Biblio

Recent disasters have shown that hazards can be unpredictable and can have catastrophic consequences. Emergency plans are key to dealing with these situations and communications play a key role in emergency management. In this paper, we provide a formalism to design resilient emergency plans in terms of communications. We exemplify how to use the formalism using a case study of a Nuclear Emergency Plan.

We consider a class of robust optimization problems that we call “robust-to-dynamics optimization” (RDO). The input to an RDO problem is twofold: (i) a mathematical program (e.g., an LP, SDP, IP, etc.), and (ii) a dynamical system (e.g., a linear, nonlinear, discrete, or continuous dynamics). The objective is to maximize over the set of initial conditions that forever remain feasible under the dynamics. The focus of this paper is on the case where the optimization problem is a linear program and the dynamics are linear. We establish some structural properties of the feasible set and prove that if the linear system is asymptotically stable, then the RDO problem can be solved in polynomial time. We also outline a semidefinite programming based algorithm for providing upper bounds on robust-to-dynamics linear programs.