Families of Exponentials The Method of Moments in Controllability Problems for Distributed Parameter Systems

This book presents the newly developed theory of non-harmonic Fourier series and its applications to the control of distributed parameter systems. The authors extend the theory to include vector exponential series. The first part of the book presents the modern theory of exponentials, using an operator theory approach. The second part of the book extends and upgrades the method of moments - one of the most powerful tools in the flourishing theory of the control of distributed parameter systems. The book then goes on to discuss the controllability of systems described by parabolic and hyperbolic PDEs for internal, boundary, initial, and pointwise control. Typical applications to optimal control problems are also considered. Researchers in control theory, operator theory, functional analysis and partial differential equations will find much to interest them in this treatise.

1. Elements of Hilbert spaces theory; 2. Families of vector-valued exponentials; 3. Fourier method in operator equations and controllability types; 4. Controllability of systems of parabolic type; 5. Controllability of systems of hyperbolic type; 6. Control of rectangular membrane vibrations; 7. Boundary control of strings system.

This book presents the newly developed theory of non-harmonic Fourier series and its applications to the control of distributed parameter systems. The modern theory of exponentials and the method of moments are the primary tools used. Applications to various types of control problems are discussed.