Classical and Modern Control -- Optimization -- Optimal Control -- Plant -- Performance Index -- Constraints -- Formal Statement of Optimal Control System -- Historical Tour -- Calculus of Variations -- Optimal Control Theory -- Calculus of Variations and Optimal Control -- Function and Functional -- Increment -- Differential and Variation -- Optimum of a Function and a Functional -- The Basic Variational Problem -- Fixed-End Time and Fixed-End State System -- Discussion on Euler-Lagrange Equation -- Different Cases for Euler-Lagrange Equation -- The Second Variation -- Extrema of Functions with Conditions -- Direct Method -- Lagrange Multiplier Method -- Extrema of Functionals with Conditions -- Variational Approach to Optimal Control Systems -- Terminal Cost Problem -- Different Types of Systems -- Sufficient Condition -- Summary of Pontryagin Procedure -- Summary of Variational Approach -- Stage I: Optimization of a Functional -- Stage II: Optimization of a Functional with Condition -- Stage III: Optimal Control System with Lagrangian Formalism -- Stage IV: Optimal Control System with Hamiltonian Formalism: Pontryagin Principle -- Salient Features -- Linear Quadratic Optimal Control Systems I -- Problem Formulation -- Finite-Time Linear Quadratic Regulator -- Symmetric Property of the Riccati Coefficient Matrix -- Optimal Control -- Optimal Performance Index -- Finite-Time Linear Quadratic Regulator: Time-Varying Case: Summary -- Salient Features -- LQR System for General Performance Index
Bibliography
Includes bibliographical references (pages 415-424) and index
