李雅普诺夫函数方法介绍系列报告

讲座名称：李雅普诺夫函数方法系列报告

讲座人：Andrey Polyakov

讲座地点：北校区会议中心303-1报告厅

讲座人介绍：Andrey Polyakov received his PhD Degree in System Analysis, Control and Information Processing from the Voronezh State University, Russia in 2005. Till 2010 he was an Associate Professor in the same university. From 2007 to 2008 he was a postdoc in CINVESTAV, Mexico. Form 2010 to 2014, Andrey Polyakov was a Leading Researcher of the Institute of Control Sciences of Russian Academy of Sciences. In 2013, he joined the Inria centre of the University of Lille in France as a researcher. His main research interests include various aspects nonlinear control and estimation.

讲座内容介绍：The concept of stability introduced A.M. Lyapunov in 1892 is one of central notions in mathematics. The Lyapunov's theory addresses the stability of trajectories of dynamical systems under small perturbations of initial conditions. The stability analysis is widely used in various practical problems in electrical and mechanical engineering. For instance, many methods of automatic control design are based on stability theory. Most of models of real physical systems are nonlinear, so their stability analysis is a difficult problem in the general case. This series of lecture give a brief introduction to the Lyapunov function method that is the main tool for stability analysis of nonlinear dynamical systems. The lectures deal with systems modelled by both continuous and discontinuous ordinary differential equations, survey stability notions and, finally, discusses various Lyapunov Function Theorems. All theoretical results are supported by many illustrative examples.

时间：2024年4月30日 10:00-11:00 地点：北校区会议中心三层303-1报告厅

报告题目：Ordinary Differential Equations and Models of Dynamical Systems

报告摘要：This lecture presents an introduction to continuous ordinary differential equations (ODEs) and the corresponding modelling framework for dynamical systems.

时间：2024年4月30日 11:00-12:00 地点：北校区会议中心三层303-1报告厅

报告题目：Continuous Ordinary Differential Equations

报告摘要：This lecture is devoted to solution existence and uniqueness problems for continuous ODEs. Continuous dependence of solutions on initial data and on parameters is studied as well.

时间：2024年5月6日 10:00-11:00 地点：北校区会议中心三层303-1报告厅

报告题目： Discontinuous Ordinary Differential Equations

报告摘要：In this lecture, some elements of Carathéodory Theory and Filippov Theory of differential equations with discontinuous right-hand side are discussed.

时间：2024年5月6日 11:00-12:00 地点：北校区会议中心三层303-1报告厅

报告题目：Differential Inclusions

报告摘要：This lecture presents an introduction to the theory of differential inclusions, which is utilized for modelling of uncertain systems as well as for solution existence analysis of discontinuous differential equations.

时间：2024年5月7日 10:00-11:00 地点：北校区会议中心三层303-1报告厅

报告题目： Classical Stability Theory

报告摘要：This lecture gives an introduction to the stability theory introduced by A.M. Lyapunov. The classical concepts of stability (such as Lyapunov and asymptotic stability) are considered.

时间：2024年5月7日 11:00-12:00 地点：北校区会议中心三层303-1报告厅

报告题目：Modern Stability Theory

报告摘要：This lecture surveys popular recent development of the stability theory such as finite/fixed-time stability and input-to-state stability.

时间：2024年5月8日 10:00-11:00 地点：北校区会议中心三层303-1报告厅

报告题目： Classical Lyapunov Theorem

报告摘要：In this lecture, the basic ideas of Lyapunov function method are discussed and classical Lyapunov theorems are presented.

时间：2024年5月8日 11:00-12:00 地点：北校区会议中心三层303-1报告厅

报告题目：Modern Lyapunov Theorems

报告摘要：This lecture surveys the extensions of the Lyapunov function method and provides many examples and applications of the method.

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