Mathematical Theory of Optimal ProcessesCRC Press, 1987. 3. 6. - 360페이지 The fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems. This one mathematical method can be applied in a variety of situations, including linear equations with variable coefficients, optimal processes with delay, and the jump condition. As with the three preceding volumes, all the material contained with the 42 sections of this volume is made easily accessible by way of numerous examples, both concrete and abstract in nature. |
목차
The Maximum Principle | 9 |
The Proof of the Maximum Principle | 75 |
Linear TimeOptimal Processes | 115 |
Miscellaneous Problems 189 | 191 |
The Maximum Principle and the Calculus of Variations | 239 |
Optimal Processes with Restricted Phase Coordinates | 257 |
A Statistical Optimal Control Problem | 317 |
| 354 | |
자주 나오는 단어 및 구문
absolutely continuous admissible control arbitrary assume boundary g(x calculus of variations Chapter cone consider constant continuous function control parameters control region control u(t convex convex cone coordinates curve defined denote derivatives differential equations dx dt dx(t entire interval exists Figure finite number follows formula functions u(t Furthermore given grad homology groups hyperplane inequality initial condition initial value interior point interval to t<t Lemma let x(t linear manifold maximum principle motion obtain optimal control optimal problem optimal trajectory origin phase point phase space phase trajectory piecewise continuous plane point xo Pontryagin position proof of Theorem r-dimensional regular point relation S₁ satisfies solution of eq solution of system system 38 t₁ tangent tion topological trajectory of system transfers the phase transversality condition variable vector function Weierstrass criterion x(t₁ x(to x₁ zero ди дх