S Tan

Recurrent neural networks: A constructive algorithm, and its properties☆

Abstract In this paper, a constructive algorithm for a general recurrent neural network is proposed based on radial basis functions. It is shown that this algorithm is globally convergent. In addition, we will present two examples to illustrate the proposed method.

Efficient identification of rbf neural-net models for nonlinear discrete-time multivariable dynamical-systems

Abstract In this paper, we propose a recursive identification technique for nonlinear discrete-time multivariable dynamical systems. Extending an early result to multivariable systems [15], the technique approaches a nonlinear system identification problem in two stages: One is to build up recursively a RBF (Radial-Basis-Function) neural net model structure including the size of the neural net and the parameters in the RBF neurons; the other is to design a stable recursive weight updating algorithm to obtain the weights of the net in an efficient way. Heuristics are employed to analyze the effect of RBF net parameters to the error of identification, leading to a simple but effective means to establish these parameters. The weight updating algorithm is developed based on ideas in the theory of adaptive control. Key stability results are proved in the paper along with illustrative examples to show the effectiveness of applying such a technique and other practical considerations.

Near-optimal construction of wavelet networks for nonlinear system modeling

This paper proposes a constructive modeling scheme for nonlinear systems using wavelet networks as its model structure. Taking the advantage of the multiresolution nature as well as the localized feature of wavelet networks, a multi-scale modeling strategy has been developed to capture both the global and local characteristics of the systems over different scales from coarse to fine. A shrinking technique has been developed to delete some of the wavelet nodes to make the whole wavelet network as compact a size as possible, and in this sense, we can approach a near-optimal model within prescribed error tolerance. Main convergence results are established in the paper along with the analysis backing up to the construction procedure. Simulation is used to evaluate the effectiveness of the scheme.

A rule-based neural controller for inverted pendulum system

It is demonstrated how a heuristic neural control approach can be used to solve a complex nonlinear control problem. As well as swinging up the pendulum, the controller is required to bring the cart back to the origin of the track. Through the solution of this specific control problem, a heuristic neural control approach with task decomposition, control rule extraction and neural net rule implementation as its basic elements is illustrated. Specializing to the pendulum problem, the global control task is decomposed into sub-tasks, namely, pendulum positioning and cart positioning. Three separate neural sub-controllers are designed to cater to the sub-tasks and their coordination. The simulation result is provided to show the actual performance of the controller.<<ETX>>

On the design of feedforward neural networks for binary mappings

Abstract This paper presents a new design technique that builds a feedforward net for an arbitrary set of binary associations. The key idea of the technique is to treat the set of associations as a binary matrix mapping, and to decompose the mapping into a cascade of the so-called primitive operations. There are only three different types of primitive operations, each of which is easily realizable into a simple feedforward subnet. The mapping, thus the set of associations, can then be readily realized by cascading the simple feedforward subnets that realize the primitive operations. The new technique has the important advantage that the computation time spent in constructing the realization is proportional to k · n , compared to k · 2 n typical of many conventional direct design approaches, where k is the number of given binary patterns, n the dimension of the patterns. Further, the generated feedforward net has k · n number of neurons, the same order of magnitude compared to many conventional methods. With such a substantial reduction in computational time, the technique can be readily employed in constructing feedforward nets for binary association problems of extremely large size.

A new learning algorithm for RBF neural networks with applications to nonlinear system identification

We have presented an identification technique for nonlinear discrete-time multivariable dynamical systems based on RBF (Radial Basis Function) neural nets. The ways to fix the neural net structure and the weights are addressed as two different problems with separately developed online algorithms for their determination. At the present stage, the determination of the RBF net structure is still heuristics-based and this may lead to modeling error, and possible breakdown of the weight updating algorithm. There is thus a real need to develop theory that can help to aid the generation of RBF neural net structures.