Kernel-based Modeling Research For Nonlinear Distributed Parameter Systems

In the fields including the process industry and the biomedical, the dynamic actions of most systems have a close relationship between time and space, many processes of which are nonlinear distributed parameter processes (DPS) related to spatial-temporal. A good modeling is critical to the systems. However, due to the distributed characteristic coming from time-space coupled, the infinite-dimensional nature of the highly nonlinear distributed system and uncertainties in the process, and besides, limited sensors and actuators in most of the DPS, it increases the difficulty of accurately modeling. This destination is aimed at designing an effective modeling strategy to make the output temperature field of DPS quickly approach the prescribed contour with as less sensors and actuators as possible.With the available prior knowledge on the modelling research of DPS, we have designed two novel modeling methods. We propose a novel DPS modeling approach, in which a high-order nonlinear Volterra series is used to separate the time/space variables. With almost no additional computational complexity, the modeling accuracy is significantly improved. The experiment has been done to validate the superiority of the algorithm. In addition, we propose a novel nonlinear DPS modelling algorithm, a spatial-temporal Hammerstein modelling approach, by extending the traditional Hammerstein modelling into the DPS. First, the static nonlinear part and the distributed dynamical linear part of the Hammerstein model are expended onto a set of spatial and temporal basis functions. In order to reduce the parametric complexity, the KL decomposition is used to find the dominant spatial bases with Laguerre polynomials selected as the temporal bases. Then, using the Galerkin method, this spatial-temporal modeling will be reduced to a traditional temporal modeling problem. The unknown parameters can be easily estimated using the least squares estimation and the singular value decomposition. In the presence of unmodeled dynamics, a multi-channel modeling framework is proposed to improve the modeling performance. The convergence of the modeling will be guaranteed at certain conditions. The simulations are presented to show the effectiveness of this modeling method and its good prospects of application. At the same time, some problems in the research domain which needs to be further improved on the paper are also pointed out, several kernel ones of which are regarded as the emphases of my future research work.