CONTROL OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH FUNCTION SPACE BOUNDARY CONDITIONS

Abstract

This chapter discusses the control of functional differential equations with function space boundary conditions. Functional differential equations play an important role in the modeling of many mechanical and electrical systems. They are also of importance in the areas of biomedical modeling of physiological and hormonal control systems. That a relationship between hyperbolic partial differential equations and functional differential equations of neutral type exists has been known for some time and this idea has been explored by a number of authors. The boundary conditions include as special cases those usually associated with transverse vibrations of a string or longitudinal vibrations of a rod, the ends of the string or rod being elastically supported. It emphasized on resolving the discrepancy between necessary conditions and sufficient conditions for relative controllability although extensions of results to systems with time-varying coefficients are also made. It was observed that for certain types of systems relative controllability is equivalent to controllability in which case the algebraic criteria are applicable.