Principles of Optimal Control Theory
Kluwer Academic/Plenum Publishers (Verlag)
978-0-306-30977-9 (ISBN)
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Although the proofs of the basic theorems presented here are far from being the shortest, I think they are fully justified from the conceptual view- point. In any case, the notions we introduce and the methods developed have one unquestionable advantage -they are constantly used throughout control theory, and not only for the proofs of the theorems presented in this book.
1. Formulation of the Time-Optimal Problem and Maximum Principle.- 1.1. Statement of the Optimal Problem.- 1.2. On the Canonical Systems of Equations Containing a Parameter and on the Pontryagin Maximum Condition.- 1.3. The Pontryagin Maximum Principle.- 1.4. A Geometrical Interpretation of the Maximum Condition..- 1.5. The Maximum Condition in the Autonomous Case.- 1.6. The Case of an Open Set U. The Canonical Formalism for the Solution of Optimal Control Problems.- 1.7. Concluding Remarks.- 2. Generalized Controls.- 2.1. Generalized Controls and a Convex Control Problem.- 2.2. Weak Convergence of Generalized Controls.- 3. The Approximation Lemma.- 3.1. Partition of Unity.- 3.2. The Approximation Lemma.- 4. The Existence and Continuous Dependence Theorem for Solutions of Differential Equations.- 4.1. Preparatory Material.- 4.2. A Fixed-Point Theorem for Contraction Mappings.- 4.3. The Existence and Continuous Dependence Theorem for Solutions of Equation (4.3).- 4.4. The Spaces ELip(G).- 4.5. The Existence and Continuous Dependence Theorems for Solutions of Differential Equations in the General Case.- 5. The Variation Formula for Solutions of Differential Equations.- 5.1. The Spaces Ex and Ex(G).- 5.2. The Equation of Variation and the Variation Formula for the Solution.- 5.3. Proof of Theorem 5.1.- 5.4. A Counterexample.- 5.5 On Solutions of Linear Matrix Differential Equations.- 6. The Varying of Trajectories in Convex Control Problems.- 6.1. Variations of Generalized Controls and the Corresponding Variations of the Controlled Equation.- 6.2. Variations of Trajectories.- 7. Proof of the Maximum Principle.- 7.1. The Integral Maximum Condition, the Pontryagin Maximum Condition, and Their Equivalence.- 7.2. The Maximum Principle in the Class of Generalized Controls.- 7.3. Construction of the Cone of Variations.- 7.4. Proof of the Maximum Principle.- 8. The Existence of Optimal Solutions.- 8.1. The Weak Compactness of the Class of Generalized Controls.- 8.2. The Existence Theorem for Convex Optimal Problems.- 8.3. The Existence Theorem in the Class of Ordinary Controls..- 8.4. Sliding Optimal Regimes.- 8.5. The Existence Theorem for Regular Problems of the Calculus of Variations.
| Reihe/Serie | Mathematical Concepts and Methods in Science and Engineering ; 7 |
|---|---|
| Zusatzinfo | biography |
| Sprache | englisch |
| Themenwelt | Schulbuch / Wörterbuch |
| Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik | |
| ISBN-10 | 0-306-30977-7 / 0306309777 |
| ISBN-13 | 978-0-306-30977-9 / 9780306309779 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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