An introduction to mathematical optimal control theory (version 0.2)
Este escrito se enfoca en presentar los fundamentos de la teora̕ de control a travš de un enfoque marcadamente matemt̀ico. Est ̀compuesto por los siguientes capt̕ulos:Introduction. The basic problem; some examples; a geometric solution; overview.Controllability, bang-bang principle. Definitions; qu...
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| Tác giả khác: | , |
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| Định dạng: | Sách |
| Ngôn ngữ: | Tiếng Anh |
| Những chủ đề: | |
| Truy cập trực tuyến: | An introduction to mathematical optimal control theory (version 0.2) |
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| Tóm tắt: | Este escrito se enfoca en presentar los fundamentos de la teora̕ de control a travš de un enfoque marcadamente matemt̀ico. Est ̀compuesto por los siguientes capt̕ulos:Introduction. The basic problem; some examples; a geometric solution; overview.Controllability, bang-bang principle. Definitions; quick review of linear ODE; controllability of linear equations; observability; bang-bang principle; references.Linear time-optimal control. Existence of time-optimal controls; the Maximum Principle for linear time-optimal control; examples; references.The Pontryagin Maximum Principle. Calculus of variations, Hamiltonian dynamics; review of Lagrange multipliers; statement of Pontryagin Maximum Principle; applications and examples; Maximum Principle with transversality conditions; more applications; Maximum Principle with state constraints; more applications; references.Dynamic programming. Derivation of Bellman<U+0092>s PDE; examples; relationship with Pontryagin Maximum Principle; references.Game theory. Definitions; dynamic programming; games and the Pontryagin Maximum Principle; application: war of attrition and attack; references.Introduction to stochastic control theory. Introduction and motivation; review of probability theory, Brownian motion; stochastic differential equations; stochastic calculus, It ̥chain rule; dynamic programming; application: optimal portfolio selection; references.Appendix: Proofs of the Pontryagin Maximum Principle. An informal derivation; simple control variations; free endpoint problem, no running payoff; free endpoint problem with running payoffs; multiple control variations; fixed endpoint problem; references.Exercises References |
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