Resumen

Este escrito se enfoca en presentar los fundamentos de la teoría de control a través de un enfoque marcadamente matemático. Está compuesto por los siguientes capítulos:

• 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’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, Itô 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

• Materias:Control de procesos industriales Control automático
• Subjects:Industrial process control Automatic control
• Palabras claves:Teoría de control, Controlabilidad, Principio bang-bang, Principio del máximo de Pontryagin, Dinámica hamiltoniana, Multiplicadores de Lagrange
• Keywords:Control theory, Controllability, Bang-bang principle, Pontryagin maximum principle, Hamiltonian dynamics, Lagrange multipliers