Redes de Petri Continuas: Expresividad, Análisis y Control de una Clase de Sistemas Lineales Conmutados

M. Silva, L. Recalde

Resumen

Gracias a la existencia de potentes teorías de análisis y síntesis, así como a su directa representabilidad gráfica, las redes de Petri constituyen uno de los formalismos más aceptados en las aplicaciones de ingeniería en las que convienen modelos (de eventos) discretos. No obstante, a veces surgen problemas de decidibilidad o, en sistemas con grandes poblaciones, de enorme complejidad computacional. En este trabajo se presenta la urdimbre y algunos flecos de la teoría desarrollada para una relajación fluida o continua de los modelos discretos y dinámicos. Con ella se puede abordar eficientemente el estudio de sistemas de otra forma no abordables, al tiempo que se establecen algunos puentes a conceptos y resultados del análisis y síntesis de prestaciones, o de la observación y control de sistemas denominados continuos, aunque las clases de modelos que se obtienen son técnicamente, a veces también conceptualmente, híbridos. Obviamente, el precio que se paga por toda relajación es una pérdida de fidelidad en los modelos. En este sentido se ha de tener en cuenta que, aunque insólito en aplicaciones de ingeniería, los modelos discretos pueden ser no continuizables, del mismo modo que no todo sistema continuo no-lineal se puede aproximar satisfactoriamente por uno lineal (piénsese, por ejemplo, en sistemas caóticos).

Palabras clave

Red de Petri; ciclo de vida; relajación matemática; teoría estructural; análisis cualitativo; análisis cuantitativo; optimización paramétrica; observación y control dinámico

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