Katsumi Yoshine

Non-linear analysis of a linear-non-linear-linear system

Abstract There are many non-linear systems in the field of biological systems, control systems and communication systems. The identification of non-linear system is a fundamental problem in these fields. Many investigations of non-linear systems have been carried out from the viewpoint of parameter identification. The so-called general model has been well studied in non-linear identification problems. The general model is a memoryless non-linearity sandwiched between two linear time-invariant subsystems. In biological systems, this model is applicable to retinal neurons in visual information processing. In physically realizable systems, we need to consider a causal system. Based on input-output causality, we develop a new complete identification method for the general model in the discrete time domain. Further, we derive a new formula for the estimation of non-linear parameters in the general model. The method developed here is simpler than conventional identification procedures. Finally, the results are ...

Estimation of kernel function of non-linear system by gaussian non-white noise

The kernel function of a non-linear system characterizes the properties of that system. The kernel function is well developed in the case of gaussian white noise. However in practice it is often necessary to apply an input of gaussian non-white noise in the control of biological systems. Although some methods have been developed that use gaussian non-white noise they do not have a simple computation. Furthermore, the kernel function obtained by these methods is not stable in practice. Here, we develop a gaussian non-white method based on a smoothing operation on the kernel function. The amplitude of the kernel function is then derived as a parameter, that characterizes the non-linear system. The kernel function obtained by a traditional method is compared by means of simulation with the smoothing method developed here.