Distributed Cooperative Learning Control For Nonlinear Systems

During the past two decades,neural networks control of uncertain nonlinear systems has been investigated widely. In these researchers,they mainly focus on that how to guarantee the closed-loop stability. Motivated by deterministic learning theory and consensus theory that are extensively studied recently,the distributed cooperative learning control scheme is proposed. This paper mainly includes two parts.In the first part,the neural tracking problem is addressed for a group of uncertain nonlinear continues-time systems where the system structures are identical but the reference signals are different. This work focuses on studying the learning capability of neural networks during the control process. First,we propose a novel control scheme,called distributed cooperative learning control scheme,by establishing the communication topology among adaptive laws of neural network weights in order to share their learned knowledge on-line. It is further proved that if the communication topology is undirected and connected,all estimated weights of neural networks can converge to small neighborhoods around their optimal values over a domain consisting of the union of all state orbits. Secondly,as a corollary,it is shown that the conclusion on the deterministic learning still holds in the decentralized adaptive neural control scheme where,however,the estimated weights of neural networks just converge to small neighborhoods of the optimal values along their own state orbits. Thus,the learned controllers obtained by distributed cooperative learning scheme have the better generalization capability than ones obtained by decentralized learning method. A simulation example is provided to verify the effectiveness and advantages of the control schemes.In the second part,for a group of uncertain nonlinear discrete-time systems where the system structures are identical but the reference signals are different,the neural tracking problem and the learning capability of neural networks are studied. By establishing the undirected and connected communication topology,it is proved that all estimated weights of neural networks can converge to small neighborhoods around their optimal values over a domain consisting of the union of all state orbits. Moreover,the learning control property using experience is studied. Finally,a simulation of decentralized learning and distributed cooperative learning is given to show the effectiveness and advantages of the distributed cooperative learning schemes.