Author | Fleming, Wendell. author |
---|---|
Title | Deterministic and Stochastic Optimal Control [electronic resource] / by Wendell Fleming, Raymond Rishel |
Imprint | New York, NY : Springer New York, 1975 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-6380-7 |
Descript | XI, 222 p. online resource |
I The Simplest Problem in Calculus of Variations -- 1. Introduction -- 2. Minimum Problems on an Abstract SpaceโElementary Theory -- 3. The Euler Equation; Extremals -- 4. Examples -- 5. The Jacobi Necessary Condition -- 6. The Simplest Problem in n Dimensions -- II The Optimal Control Problem -- 1. Introduction -- 2. Examples -- 3. Statement of the Optimal Control Problem -- 4. Equivalent Problems -- 5. Statement of Pontryaginโs Principle -- 6. Extremals for the Moon Landing Problem -- 7. Extremals for the Linear Regulator Problem -- 8. Extremals for the Simplest Problem in Calculus of Variations -- 9. General Features of the Moon Landing Problem -- 10. Summary of Preliminary Results -- 11. The Free Terminal Point Problem -- 12. Preliminary Discussion of the Proof of Pontryaginโs Principle -- 13. A Multiplier Rule for an Abstract Nonlinear Programming Problem -- 14. A Cone of Variations for the Problem of Optimal Control -- 15. Verification of Pontryaginโs Principle -- III Existence and Continuity Properties of Optimal Controls -- 1. The Existence Problem -- 2. An Existence Theorem (Mayer Problem U Compact) -- 3. Proof of Theorem 2.1 -- 4. More Existence Theorems -- 5. Proof of Theorem 4.1 -- 6. Continuity Properties of Optimal Controls -- IV Dynamic Programming -- 1. Introduction -- 2. The Problem -- 3. The Value Function -- 4. The Partial Differential Equation of Dynamic Programming -- 5. The Linear Regulator Problem -- 6. Equations of Motion with Discontinuous Feedback Controls -- 7. Sufficient Conditions for Optimality -- 8. The Relationship between the Equation of Dynamic Programming and Pontryaginโs Principle -- V Stochastic Differential Equations and Markov Diffusion Processes -- 1. Introduction -- 2. Continuous Stochastic Processes; Brownian Motion Processes -- 3. Itoโs Stochastic Integral -- 4. Stochastic Differential Equations -- 5. Markov Diffusion Processes -- 6. Backward Equations -- 7. Boundary Value Problems -- 8. Forward Equations -- 9. Linear System Equations; the Kalman-Bucy Filter -- 10. Absolutely Continuous Substitution of Probability Measures -- 11. An Extension of Theorems 5.1,5.2 -- VI Optimal Control of Markov Diffusion Processes -- 1. Introduction -- 2. The Dynamic Programming Equation for Controlled Markov Processes -- 3. Controlled Diffusion Processes -- 4. The Dynamic Programming Equation for Controlled Diffusions; a Verification Theorem -- 5. The Linear Regulator Problem (Complete Observations of System States) -- 6. Existence Theorems -- 7. Dependence of Optimal Performance on y and ? -- 8. Generalized Solutions of the Dynamic Programming Equation -- 9. Stochastic Approximation to the Deterministic Control Problem -- 10. Problems with Partial Observations -- 11. The Separation Principle -- Appendices -- A. Gronwall-Bellman Inequality -- B. Selecting a Measurable Function -- C. Convex Sets and Convex Functions -- D. Review of Basic Probability -- E. Results about Parabolic Equations -- F. A General Position Lemma