Cellular Automaton Models In Analysis Of Nonlinear Systems

In recent years, the analysis of nonlinear system is receiving increasing attention of the vast numbers of scholars. Because of the nonlinear of the system itself, the analysis, solution and control design of nonlinear systems becomes a dilemma. The problem about control of nonlinear system didn't get exciting analysis and control methods. The nonlinear system modeling method which based on the input - output data samples is the hot of the method of system modeling. It provides a new platform for analysis of nonlinear systems. Function approximation is an analysis method based on data. It can transform the nonlinear system model to a new algebraic space by Construction of the basis function. Then analysis and control the nonlinear system in the new space. Multi-Radial Basis Function has a good approximate ability, special in its capacity of local approximation. It can approximate the nonlinear systems by Arbitrary precision. It provides a theoretical foundation for the modeling method based on the input-output data. This paper will study the modeling method basic on the Multi-Radial Basis Function approximation-modeling of approximation element-space, and research the intelligent modeling analysis and control of complex system.In this paper, interpolation node structure method based on Multi-approximation theory is researched. We analyze the approximate ability of the modeling method of the approximation element-space, give the principle of state-space division and the method of constructing interpolation node by divide state-space of nonlinear systems. At last, to consider the computing time and accuracy of expression, we improve the intelligent nonlinear system model- element approximation model. This paper gives the concept of compactly supported Radial Basis Function, and proves the superiority of the compactly supported Radial Basis Function in computing time. This approximation element-space modeling method only need to sampling of data or construct nonlinear system model interpolation node, and then modeling to non-linear system used the data. Based on the approximation element-space method, we can change the nonlinear systems analysis and control synthesis problem from state-space of to element-space. It can avoid the complex nonlinear differential equations and the solution of differential equations. It is a new integrated approach of nonlinear systems analysis and Control which has a larger value of theoretical research and application prospects.