Control of Distributed Parameter Systems covers the proceedings of the Second IFAC Symposium, Coventry, held in Great Britain from June 28 to July 1, 1977. The book focuses on the methodologies, processes, and techniques in the control of distributed parameter systems, including boundary value control, digital transfer matrix, and differential equations. The selection first discusses the asymptotic methods in the optimal control of distributed systems; applications of distributed parameter control theory of a survey; and dual variational inequalities for external eigenvalue problems. The book also ponders on stochastic differential equations in Hilbert space and their application to delay systems and linear quadratic optimal control problem over an infinite time horizon for a class of distributed parameter systems. The manuscript investigates the semigroup approach to boundary value control and stability of nonlinear distributed parameter systems. Topics include boundary control action implemented through a dynamical system; classical boundary value controls; stability of nonlinear systems; and feedback control on the boundary. The text also focuses on the functional analysis interpretation of Lyapunov stability; method of multipliers for a class distributed parameter systems; and digital transfer matrix approach to distributed system simulation. The selection is a dependable source of data for readers interested in the control of distributed parameter systems.

Distributed parameter systems (DPS) are systems that have their evolution through time and in space. These systems are present in every type of industrial process, from chemical to electrical applications. Thus, proper modeling and control of DPS are indispensable for the optimization and control of such processes. Due to their spatiotemporal dynamics, these systems are generally represented by partial integro-differential equations (PIDEs), which brings issues with the control and monitoring of such applications. This thesis studies the modeling and control of such systems, specifically the ones modelled by first and second-order hyperbolic PDEs, not relying on the spatial approximation generally applied to deal with the PIDEs. First, an alternative model for transport-reaction processes is analyzed, taking into account the possible inertia present in the transport. Second, the regulator design of a heat exchanger system in the continuous-time setting is developed, ensuring disturbance rejection and proper output tracking. Then, the leap from the continuous to the discrete-time is taken by studying the regulator design for the sediment-filled water canal dynamics. Lastly, the optimal constrained controller is developed in the last chapters, to take into account constraints applied to the system. First, an autothermal reactor operating in an unstable condition is considered. The simulations show the controller performance and proper convergence to the desired steady-state. In the subsequent chapter, the constrained control problem is solved for the alternative model of transport-reaction processes. The difference in the system response of the commonly used model and the proposed model is noticeable. The discrete representation used for the systems in the discrete-time setting does not consider the early spatial approximation generally used when dealing with DPS.

The report is a survey of theoretical and computational methods in the field of optimal control of distributed parameter systems. This includes systems described by integral equations and partial differential equations. The various studies which have been done are grouped according to the method employed. A number of applications and potential applications of these methods are discussed, and certain deficiencies in the current state of knowledge are noted. Difficulties and opportunities in practical applications are discussed, and suggestions are offered for directions of research to render the results more readily usable. A list of references is included numbering more than 250 items: papers, report, and books.

This book represents an extended and substantially revised version of my earlierbook, Optimal Control in Problems ofMathematical Physics,originally published in Russian in 1975. About 60% of the text has been completely revised and major additions have been included which have produced a practically new text. My aim was to modernize the presentation but also to preserve the original results, some of which are little known to a Western reader. The idea of composites, which is the core of the modern theory of optimization, was initiated in the early seventies. The reader will find here its implementation in the problem of optimal conductivity distribution in an MHD-generatorchannel flow.Sincethen it has emergedinto an extensive theory which is undergoing a continuous development. The book does not pretend to be a textbook, neither does it offer a systematic presentation of the theory. Rather, it reflects a concept which I consider as fundamental in the modern approach to optimization of dis tributed systems. Bibliographical notes,though extensive, do not pretend to be exhaustive as well. My thanks are due to ProfessorJean-Louis Armand and ProfessorWolf Stadler whose friendly assistance in translating and polishing the text was so valuable. I am indebted to Mrs. Kathleen Durand and Mrs. Colleen Lewis for the hard job of typing large portions of the manuscript.