This paper studies a variant of an overhead crane model's problem, with a control force in velocity and rotating velocity on the platform. We obtain under certain conditions the well-posedness and the strong stabilization of the closed-loop system. We then analyze the spectrum of the system. Using a method due to Shkalikov, we prove the existence of a sequence of generalized eigenvectors of the system, which forms a Riesz basis for the state energy Hilbert space.

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Abstract:In this paper, we use asymptotic techniques and the finite differences method to study the spectrum of differential operator arising in exponential stabilization of Euler-Bernoulli beam with nonuniform thickness or density that is clamped at one end and is free at the other. To stabilize the system, we apply at the free end, the following shear force feedback control:We build a numerical scheme and investigate the eigenvalues locus as a function of the positive feedback parameters α and β.

Vehicular Delay-Tolerant Networks (VDTNs) are vehicle networks where there is no end-to-end connectivity between source and destination. As a result, VDTNs rely on cooperation between the different nodes to improve its performance. However, the presence of selfish nodes that refuse to participate in the routing protocol causes a deterioration of the overall performance of these networks. In order to reduce the impact of these selfish nodes, proposed strategies, on the one hand, use the nodes transmission rate that does not take into account the message priority class of service, and on the other hand, are based on traditional buffer management systems (FIFO, Random). As a result, quality of service is not guaranteed in this type of network where different applications are derived from messages with different priorities. In this paper, we propose a strategy for detecting selfish nodes and taking action against them in relation to priority classes in order to reduce their impacts. The operation of this strategy is based, on a partitioned memory management system taking into account the priority and the lifetime of messages, on the calculation of the transmission rate of the node with respect to the priority class of the node with the highest delivery predictability, on a mechanism for calculating the nodes degree of selfishness with respect to the priority class, and on the monitoring mechanism. . The simulations carried out show that the proposed model can detect selfish nodes and improve network performance in terms of increasing the delivery rate of high-priority messages, reducing the delivery delay of high-priority messages, and reducing network overload.