Optimization And Dynamical Systems

Software intensive systems are systems, which heavily interact with other systems, sensors, actuators, devices, other software systems, and users. More and more domains are involved with software intensive systems, e.g., automotive, telecommunication systems, embedded systems in general, industrial automation systems, and business applications. Moreover, the outcome of web services delivers a new platform for enabling software intensive systems.

This monograph is a revised and expanded version of lecture notes from a class given at Harvard University, Nankai University, and the Graduate School of the Academia Sinica during the academic year 1981-82. The objective was to present the formalism, together with numerous illustrative examples, of the calculus of variations for functionals whose domain of definition consists of integral manifolds of an exterior differential system. This includes as a special case the Lagrange problem of analyzing classical functionals with arbitrary (i.e., nonholonomic as well as holonomic) constraints. A secondary objective was to illustrate in practice some aspects of the theory of exterior differential systems. In fact, even though the calculus of variations is a venerable subject about which it is hard to say something new, (l) we feel that utilizing techniques from exterior differential systems such as Cauchy characteristics, the derived flag, and prolongation allows a systematic treatment of the subject in greater generality than customary and sheds new light on even the classical Lagrange problem.

This work is a revised and enlarged edition of a book with the same title published in Romanian by the Publishing House of the Romanian Academy in 1989. It grew out of lecture notes for a graduate course given by the author at the University if Ia~i and was initially intended for students and readers primarily interested in applications of optimal control of ordinary differential equations. In this vision the book had to contain an elementary description of the Pontryagin maximum principle and a large number of examples and applications from various fields of science. The evolution of control science in the last decades has shown that its meth­ ods and tools are drawn from a large spectrum of mathematical results which go beyond the classical theory of ordinary differential equations and real analy­ ses. Mathematical areas such as functional analysis, topology, partial differential equations and infinite dimensional dynamical systems, geometry, played and will continue to play an increasing role in the development of the control sciences. On the other hand, control problems is a rich source of deep mathematical problems. Any presentation of control theory which for the sake of accessibility ignores these facts is incomplete and unable to attain its goals.

Probability, Random Processes, and Ergodic Properties is for mathematically inclined information/communication theorists and people working in signal processing. It will also interest those working with random or stochastic processes, including mathematicians, statisticians, and economists.

This book, following the three published volumes of the book, provides the main purpose to collect research papers and review papers to provide an overview of the main issues, results, and open questions in the cutting-edge research on the fields of modeling, optimization, and dynamics and their applications to biology, economy, energy, industry, physics, psychology and finance. Assuming the scientific relevance of the presenting innovative applications as well as merging issues in these areas, the purpose of this book is to collect papers of the world experts in mathematics, economics, and other applied sciences that is seminal to the future research developments.

This book applies a step-by-step treatment of the current state-of-the-art of ordinary differential equations used in modeling of engineering systems/processes and beyond. It covers systematically ordered problems, beginning with first and second order ODEs, linear and higher-order ODEs of polynomial form, theory and criteria of similarity, modeling approaches, phase plane and phase space concepts, stability optimization and ending on chaos and synchronization.

Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those – well-known – based on differential geometry. The authors cover many aspects of nonlinear systems including stability theory, control design and extensions to distributed parameter systems.

This monograph applies the relative optimization approach to time nonhomogeneous continuous-time and continuous-state dynamic systems. The approach is intuitively clear and does not require deep knowledge of the mathematics of partial differential equations. The topics covered have the following distinguishing features: long-run average with no under-selectivity, non-smooth value functions with no viscosity solutions, diffusion processes with degenerate points, multi-class optimization with state classification, and optimization with no dynamic programming.