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In this article, a notion of viscosity solutions is introduced for second order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for pathdependent stochastic differential equations. We identify the value functional of optimal control problems as unique viscosity solution to the associated PHJB equations. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property. Applications to backward stochastic Hamilton-Jacobi-Bellman equations are also given.

Abstract:Clustering Algorithm is a kind of key technique used to reduce energy consumption, which can increase network scalability and lifetime. The main goal of this research is concerning protocols to contain in-motion sensor nodes in large-scale topologies, and constitute a fleet wireless sensor network which can assistant in-flight localization and alignment for carrier-based aircraft. In this paper, we abstract network model according to specific conditions of F-WSN, and select performance indicators to evaluate it. A distributed multiple-weight data gathering and aggregation protocol (DMDG) is proposed, which contains all-sided active clustering scheme and realizes long-range realtime communication by tacical data link under a TDMA/CSMA channel sharing mechanism. An analytical paradigm facilitating the most appropriate choice of the next relay is proposed. Experimental results have shown that DMDG scheme can balance the energy consumption and extend the network lifetime notably, outperform LEACH, PEACH, and DEEC in terms of network lifetime and coverage rate, especially in sparse node density or anisotropic topologies.

Electrocatalytic oxidation is regarded as an effective technique for decomposing refractory organic compounds like perfluorooctanoic acid (PFOA). However, achieving highly efficient and long-life electrodes is still a great challenge. Herein,...