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Deterministic and stochastic control systems with aftereffect are considered. Necessary and sufficient conditions for the optimality of such systems are obtained. Various methods for the construction of exact and approximate solutions of optimal control problems are suggested. Problems of adaptive control for systems with aftereffect are analyzed. Numerous applications are described. The book can be used by researchers, engineers, and graduate students working in optimal control theory and various applications.
Hereditary systems (or systems with either delay or after-effects) are widely used to model processes in physics, mechanics, control, economics and biology. An important element in their study is their stability. Stability conditions for difference equations with delay can be obtained using a Lyapunov functional. Lyapunov Functionals and Stability of Stochastic Difference Equations describes a general method of Lyapunov functional construction to investigate the stability of discrete- and continuous-time stochastic Volterra difference equations. The method allows the investigation of the degree to which the stability properties of differential equations are preserved in their difference analogues. The text is self-contained, beginning with basic definitions and the mathematical fundamentals of Lyapunov functional construction and moving on from particular to general stability results for stochastic difference equations with constant coefficients. Results are then discussed for stochastic difference equations of linear, nonlinear, delayed, discrete and continuous types. Examples are drawn from a variety of physical systems including inverted pendulum control, study of epidemic development, Nicholson’s blowflies equation and predator–prey relationships. Lyapunov Functionals and Stability of Stochastic Difference Equations is primarily addressed to experts in stability theory but will also be of use in the work of pure and computational mathematicians and researchers using the ideas of optimal control to study economic, mechanical and biological systems.
The book consists mainly of two parts: Chapter 1 - Chapter 7 and Chapter 8 - Chapter 14. Chapter 1 and Chapter 2 treat design techniques based on linearization of nonlinear systems. An analysis of nonlinear system over quantum mechanics is discussed in Chapter 3. Chapter 4 to Chapter 7 are estimation methods using Kalman filtering while solving nonlinear control systems using iterative approach. Optimal approaches are discussed in Chapter 8 with retarded control of nonlinear system in singular situation, and Chapter 9 extends optimal theory to H-infinity control for a nonlinear control system.Chapters 10 and 11 present the control of nonlinear dynamic systems, twin-rotor helicopter and 3D crane system, which are both underactuated, cascaded dynamic systems. Chapter 12 applies controls to antisynchronization/synchronization in the chaotic models based on Lyapunov exponent theorem, and Chapter 13 discusses developed stability analytic approaches in terms of Lyapunov stability. The analysis of economic activities, especially the relationship between stock return and economic growth, is presented in Chapter 14.
Advanced Control Systems: Theory and Applications provides an overview of advanced research lines in control systems as well as in design, development and implementation methodologies for perspective control systems and their components in different areas of industrial and special applications. It consists of extended versions of the selected papers presented at the XXV International Conference on Automatic Control “Automatics 2018” (September 18-19, 2018, Lviv, Ukraine) which is the main Ukrainian Control Conference organized by Ukrainian Association on Automatic Control (National member organization of IFAC) and Lviv National University “Lvivska Politechnica”. More than 100 papers were presented at the conference with topics including: mathematical problems of control, optimization and game theory; control and identification under uncertainty; automated control of technical, technological and biotechnical objects; controlling the aerospace craft, marine vessels and other moving objects; intelligent control and information processing; mechatronics and robotics; information measuring technologies in automation; automation and IT training of personnel; the Internet of things and the latest technologies. The book is divided into two main parts, the first concerning theory (7 chapters) and the second concerning applications (7 chapters) of advanced control systems. The first part “Advances in Theoretical Research on Automatic Control” consists of theoretical research results which deal with descriptor control impulsive delay systems, motion control in condition of conflict, inverse dynamic models, invariant relations in optimal control, robust adaptive control, bio-inspired algorithms, optimization of fuzzy control systems, and extremal routing problem with constraints and complicated cost functions. The second part “Advances in Control Systems Applications” is based on the chapters which consider different aspects of practical implementation of advanced control systems, in particular, special cases in determining the spacecraft position and attitude using computer vision system, the spacecraft orientation by information from a system of stellar sensors, control synthesis of rotational and spatial spacecraft motion at approaching stage of docking, intelligent algorithms for the automation of complex biotechnical objects, an automatic control system for the slow pyrolysis of organic substances with variable composition, simulation complex of hierarchical systems based on the foresight and cognitive modelling, and advanced identification of impulse processes in cognitive maps. The chapters have been structured to provide an easy-to-follow introduction to the topics that are addressed, including the most relevant references, so that anyone interested in this field can get started in the area. This book may be useful for researchers and students who are interesting in advanced control systems.
When solving the control and design problems in aerospace and naval engi neering, energetics, economics, biology, etc., we need to know the state of investigated dynamic processes. The presence of inherent uncertainties in the description of these processes and of noises in measurement devices leads to the necessity to construct the estimators for corresponding dynamic systems. The estimators recover the required information about system state from mea surement data. An attempt to solve the estimation problems in an optimal way results in the formulation of different variational problems. The type and complexity of these variational problems depend on the process model, the model of uncertainties, and the estimation performance criterion. A solution of variational problem determines an optimal estimator. Howerever, there exist at least two reasons why we use nonoptimal esti mators. The first reason is that the numerical algorithms for solving the corresponding variational problems can be very difficult for numerical imple mentation. For example, the dimension of these algorithms can be very high.
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Time-Lag Control Systems