Variable neural networks for adaptive control of nonlinear systems

This paper is concerned with the adaptive control of continuous-time nonlinear dynamical systems using neural networks. A novel neural network architecture, referred to as a variable neural network, is proposed and shown to be useful in approximating the unknown nonlinearities of dynamical systems. In the variable neural networks, the number of basis functions can be either increased or decreased with time, according to specified design strategies, so that the network will not overfit or underfit the data set. Based on the Gaussian radial basis function (GRBF) variable neural network, an adaptive control scheme is presented. The location of the centers and the determination of the widths of the GRBFs in the variable neural network are analyzed to make a compromise between orthogonality and smoothness. The weight-adaptive laws developed using the Lyapunov synthesis approach guarantee the stability of the overall control scheme, even in the presence of modeling error(s). The tracking errors converge to the required accuracy through the adaptive control algorithm derived by combining the variable neural network and Lyapunov synthesis techniques. The operation of an adaptive control scheme using the variable neural network is demonstrated using two simulated example

Identification and control of dynamic systems using neural networks.

The aim of this thesis is to contribute in solving problems related to the on-line identification and control of unknown dynamic systems using feedforward neural networks. In this sense, this thesis presents new on-line learning algorithms for feedforward neural networks based upon the theory of variable structure system design, along with mathematical proofs regarding the convergence of solutions given by the algorithms; the boundedness of these solutions; and robustness features of the algorithms with respect to external perturbations affecting the neural networks' signals. In the thesis, the problems of on-line identification of the forward transfer operator, and the inverse transfer operator of unknown dynamic systems are also analysed, and neural networks-based identification schemes are proposed. These identification schemes are tested by computer simulations on linear and nonlinear unknown plants using both continuous-time and discrete-time versions of the proposed learning algorithms. The thesis reports about the direct inverse dynamics control problems using neural networks, and contributes towards solving these problems by proposing a direct inverse dynamics neural network-based control scheme with on-line learning capabilities of the inverse dynamics of the plant, and the addition of a feedback path that enables the resulting control scheme to exhibit robustness characteristics with respect to external disturbances affecting the output of the system. Computer simulation results on the performance of the mentioned control scheme in controlling linear and nonlinear plants are also included. The thesis also formulates a neural network-based internal model control scheme with on-line estimation capabilities of the forward transfer operator and the inverse transfer operator of unknown dynamic systems. The performance of this internal model control scheme is tested by computer simulations using a stable open-loop unknown plant with output signal corrupted by white noise. Finally, the thesis proposes a neural network-based adaptive control scheme where identification and control are simultaneously carried out

Adaptive Predictive Control Using Neural Network for a Class of Pure-feedback Systems in Discrete-time

10.1109/TNN.2008.2000446IEEE Transactions on Neural Networks1991599-1614ITNN

Mathematical problems for complex networks

Copyright @ 2012 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is made available through the Brunel Open Access Publishing Fund.Complex networks do exist in our lives. The brain is a neural network. The global economy is a network of national economies. Computer viruses routinely spread through the Internet. Food-webs, ecosystems, and metabolic pathways can be represented by networks. Energy is distributed through transportation networks in living organisms, man-made infrastructures, and other physical systems. Dynamic behaviors of complex networks, such as stability, periodic oscillation, bifurcation, or even chaos, are ubiquitous in the real world and often reconfigurable. Networks have been studied in the context of dynamical systems in a range of disciplines. However, until recently there has been relatively little work that treats dynamics as a function of network structure, where the states of both the nodes and the edges can change, and the topology of the network itself often evolves in time. Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication and bioinformatics