Yet,the confrontation of reliability with control theory looks
very promising.In this paper,it led to the formal definition of
coupled design and maintenance problems without restrictive
hypotheses on the aging of the system with time,nor on the
effects of maintenance.While stochastic viability was used,other
branches of control theory maybe relevant to such design and
maintenance problems,both in the closed- and open-loop cases.
In fact some works are very closet oviability theory,such as the
invariance framework [37] or reach-avoid problems inprobabil-
istic hybrid systems,e.g. [41,42]. They may help in the formulation
and/or there solution of time-variant reliability problems.Con-
versely,reliability may be instrumental in solving control pro-
blems. For instance,it i snecessary to know PðXðt; yðtÞÞASðtÞÞ in
viability problems,but this knowledge may not be easy to get.
Time-invariant reliability methods may then provide efficient
approximations of these probabilities.