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|a 519.6
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|a Upreti, Simant Ranjan.
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|a Optimal Control for Chemical Engineers.
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|a 1st ed.
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|a Milton :
|b Taylor & Francis Group,
|c 2012.
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|c ©2013.
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|a 1 online resource (309 pages)
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|a text
|b txt
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|a computer
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|a online resource
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|a Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- Notation -- 1 Introduction -- 1.1 Definition -- 1.2 Optimal Control versus Optimization -- 1.3 Examples of Optimal Control Problems -- 1.3.1 Batch Distillation -- 1.3.2 Plug Flow Reactor -- 1.3.3 Heat Exchanger -- 1.3.4 Gas Diffusion in a Non-Volatile Liquid -- 1.3.5 Periodic Reactor -- 1.3.6 Nuclear Reactor -- 1.3.7 Vapor Extraction of Heavy Oil -- 1.3.8 Chemotherapy -- 1.3.9 Medicinal Drug Delivery -- 1.3.10 Blood Flow and Metabolism -- 1.4 Structure of Optimal Control Problems -- Bibliography -- Exercises -- 2 Fundamental Concepts -- 2.1 From Function to Functional -- 2.1.1 Functional as a Multivariable Function -- 2.2 Domain of a Functional -- 2.2.1 Linear or Vector Spaces -- 2.2.2 Norm of a Function -- 2.3 Properties of Functionals -- 2.4 Differential of a Functional -- 2.4.1 Fréchet Differential -- 2.4.2 Gâteaux Differential -- 2.4.3 Variation -- 2.4.4 Summary of Differentials -- 2.4.5 Relations between Differentials -- 2.5 Variation of an Integral Objective Functional -- 2.5.1 Equivalence to Other Differentials -- 2.5.2 Application to Optimal Control Problems -- 2.6 Second Variation -- 2.6.1 Second Degree Homogeneity -- 2.6.2 Contribution to Functional Change -- 2.A Second-Order Taylor Expansion -- Bibliography -- Exercises -- 3 Optimality in Optimal Control Problems -- 3.1 Necessary Condition for Optimality -- 3.2 Application to Simplest Optimal Control Problem -- 3.2.1 Augmented Functional -- 3.2.2 Optimal Control Analysis -- 3.2.3 Generalization -- 3.3 Solving an Optimal Control Problem -- 3.3.1 Presence of Several Local Optima -- 3.4 Sufficient Conditions -- 3.4.1 Weak Sufficient Condition -- 3.5 Piecewise Continuous Controls -- 3.A Differentiability of λ -- 3.B Vanishing of (Fy + λGy + λ) at t=0 -- 3.C Mangasarian Sufficiency Condition.
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|a Bibliography -- Exercises -- 4 Lagrange Multipliers -- 4.1 Motivation -- 4.2 Role of Lagrange Multipliers -- 4.3 Lagrange Multiplier Theorem -- 4.3.1 Generalization to Several Equality Constraints -- 4.3.2 Generalization to Several Functions -- 4.3.3 Application to Optimal Control Problems -- 4.4 Lagrange Multiplier and Objective Functional -- 4.4.1 General Relation -- 4.5 John Multiplier Theorem for Inequality Constraints -- 4.5.1 Generalized John Multiplier Theorem -- 4.5.2 Remark on Numerical Solutions -- 4.A Inverse Function Theorem -- Bibliography -- Exercises -- 5 Pontryagin's Minimum Principle -- 5.1 Application -- 5.2 Problem Statement -- 5.2.1 Class of Controls -- 5.2.2 New State Variable -- 5.2.3 Notation -- 5.3 Pontryagin's Minimum Principle -- 5.3.1 Assumptions -- 5.3.2 Statement -- 5.4 Derivation of Pontryagin's Minimum Principle -- 5.4.1 Pulse Perturbation of Optimal Control -- 5.4.2 Temporal Perturbation of Optimal Control -- 5.4.3 Effect on Final State -- 5.4.4 Choice of Final Costate -- 5.4.5 Minimality of the Hamiltonian -- 5.4.6 Zero Hamiltonian at Free Final Time -- 5.A Convexity of Final States -- 5.B Supporting Hyperplane of a Convex Set -- Bibliography -- 6 Different Types of Optimal Control Problems -- 6.1 Free Final Time -- 6.1.1 Free Final State -- 6.1.2 Fixed Final State -- 6.1.3 Final State on Hypersurfaces -- 6.2 Fixed Final Time -- 6.2.1 Free Final State -- 6.2.2 Fixed Final State -- 6.2.3 Final State on Hypersurfaces -- 6.3 Algebraic Constraints -- 6.3.1 Algebraic Equality Constraints -- 6.3.2 Algebraic Inequality Constraints -- 6.4 Integral Constraints -- 6.4.1 Integral Equality Constraints -- 6.4.2 Integral Inequality Constraints -- 6.5 Interior Point Constraints -- 6.6 Discontinuous Controls -- 6.7 Multiple Integral Problems -- Bibliography -- Exercises -- 7 Numerical Solution of Optimal Control Problems.
