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Second of a two-volume treatise on deterministic control systems modeled by multi-dimensional partial differential equations.
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.
The present proceedings volume is devoted to two subjects. Stabilization with emphasis on exact controllability: considering a physical system, such as a vibrating plate, one can reach a steady state in a finite time by acting on the boundary. Control of boundaries: given a physical system find the geometry of the domain (optimal shape) which minimizes a cost related to the solution of a boundary value problem in this domain, for example find a minimum drag profile. Many lectures included mathematical analysis as well as engineering applications and numerical simulation.
Control and Dynamic Systems: Advances in Theory and Applications, Volume 36 reviews advances in theory and applications of large scale control and dynamic systems. Contributors focus on production control and the determination of optimal production rates, along with active control systems, uncertainty in control system design, and methods for analyzing multistage commodity markets. This volume is organized into eight chapters and begins with an introduction to multiobjective decision-tree analysis and its significance in applied situations, with two substantive examples. It then shifts to important techniques for the determination of robust economic policies, methods used in the analysis of multistage commodity markets, and a computationally effective algorithm for the determination of the optimal production rate. This book also describes many highly effective techniques for near optimal and robust model truncation. Robust adaptive identification and control algorithms for disturbances and unmodeled system dynamics are given consideration. The final chapter provides examples of the applied significance of the techniques presented in this book, including such large scale systems areas as aerospace, defense, chemical, environmental, and infrastructural industries. This book will be of interest to students and researchers in engineering and computer science.
Many infinite-dimensional linear systems can be modelled in a Hilbert space setting. Others, such as those dealing with heat transfer or population dynamics, need to be set more generally in Banach spaces. This is the first book dealing with well-posed infinite-dimensional linear systems with an input, a state, and an output in a Hilbert or Banach space setting. It is also the first to describe the class of non-well-posed systems induced by system nodes. The author shows how standard finite-dimensional results from systems theory can be extended to these more general classes of systems, and complements them with new results which have no finite-dimensional counterpart. Much of the material presented is original, and many results have never appeared in book form before. A comprehensive bibliography rounds off this work which will be indispensable to all working in systems theory, operator theory, delay equations and partial differential equations.
Contains contributions originating from the 'Conference on Optimal Control of Coupled Systems of Partial Differential Equations', held at the 'Mathematisches Forschungsinstitut Oberwolfach' in March 2008. This work covers a range of topics such as controllability, optimality systems, model-reduction techniques, and fluid-structure interactions.
Distributed Parameter Control Systems: Theory and Application is a two-part book consisting of 10 theoretical and five application-oriented chapters contributed by well-known workers in the distributed-parameter systems. The book covers topics of distributed parameter control systems in the areas of simulation, identification, state estimation, stability, control (optimal, stochastic, and coordinated), numerical approximation methods, optimal sensor, and actuator positioning. Five applications works include chemical reactors, heat exchangers, petroleum reservoirs/aquifers, and nuclear reactors. The text will be a useful reference for both graduate students and professional researchers working in the field.
This paper concerns the question of minimizing a quadratic cost functional associated with a linear symmetric hyperbolic control system over a finite time interval. A necessary and sufficient condition for a solution to exist is developed in terms of the solution of a two-point boundary value problem (TPBVP). The TPBVP is solved under various conditions. The limit case of an infinite time interval is also considered.
This book contains twenty four papers, presented at the conference on Volterra and Functional Differential Equations held in Virginia in 1981, on various topics, including Liapunov stability, Volterra equations, integral equations, and functional differential equations.