The three principal investigators propose to conduct research into the mathematical theory of control, stabilization, and optimization of infinite dimensional systems - in particular, distributed parameter systems governed by partial differential equations (PDE) and hereditary systems governed by differential- delay (DDE) or more general functional -differential equations (FDE). These investigations will concentrate on the problems of Hybrid Control Systems in which an infinite dimensional system is linked or coupled to a simpler system, usually a finite dimensional process controlled through ordinary differential equations (ODE). These mathematical questions are motivated by a multitude of control-theoretic problems of importance in current advanced engineering projects (aerospace guidance, space platform and space station control and stabilization), as well as in industrial engineering projects (tape processing). In this sense the investigators recognize the two-way interaction between classical mathematical analysis, and physical and engineering sciences; but this research project will concentrate on the mathematical side, although the research will necessarily be motivated by the areas of applications.
