Introduction to the Calculus of Variations and Control with Modern Applications

ISBN: 9780367379551 出版年：2013 页码：558 Burns, John A CRC Press

Calculus of Variations Historical Notes on the Calculus of Variations Some Typical Problems Some Important Dates and People Introduction and Preliminaries Motivating Problems Mathematical Background Function Spaces Mathematical Formulation of Problems The Simplest Problem in the Calculus of Variations The Mathematical Formulation of the SPCV The Fundamental Lemma of the Calculus of Variations The First Necessary Condition for a Global Minimizer Implications and Applications of the FLCV Necessary Conditions for Local Minima Weak and Strong Local Minimizers The Euler Necessary Condition - (I) The Legendre Necessary Condition - (III) Jacobi Necessary Condition - (IV) Weierstrass Necessary Condition - (II) Applying the Four Necessary Conditions Sufficient Conditions for the Simplest Problem A Field of Extremals The Hilbert Integral Fundamental Sufficient Results Summary for the Simplest Problem Extensions and Generalizations Properties of the First Variation The Free Endpoint Problem The Simplest Point to Curve Problem Vector Formulations and Higher Order Problems Problems with Constraints: Isoperimetric Problem Problems with Constraints: Finite Constraints An Introduction to Abstract Optimization Problems Applications Solution of the Brachistochrone Problem Classical Mechanics and Hamilton's Principle A Finite Element Method for the Heat Equation Optimal Control Optimal Control Problems An Introduction to Optimal Control Problems The Rocket Sled Problem Problems in the Calculus of Variations Time Optimal Control Simplest Problem in Optimal Control SPOC: Problem Formulation The Fundamental Maximum Principle Application of the Maximum Principle to Some Simple Problems Extensions of the Fundamental Maximum Principle A Fixed-Time Optimal Control Problem Application to Problems in the Calculus of Variations Application to the Farmer's Allocation Problem Application to a Forced Oscillator Control Problem Application to the Linear Quadratic Control Problem The Maximum Principle for a Problem of Bolza The Maximum Principle for Nonautonomous Systems Application to the Nonautonomous LQ Control Problem Linear Control Systems Introduction to Linear Control Systems Linear Control Systems Arising from Nonlinear Problems Linear Quadratic Optimal Control The Riccati Differential Equation for a Problem of Bolza Estimation and Observers The Time Invariant Infinite Interval Problem The Time Invariant Min-Max Controller Problems appear at the end of each chapter.