The Researches On Quadratic System Decoupling Based On Neural Network Optimization Algorithms

Quadratic system is a form that control systems classified according to the mathematicalmodel, described by second-order differential equations system, dynamic characteristics ofmany engineering problems are used to quadratic system to characterized. Decoupledquadratic system is to reduce a complicated high-degree-of freedom system to some simplerlow-degree-of freedom subsystems, in numerical algebra algorithms ia to Structure PreservingIsospectraal Flows(SPIF) method, it is achieved by maintaining the Lancaster structuredecoupled quadratic system, the algorithm is currently too idealistic, still in the theoreticalstage. Therefore to address the actual needs of the field of engineering, on the dasis ofexisting theory to find practical and easy to have a numerical decoupling algorithm is veryimportant.This paper studied the methods of quadratic system decoupling of maintain Lancasterstructure, based on the original numerical methods and theoretical, to decouple the process ofnonlinear equations to be solved into a nonlinear constrained optimization problem, for thisoptimization problem to the original continuous Hopfield Network energy function rewrittenin the form of new, and make appropriate adjustments network structure, then determinenetwork parameters adjusted network, finally, the use of improved continuous HopfieldNetwork to complete a quadratic system of the original numerical decoupling.Based on the algorithm described and analysis, use the Python programming language toachieve the numerical simulation, on a two-dimensional system and a three-dimensionalsystem carried numerical experiments, analysis of experimental results show that, afteriteration in a certain accuracy constraints, this method is realized approximation decouplingof quadratic system, and good results. Finally, the algorithm presented in this paper and SPIFwith a comparative analysis, actual analysis shows that Neural Network optimizationalgorithm to solve the problem of quadratic system decoupling is a simple and practical valueof the method.This study is an attempt to quadratic system decoupling method has importantsignificance.