An Introduction to Optimal Control Theory

1. Introduction -- 2. Control Problem -- Notation and definitions, motivation of later results -- 3. Railroad Train Example -- Motivation of a “bang-bang principle,” the time optimal and minimum fuel problems -- 4. Controllability -- Restricted and unrestricted control, the controllability matrix -- 5. Controllability Using Special Controls -- Piecewise constant controls and bang-bang controls -- 6. Linear Time Optimal Systems -- Existence, necessary conditions, extremal control, reachable cone, normal systems and bang-bang controls, application to synthesis of railroad train example -- 7. General Control Systems: Existence -- Motivation behind existence results, two existence theorems and extensions, examples -- 8. General Control Systems: Necessary Conditions -- Principle of Optimality, Pontryagin maximum principle, transversality conditions, application to synthesis of railroad train example -- 9. Further Topics -- References -- List of Symbols -- Index for Definitions.