双切换系统的分析与控制

For the dual switching hybrid object is subject to a deterministic switching signal and a stochastic Markovain switching signal. Firstly, based on some existing stability results of the dual-switching, we give the Robust control and H∞ control design algorithm of fixed double-switching linear system and variable dual-switching linear system with fractional uncertainty under the meaning of mean square and almost everywhere, respectively. Secondly, based on stochastic Multi-steps Multiple Lyapunov function methods, we discus Mean-Square Stability and Almost Everywhere Stability of dual-switching hybrid objects with co-existence and interaction of deterministic switching signal and a stochastic Markovain switching signal, moreover, given the predetermined definite switching time sequence, some criterions of the mean square stability and almost everywhere stability for fixed dual switched nonlinear systems and variable dual switched nonlinear systems are given under pre-given time-dependent switching signals. Finally, according to the approximating capability of deep neural network for super-complex and nonlinear functions, deep neural network structure and more “intelligent” deep neural network switching control algorithm are designed by combining deep neural network and switching ideas to improve the tracking and Disturbance rejection performance of fixed double-switching nonlinear systems and variable double-switching nonlinear systems. Efforts should be made to develop the theory of double-switching systems and to expand the application fields of deep learning. Furthermore, the theory of hybrid dynamic systems and the framework of deep learning theory are enriched.

针对确定切换信号和随机切换信号共存且相互作用的双切换混杂对象，首先利用已有的稳定性结果，分别在均方和几乎处处的意义之下，给出具有分式不确定的固定双切换线性系统和可变双切换线性系统的鲁棒控制和H∞控制设计算法；其次基于随机多步多李雅普若函数方法，深入研究具有切换信号和随机切换信号共存且相互作用的双切换混杂对象的均方稳定性和几乎处处稳定性，给出在预先给定的确定切换时间序列之下，固定双切换非线性系统和可变双切换非线性系统的均方稳定性和几乎处处稳定性判定算法；最后，利用深度神经网络模拟超强复杂非线性函数的强大能力，将深度神经网络与切换思想相结合，设计合理的深度神经网络结构和更具“智能”的深度神经网络切换控制算法，以提高固定双切换非线性系统和可变双切换非线性系统的跟踪性能和抗干扰等性能。努力在理论上发展双切换系统理论、拓展深度学习的应用领域，进一步丰富混杂动态系统综合的理论和深度学习理论体系框架。

双切换系统是一类同时存在确定性切换机制和随机切换机制且这两种不同性质的切换信号之间进行相互作用的一类新型切换系统，近年来在新型电力、信息技术等多学科领域得到了广泛的关注，风力发电和储能以及具有容量有限和故障共同影响的通信信道的多回路网络是其具体表现形式。本项目研究了确定性切换和Markov切换共存的双切换系统，并在此基础上研究了分数阶切换系统和多智能体系统。项目基本按照计划进行展开，并取得了一些成果，共发表相关论文21篇，培养研究生9名。具体内容表述如下：首先研究了双切换线性系统在几乎处处渐近稳定性和指数几乎处处稳定的条件，并给出了不确定双切换线性系统的鲁棒控制和H∞控制设计算法；其次基于随机多李雅普若函数方法和Markov过程的暂态性能，利用均方能量衰减原则设计确定性切换规则，给出了双切换非线性系统在预先给定的确定性切换规则之下的几乎处处渐近稳定和指数几乎处处稳定的判定算法；再次，利用神经网络模拟超强复杂非线性函数的强大能力，将神经网络引入双切换非线性系统的研究中，设计了神经网络确定性切换控制算法，以提高双切换非线性系统的跟踪性能；最后，将理论成果应用于变阶分数阶切换系统、多智能体系统的研究中。