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|a 7.1 Gradient Method -- 7.1.1 Free Final Time and Free Final State -- 7.1.2 Iterative Procedure -- 7.1.3 Improvement Strategy -- 7.1.4 Algorithm for the Gradient Method -- 7.1.5 Fixed Final Time and Free Final State -- 7.2 Penalty Function Method -- 7.2.1 Free Final Time and Final State on Hypersurfaces -- 7.2.2 Free Final Time but Fixed Final State -- 7.2.3 Algebraic Equality Constraints -- 7.2.4 Integral Equality Constraints -- 7.2.5 Algebraic Inequality Constraints -- 7.2.6 Integral Inequality Constraints -- 7.3 Shooting Newton-Raphson Method -- 7.A Derivation of Steepest Descent Direction -- 7.A.1 Objective -- 7.A.2 Sufficiency Check -- Bibliography -- Exercises -- 8 Optimal Periodic Control -- 8.1 Optimality of Periodic Controls -- 8.1.1 Necessary Conditions -- 8.2 Solution Methods -- 8.2.1 Successive Substitution Method -- 8.2.2 Shooting Newton-Raphson Method -- 8.3 Pi Criterion -- 8.4 Pi Criterion with Control Constraints -- 8.A Necessary Conditions for Optimal Steady State -- 8.B Derivation of Equation (8.12) -- 8.C Fourier Transform -- 8.D Derivation of Equation (8.25) -- Bibliography -- Exercises -- 9 Mathematical Review -- 9.1 Limit of a Function -- 9.2 Continuity of a Function -- 9.2.1 Lower and Upper Semi-Continuity -- 9.3 Intervals and Neighborhoods -- 9.4 Bounds -- 9.5 Order of Magnitude -- 9.5.1 Big-O Notation -- 9.6 Taylor Series and Remainder -- 9.7 Autonomous Differential Equations -- 9.7.1 Non-Autonomous to Autonomous Transformation -- 9.8 Differential -- 9.9 Derivative -- 9.9.1 Directional Derivative -- 9.10 Leibniz Integral Rule -- 9.11 Newton-Raphson Method -- 9.12 Composite Simpson's 1/3 Rule -- 9.13 Fundamental Theorem of Calculus -- 9.14 Mean Value Theorem -- 9.14.1 For Derivatives -- 9.14.2 For Integrals -- 9.15 Intermediate Value Theorem -- 9.16 Implicit Function Theorem -- 9.17 Bolzano-Weierstrass Theorem.
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|a 9.18 Weierstrass Theorem -- 9.19 Linear or Vector Space -- 9.20 Direction of a Vector -- 9.21 Parallelogram Identity -- 9.22 Triangle Inequality for Integrals -- 9.23 Cauchy-Schwarz Inequality -- 9.24 Operator Inequality -- 9.25 Conditional Statement -- 9.26 Fundamental Matrix -- Bibliography -- Index.
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|a Description based on publisher supplied metadata and other sources.
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|a Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2023. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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|a Electronic books.
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|i Print version:
|a Upreti, Simant Ranjan
|t Optimal Control for Chemical Engineers
|d Milton : Taylor & Francis Group,c2012
|z 9781439838945
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| 797 |
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|a ProQuest (Firm)
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| 856 |
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|u https://ebookcentral.proquest.com/lib/matrademy/detail.action?docID=7245632
|z Click to View
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