSO算法结构、稳定性及收敛性的研究，提出了一种以概率1全局收敛PSO算法，并进一步推广为神经网络离线学习算法。该算法通过加强对微粒群最优位置的局部搜索能力，提高了收敛的速度和精度；同时缩小了粒子群规模，提高了运行效率。与传统的BPTT算法相比，该算法无论是收敛速度、精度还是泛化能力，都有明显提高。
三、根据信号流图理论，设计并推导了一种神经网络的在线学习算法，并利用Lyapunov稳定性定理分析了算法的稳定性，提出了可以保证算法收敛的自适应学习速率。对于动态神经网络在线学习而言，该算法避免了传统梯度计算中复杂的链式求导过程，利用神经网络的信号流图及其线性的伴随流图，可以直接计算任何变量的梯度信息。并且，自适应的学习速率确保了动态神经网络稳定和算法的收敛。
四、结合两种现有非线性自适应逆控制系统的结构特点，提出了一种改进的非线性自适应逆控制系统扰动消除结构，在自适应过程收敛后，该系统能迅速消除输出扰动，且不影响系统自适应过程。最后，提出了一种用于非线性对象控制的近似线性自适应逆控制系统，它利用一组线性自适应LMS滤波器构建系统辨识器、控制器及对象逆模型，从而简化了非线性自适应逆控制系统结构和算法。
Adaptive inverse control (AIC) is a new method for the control problems. Itsrealization is based on adaptive filtering technology. Dynamical neural networks areimportant tools for design and control of nonlinear adaptive inverse control systems(NAICSs). In this dissertation, the architecture and learning algorithms of a certaindynamical neural networks and NAICSs based on that are studied. The main contents andresults are concluded as follow:
A novel dynamical neuron model is proposed for deal with temproal and spatialsignals. It is a kind of IIR filter synapses neuron, but the weights of the filters are adaptiveand the architecture is simpler than traditional ones. Feedforward neural networks based onsuch neurons, called DAFNNs, are locally recurrent neural networks, a kind of dynamicalneural networks. Compared with traditional recurrent neural networks, DAFNNs haveadaptive temporal depth and resolution. So they are good solutions for NAICSs.
A modified PSO (Particle Swarm Optimization) algorithm is proposed for nonlinearfuntions optimization. It has high convergence velocity and great convergence precision byimprove the locally searcher ability on best position of the swarm. Such PSO algorithm isused as a off-line training algorithm for neural networks. It can converge to global bestsolution in theory. Simulation results also show the neural networks trained with it havebetter generalization ability than that of BPTT algorithm.
A kind of on-line gradient learning algorithms based on signal flow graphs isproposed for neural networks on-line training. The signal flow graph and adjoint one of aneural network are used to compute the its gradients. The adaptive learning rate is designedby Lypunov theory for such on-line training algorithms.
A modified NAICS is proposed for improve the output disturbance cancellationability of the system. Such systems can cancel the disturbance immediately withoutaffecting other adaptive processings. Another NAICS is proposed in the paper. A set ofadaptive LMS filters are used as identifiers and controllers in the systems. The architectureof the systems is similar to a linear AIC. So the adaptive algorithms of the systems aresimpler than that of typical NAICSs.
引文
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