摘要
分析一类由对合Cauchy-Hadamard型微分方程构成的非线性系统的平稳周期稳定解,对提高非线性控制系统的参数自整定性和控制稳定性具有数学理论基础意义。传统的稳定解分析方法一直存在分析精度低、效率差的问题。提出采用对合Cauchy-Hadamard型非线性方程进行非线性系统的拟合,在齐次Sobolev空间中采用能量超临界波动的广义伪随机特征分析方法进行非线性系统平稳周期稳定解的微分逼近,在马尔尼数链中采用五次波动方程进行平稳周期稳定解的Lyapunove泛函,求得具有平稳周期稳定解的收敛性条件,最后进行了平稳周期解的稳定性和渐进收敛性证明。实验结果表明,该类非线性系统在非确定性凸优化条件下具有平稳周期稳定解,能有效满足稳定性控制需求。
The paper analyzes the periodic solutions to a class of stable nonlinear systems composed of Cauchy-Hadamard differential equations and shows that self-stabilization and stability are fundamental parameters of mathematical theory of nonlinear control systems.The method of traditional stability analysis always has the problem of low precision and poor efficiency.The fitting of nonlinear systems of Cauchy-Hadamard type nonlinear equation in homogeneous Sobolev space is investigated and the differential stable periodic solutions of nonlinear system are approximated by using the feature analysis method of energy supercritical fluctuation of generalized pseudorandom.The number of chain Marney in steady periodic stable solutions is obtained by using the Lyapunove function for the fifth-order wave equations.The conditions for convergence are obtained for stable periodic solution and the stability of stationary periodic solutions is proved.Experimental results show that the nonlinear system has a stable periodic solution under the condition of non-deterministic convex optimization,which can effectively meet the demand of stability control.
作者
余平洋
YU Pingyang(School of Information Engineering,Kaifeng University,Kaifeng,Henan 475004,China)
出处
《南昌大学学报（理科版）》
CAS
北大核心
2020年第6期529-533,共5页
Journal of Nanchang University(Natural Science)
基金
新疆维吾尔自治区自然科学基金资助项目(2017D01A13)。
关键词
非线性系统
平稳周期稳定解
泛函
收敛性
nonlinear system
stable periodic solution
functional
convergence
