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Reparable systems are systems that are characterized by their ability to undergo maintenance actions when failures occur. These systems are often described by transport equations, all coupled through an integro-differential equation. In this paper, we address the understudied aspect of the controllability of reparable systems. In particular, we focus on a two-state reparable system and our goal is to design a control strategy that enhances the system availability- the probability of being operational when needed. We establish bilinear controllability, demonstrating that appropriate control actions can manipulate system dynamics to achieve desired availability levels. We provide theoretical foundations and develop control strategies that leverage the bilinear structure of the equations. 

The problem of sensor placement for second order infinite dimensional systems is examined within the context of a disturbance-decoupling observer. Such an observer takes advantage of the knowledge of the spatial distribution of disturbances to ensure that the resulting estimation error dynamics are not affected by the temporal component of the disturbances. When such an observer is formulated in a second order setting, it results in a natural observer. Further, when the natural observer is combined with a disturbance decoupling observer, the necessary operator identities needed to ensure the well-posedness of the observer, are expressed in terms of the stiffness, damping, input and output operators. A further extension addresses the question of where to place sensors so that the resulting natural disturbance decoupling observer is optimal with respect to an appropriately selected performance measure. This paper proposes this performance measure which is linked to the mechanical energy of second order infinite dimensional systems. The proposed sensor optimization is demonstrated by a representative PDE in a second order setting.