ABSTRACT
Fault diagnosis problem is discussed for discrete events systems described by partially observed Petri nets. Our goal is to detect and identify faults that may have occurred in both transitions and places assuming that we can measure some of them. The proposed approach is based on two mains steps (i) designing an algebraic observer for estimating the markings and the transitions of a partially observed Petri nets and (ii) presenting algorithms to detect and identify faults based on comparing the estimation of both the transitions and markings of the faulty system provided by an algebraic observer with those of the normal system. The effectiveness of the proposed approach is illustrated through a simple and a manufacturing example.
ABSTRACT
Therapeutic strategies to correct an excessive immune response to pathogenic infection is investigated as an optimal control problem. The control problem is formulated around a four dimensional mathematical model describing the inflammatory response to a pathogenic insult with two therapeutic control inputs which have either a direct pro- or anti-inflammatory effect in the given system. We use Pontryagin's maximum principle and discuss necessary optimality conditions. We consider both an L1 type objective functional as well as an L2 type objective. For the former, the presence of singular control will be addressed. For each case, numerical simulations using a nonlinear programming optimization solver to acquire different drug treatment strategies are presented and discussed. The results provide insight for possible treatment strategies and the methods could be a relevant tool for future practice to assist in better prediction of clinical outcomes and subsequently better treatment for patients.
