Control and Observation of a Class of Infinite Dimensional Systems with Age Structure

Given a linear dynamical system, we investigate the linear infinite dimensional system obtained by grafting an age structure. Such systems appear essentially in population dynamics with age structure when phenomena like spatial diffusion or transport are also taken into consideration, but they are of more general interest. We first show that the new system preserves some of the wellposedness properties of the initial one. Our main result asserts that if the initial system is null controllable in a time small enough than the structured system is also null controllable in a time depending on the various involved parameters. We also discuss an associated time optimal control problem. In some particular cases we discuss the dual problem of reconstructing the state of the system using a partial observations. We end up by stating several related open questions.

举办单位：数学与统计学院

发 布 人：吴双 发布时间： 2019-05-31

发 布 人：吴双 发布时间： 2019-05-31

Marius Tucsnak, chair professor at University of Bordeaux France. His main research interests are control of systems governed by partial differential equations (such as the parabolic, hyperbolic, Schrödinger or nonlinear plate equations) and the analysis and control of fluid-structure interactions. He is a coauthor (with George Weiss) of the book Observation and Control for Operator Semigroups (Birkhauser, 2009). He published around 80 papers in internationally referred journals, including Archive for Rational Mechanics and Analysis, Journal of the European Mathematical Society, Transactions of the American Mathematical Society, Journal of Differential Equations, SIAM Journal on Control or Automatica. He is currently corresponding editor for ESAIM COCV and associated editor for SIAM Journal on Control, MCSS, MCRF, JMFM. In 2013 he was elected member of the “Institut Universitaire de France” and in 2018 he received the Spiru Haret Prize of the Romanian Academy.