MINIMAL TIME CONTROL OF THE TWO TANKS GRADOSTAT MODEL UNDER A CASCADE INPUT CONSTRAINT?

摘要

We study the minimum time control problem of a series of two interconnected chemostats under the input constraint u_2 ≤ u_1, where u_i are the respective dilution rates in the tanks. This constraint brings controllability issues in the study of the optimal strategies. We overcome this difficulty by splitting the state domain into two subdomains, one with no lack of controllability of the target, and its complement where any optimal trajectory satisfies u_1 = u_2. We explicitly compute the complete optimal synthesis that depends on the position of the target with respect to a semipermeable curve that passes through a steady-state singular point.