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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. 

Abstract The problem of parameter identification appears in many physical applications. A parameter of particular interest in cancer treatment is permeability, which modulates the fluidic streamlines in the tumor microenvironment. Most of the existing permeability identification techniques are invasive and not feasible to identify the permeability with minimal interference with the porous structure in their working conditions. In this paper, a theoretical framework utilizing partial differential equation (PDE)-constrained optimization strategies is established to identify a spatially distributed permeability of a porous structure from its modulated external velocity field measured around the structure. In particular, the flow around and through the porous media are governed by the steady-state Navier–Stokes–Darcy model. The performance of our approach is validated via numerical and experimental tests for the permeability of a 3D printed porous surrogate in a micro-fluidic chip based on the sampled optical velocity measurement. Both numerical and experimental results show a high precision of the permeability estimation.