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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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This book provides a blend of Matrix and Linear Algebra Theory, Analysis, Differential Equations, Optimization, Optimal and Robust Control. It contains an advanced mathematical tool which serves as a fundamental basis for both instructors and students who study or actively work in Modern Automatic Control or in its applications. It is 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 System and Automatic Control Theories * Provides comprehensive theory of matrices, real, complex and functional analysis * Provides practical examples of modern optimization methods that can be effectively used in variety of real-world applications * Contains worked proofs of all theorems and propositions presented.

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Artificial intelligence --- Machine learning --- Self-organizing systems

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Featuring original research from well-known experts in the field of sliding mode control, this monograph presents new design schemes for implementing LQ control solutions in situations where the output system is the only information provided about the state of the plant. This new design works under the restrictions of matched disturbances without losing its desirable features. On the cutting-edge of optimal control research, Robust Output LQ Optimal Control via Integral Sliding Modes is an excellent resource for both graduate students and professionals involved in linear systems, optimal control, observation of systems with unknown inputs, and automatization. In the theory of optimal control, the linear quadratic (LQ) optimal problem plays an important role due to its physical meaning, and its solution is easily given by an algebraic Riccati equation. This solution turns out to be restrictive, however, because of two assumptions: the system must be free from disturbances and the entire state vector must be known. A new technique, called  output integral sliding modes, eliminates the effects of disturbances acting in the same subspace as the control. By using LQ-optimal control together with integral sliding modes, the former is made robust and based on output information only. Thus optimal control theory improves its applicability.

Sliding mode control. --- Robust control. --- Robustness (Control systems) --- Automatic control --- Systems theory. --- Mathematical optimization. --- Engineering mathematics. --- Engineering design. --- Vibration. --- Systems Theory, Control. --- Control and Systems Theory. --- Calculus of Variations and Optimal Control; Optimization. --- Mathematical and Computational Engineering. --- Engineering Design. --- Vibration, Dynamical Systems, Control. --- Cycles --- Mechanics --- Sound --- Design, Engineering --- Engineering --- Industrial design --- Strains and stresses --- Engineering analysis --- Mathematical analysis --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Design --- Mathematics --- System theory. --- Control engineering. --- Calculus of variations. --- Applied mathematics. --- Dynamical systems. --- Dynamics. --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Physics --- Statics --- Isoperimetrical problems --- Variations, Calculus of --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Systems, Theory of --- Systems science --- Science --- Philosophy

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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