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The problem to be solved involves a highway automation project. The overall system consists of N vehicles (the platoon). Each vehicle is driven by the same input u and the state of the kth vehicle affects the dynamics of the (k+1)th vehicle. Furthermore, the dynamics of each vehicle is affected by its (local) state-feedback controller. Under very general conditions, it is shown that for sufficiently slowly varying inputs, decentralized controllers can be designed so that the platoon maintains its cohesion.>
Sheikholeslam et al. (Mon,) studied this question.