CAREER: Novel Representations for Distributed Control of String Networks in Vehicle Platooning and Supply Chain Management

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A certain class of oscillatory behaviors, popularly known as the butterfly effect or the bullwhip effect are quite habitual to large scale networks of dynamical systems, such as electrical networks, supply chains or transportation networks. They essentially describe as tiny perturbations (or fluctuations) in the functional parameters occurring in one area of the network, start to amplify while propagating through the dynamics of the network and ultimately result in extremely large deviations from the operational parameters in other parts of the network. This undesired phenomenon is very common and difficult to avert in important practical applications. The proposal brings forth a novel mathematical description of dynamical networks introduced by the PI, which is capable of capturing simultaneously both the dynamics and the topology of a given network. Preliminary results for the case of a string of dynamical agents (vehicles platooning) showed that coupled with concepts and methods from classical control theory, this new mathematical description will be investigated for the development of practical methods for the design of distributed controllers.For the case of networks with linear and time invariant dynamics, the distributed nature of the controller is cast as sparsity constraints on the controller left coprime factors, to be used in tandem with sparsity constraints imposed on the closed-loop maps. While delineating costs to specific nodes of the network, the constraints on the closed-loop map guarantee the tractability of the distributed, optimal controller design problem and characterize the manner in which disturbances propagate through the closed loop, thus eliminating the bullwhip effect. The goal is to investigate the needed adaptation of the concept of internal stability of the feedback loop, which becomes necessary in the current paradigm of the distributed implementation of controllers.