演讲人Speaker：     李岩

题目：Finite energy Lyapunov function candidate for fractional order general nonlinear systems

时间Date：2019年11月27日       Time：10：00—11：00

地点Venue： A栋307室

内容摘要Abstract：

The construction of Lyapunov function candidates and the norm of infinite energy solu- tions remain among the most elusive unsolved problems of fractional order systems. This paper develops a new framework to construct finite energy Lyapunov function candidates for fractional order general nonlinear systems with randomness, uncertainty, time-delay or memory. Fundamentals of fractional order system and equilibrium are revisited to start up the investigation, where the pseudo and true states of fractional order systems are consid- ered. The process of constructing fractional order Lyapunov function candidate is mainly divided into three steps: Firstly, converting the original system into an equivalent Volterra integro-differential equation, where the weak singularity of fractional order system is in- cluded. Secondly, the fractional order Lyapunov function candidate is derived by canceling out the weak singularity that acts as the catalyst, and is absorbed into the fractional finite energy terms. Lastly, the first order derivative of the proposed Lyapunov function candidate is negative definite and bounded by power-law relevant terms. From finite energy aspect, the proposed fractional order Lyapunov function candidate is composed of potential, ki- netic and/or Riesz potential energies in terms of physics. The fractional order Lyapunov’s theorem and asymptotic stability of equilibrium points are discussed, and some non- L p sta- ble cases have been shown as fractional order finite energy ones. The impacts of fractional order, region of attraction and initialization state on the stability of equilibrium points are presented as well. Some classical integer order and fractional order results can be deduced from this work. A number of examples are illustrated to substantiate the effectiveness of the proposed unified framework.  

个人简介(About the speaker):

李岩，山东大学控制科学与工程学院教授、博导。长期从事生物建模、电池建模、精密测量仪器控制策略与控制器设计、分数阶控制系统的理论与应用等方面研究。近年来，承担或完成国家自然科学基金4项，省部级项目4项，并将分数阶建模与控制的结果成功应用于精密仪器加工、机器人精确轨迹控制、动力电池综合测试与智能模拟等领域。在国际国内控制和电气领域的权威期刊和会议上发表论文八十余篇，论文谷歌学术他引数千次，曾获分数阶微积分领域最高理论奖Riemann-Liouville奖、曾受邀在第四十届“二十一世纪智利自动控制大会”上作一小时大会报告。现任中国自动化学会分数阶系统与控制专业委员会副主任委员（负责学术交流）和数据驱动控制、学习与优化专业委员会委员，并与国内外相关领域学者、企业界同仁保持着良好的合作关系。