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The second volume of this work continues the approach of the first volume, providing mathematical tools for the control engineer and examining such topics as random variables and sequences, iterative logarithmic and large number laws, differential equations, stochastic measurements and optimization, discrete martingales and probability space. It includes proofs of all theorems and contains many examples with solutions.It is written for researchers, engineers and advanced students who wish to increase their familiarity with different topics of modern and classical mathematics related to

Automatic control. --- Engineering instruments. --- Instruments, Engineering --- Scientific apparatus and instruments --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers

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Both refining and extending previous publications by the authors, the material in this monograph has been class-tested in mathematical institutions throughout the world. Covering some of the key areas of optimal control theory (OCT)—a rapidly expanding field that has developed to analyze the optimal behavior of a constrained process over time—the authors use new methods to set out a version of OCT’s more refined ‘maximum principle’ designed to solve the problem of constructing optimal control strategies for uncertain systems where some parameters are unknown. Referred to as a ‘min-max’ problem, this type of difficulty occurs frequently when dealing with finite uncertain sets. The text begins with a standalone section that reviews classical optimal control theory, covering the principal topics of the maximum principle and dynamic programming and considering the important sub-problems of linear quadratic optimal control and time optimization. Moving on to examine the tent method in detail, the book then presents its core material, which is a more robust maximum principle for both deterministic and stochastic systems. The results obtained have applications in production planning, reinsurance-dividend management, multi-model sliding mode control, and multi-model differential games. Key features and topics include: * A version of the tent method in Banach spaces * How to apply the tent method to a generalization of the Kuhn-Tucker Theorem as well as the Lagrange Principle for infinite-dimensional spaces * A detailed consideration of the min-max linear quadratic (LQ) control problem * The application of obtained results from dynamic programming derivations to multi-model sliding mode control and multi-model differential games * Two examples, dealing with production planning and reinsurance-dividend management, that illustrate the use of the robust maximum principle in stochastic systems Using powerful new tools in optimal control theory, The Robust Maximum Principle explores material that will be of great interest to post-graduate students, researchers, and practitioners in applied mathematics and engineering, particularly in the area of systems and control.

Control theory -- Mathematical models. --- Engineering mathematics. --- Mathematical optimization. --- Mathematics. --- Systems theory. --- Mathematical optimization --- Control theory --- Civil & Environmental Engineering --- Mechanical Engineering --- Engineering & Applied Sciences --- Operations Research --- Mechanical Engineering - General --- Mathematical models --- Mathematical models. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- System theory. --- Calculus of variations. --- Vibration. --- Dynamical systems. --- Dynamics. --- Control engineering. --- Systems Theory, Control. --- Control. --- Calculus of Variations and Optimal Control; Optimization. --- Vibration, Dynamical Systems, Control. --- Mathematical and Computational Engineering. --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Control and Systems Theory. --- Engineering --- Engineering analysis --- Cycles --- Mechanics --- Sound --- Mathematics --- Applied mathematics. --- Systems, Theory of --- Systems science --- Science --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Physics --- Statics --- Isoperimetrical problems --- Variations, Calculus of --- Control engineering --- Control equipment --- Engineering instruments --- Automation --- Programmable controllers --- Philosophy

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This book deals with continuous time dynamic neural networks theory applied to the solution of basic problems in robust control theory, including identification, state space estimation (based on neuro-observers) and trajectory tracking. The plants to be identified and controlled are assumed to be a priori unknown but belonging to a given class containing internal unmodelled dynamics and external perturbations as well. The error stability analysis and the corresponding error bounds for different problems are presented. The effectiveness of the suggested approach is illustrated by its ap

Neural networks (Computer science) --- Nonlinear control theory. --- Control theory --- Nonlinear theories --- Artificial neural networks --- Nets, Neural (Computer science) --- Networks, Neural (Computer science) --- Neural nets (Computer science) --- Artificial intelligence --- Natural computation --- Soft computing