Time-Varying Neural Network Based Iterative Learning Identification And Control Of Time-Varying Nonlinear Systems

Neural networks have powerful approximation, which have been widely used for identification and control of nonlinear systems. The weight of conventional neural network is always constant that updated by integral learning law. However, time-varying neural networks have variant weights. After the structure of networks has been known, how to train connection weights becomes the most important key that directly decides the pratical application of time-varying neural networks. Iterative learning control and repetitive control both achieve perfect tracking property under some assumptions. Time-varying weights updated by iterative learning algprithm become a feasible alternative. Time-varying nonlinear systems have sophisticated dynamical time-varying properties. Until now, research results in the literature for identification and control of time-varying nonlinear systems is comparatively little.In this paper, time-varying RBF networks and time-varying dynamical neural networks are presented and the weights are updated by iterative learning algorithm along iteration. Identification and control of time-varying nonlinear systems are solved by two kinds of the developed time-varying neural networks. The mian work and achievements are as follows:1. Time-varying RBF networks are proposed on the basis of conventional RBF networks. Two kinds of RBF networks having different connection weights are used to identify time-varying nonlinear systems, repectively. With approximation error, integral learning law with dead-zone is adopted to update connection weights of conventional RBF networks while partially-saturated iterative learning algorithm with dead-zone is proposed to adjust connection weights of time-varying RBF networks. What’s more, theoretical analysis ensures the effectiveness of proposed identification algorithm.2. Time-varying dynamical neural networks (DNNs) are presented by the architecture of conventional high-order DNNs with connection weights varying with time. Conventional DNNs and time-varying DNNs are both used to identify time-varying nonlinear systems. The weights of conventional DNNs are updated by least squares (LS) integral learning law with dead-zone. For time-varying case, iterative learning LS and its improved algorithms are used to update connection weights. Time-varying vectors are introduced to analyze that the proposed identification algorithm enables identification error asymptotically converging to neighbourhood of the dead-zone.3. Periodic RBF networks are presented by introducing repeating idears into the connection weights of RBF networks. Perfect identification results are established when the identification model contains compensation of approximation error. Integral learning law is adopted to adjust constant weights and then fully-saturated repetitive learning algorithm is applied to update the weights of periodic RBF networks based on repeated properties of nonlinear periodic systems.4. The connection weights of conventional high-order DNNs are replaced by periodic varying weights, which become periodic DNNs. In order to obtain ideal identify results, the estimation of approximation error upper bound is introduced in the learning mechanism to eliminate the influence of the approximation error. The least squares integral learning law is used to update the constant weights and least squares repetitive learning algorithm is used to adjust the weights of periodic DNNs. The introduction of periodic vectors successfully analyzed effectiveness of the proposed idenfication algorithm.5. For a class of time-varying nonlinear systems, time-vary ing neural networks are used to approximate the unknown nonlinear part in the controller, and the upper boundedness of approximation error is estimated by adaptive learning law. The compensation of approximation error is introduced into the designed adaptive iterative learning controller to make perfect tracking performance is achieved. The theoretical analysis ensures the boundedness of all the signals in the closed-loop system, even the tracking error and its derivative asymptotically converge to zero along the iteration increases.6. Adaptive iterative learning controller is directly designed based on time-varying DNNs for a class of time-varying nonlinear systems. To deal with approximation error, the weights are adjusted by iterative learning LS algorithm with dead-zone. The Lyapunov-like method ensures the boundedness of all the signals in closed-loop system, and the tracking error converges to the neighbourhood of the dead-zone along the iteration.7. For the tracking of nonlinear periodic time-varying systems, periodic RBF network based adaptive repetitive controller is designed and repetitive learning projection algorithm is used to adjust the weights of periodic RBF network. The estimation of approximation error upper bound by adaptive algorithm is introduced into the controller to eliminate the influence of approximation error. The boundedness of all the signals in the closed-loop system is ensured and the tracking error asymptotically converges to zero through theoretical analysis.