Optimal Control and the Calculus of Variations.

Cover -- Title Page -- Copyright -- Preface -- Contents -- 1. Introduction -- The maxima and minima of functions -- The calculus of variations -- Optimal control -- 2. Optimization in Rn -- Functions of one variable -- Critical points, end-points, and points of discontinuity -- Functions of several variables -- Minimization with constraints -- A geometrical interpretation -- Distinguishing maxima from minima -- 3. The calculus of variations -- The fixed end-point problem -- Problems in which the end-points are not fixed -- Finding minimizing curves -- Isoperimetric problems -- Sufficiency conditions -- Fields of extremals -- Hilbert's invariant integral -- Semi-fields and the Jacobi condition -- 4. Optimal control I: Theory -- Introduction -- Control of a simple first-order system -- Systems governed by ordinary differential equations -- The optimal control problem -- The Pontryagin maximum principle -- Optimal control to target curves -- 5. Optimal control II: Applications -- Introduction -- Time-optimal control of linear systems -- Optimal control to target curves -- Singular controls -- Fuel-optimal control -- Problems where the cost depends on x(t1) -- Linear systems with quadratic cost -- The steady-state Riccati equation -- The calculus of variations revisited -- 6. Proof of the maximum principle of Pontryagin -- Convex sets in Rn -- The linearized state equations -- The behaviour of H on an optimal path -- Sufficiency conditions for optimal control -- Appendix: Answers and hints for the exercises -- Bibliography -- Index.

This introduction to optimal control theory is intended for undergraduate mathematicians and for engineers and scientists with some knowledge of classical analysis. It includes sections on classical optimization and the calculus of variations. All the important theorems are carefully proved. There are many worked examples and exercises for the reader to attempt.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.