The Radial Basis Function Networks In Nonlinear Control

Radial basis function neural networks have recently gained considerable attention for the advantages such as the theoretic basis, the linearity-in-the-parameters and the availability of fast and efficient training methods. The dissertation focuses on RBF networks and nonlinear control. The author has done great research work on algorithms and control strategies. The major contributions of the dissertation are stated as follows:1) A new training algorithm is proposed to obtain RBF centers. It is very important to select appropriate centers because the performance of the RBF networks depends critically upon the given centers. The classical K-means clustering, competitive learning(CL) and frequency sensitive competitive learning(FSCL) have their own disadvantages. The most common algorithm rival penalized competitive learning(RPCL) contradicts to FSCL algorithm, which is consisted in RPCL algorithm. By combining FSCL and the method of rival penalization, a new clustering algorithm is achieved. This algorithm can exclude the redundant centers. Another advantage is that the number of the redundant centers, which are far away from the sample space, can be controlled. These remained redundant centers can be stored for new clusters in the future.2) Nonlinear control plays an important role in the control science. Especially in the recent years , nonlinear control improved greatly due to the creation of the theory of feedback linearization. But feedback linearization requires that the nonlinear part is analytical, that restricts its wide applications. Fortunately, it is easy for neural networks to approximate nonlinear mapping. By analyzing profoundly the popular inverse system method, the author presents the direct controller based on the RBF networks and derives strict proof of the existence of the controller. A controller can be designed further for the pseudo linear system constructed by the inverse model and the plant.3) Controller design is usually based on the obtained plant model. In practice, model error is unavoidable. According to information...