Optimal Control for Chemical Engineers 1st Upreti Solution Manual

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Table of contents:

Introduction Definition Optimal Control versus Optimization Examples of Optimal Control Problems Structure of Optimal Control Problems Fundamental Concepts From Function to Functional Domain of a Functional Properties of Functionals Differential of a Functional Variation of an Integral Objective Functional Second Variation Optimality in Optimal Control Problems Necessary Condition for Optimality Application to Simplest Optimal Control Problem Solving an Optimal Control Problem Sufficient Conditions Piecewise Continuous Controls Lagrange Multipliers Motivation Role of Lagrange Multipliers Lagrange Multiplier Theorem Lagrange Multiplier and Objective Functional John Multiplier Theorem for Inequality Constraints Pontryagin’s Minimum Principle Application Problem Statement Pontryagin’s Minimum Principle Derivation of Pontryagin’s Minimum Principle Different Types of Optimal Control Problems Free Final Time Fixed Final Time Algebraic Constraints Integral Constraints Interior Point Constraints Discontinuous Controls Multiple Integral Problems Numerical Solution of Optimal Control Problems Gradient Method Penalty Function Method Shooting Newton-Raphson Method Optimal Periodic Control Optimality of Periodic Controls Solution Methods Pi Criterion Pi Criterion with Control Constraints Mathematical Review Limit of a Function Continuity of a Function Intervals and Neighborhoods Bounds Order of Magnitude Tayor Series and Remainder Autonomous Differential Equations Differential Derivative Newton-Raphson Method Fundamental Theorem of Calculus Mean Value Theorem Intermediate Value Theorem Implicit Function Theorem Bolzano-Weierstrass Theorem Weierstrass Theorem Linear or Vector Space Direction of a Vector Parallelogram Identity Triangle Inequality for Integrals CauchySchwarz Inequality Operator Inequality Conditional Statement Fundamental Matrix Index Bibliography and Exercises appear at the end of each chapter.

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