THE MAXIMUM PRINCIPLE FOR PARTIALLY OBSERVED OPTIMAL CONTROL OF FORWARD-BACKWARD STOCHASTIC SYSTEMS WITH RANDOM JUMPS

This paper studies the problem of partially observed optimal control for forward-backward stochastic systems which are driven both by Brownian motions and an independent Poisson random measure. Combining forward-backward stochastic differential equation theory with certain classical convex variational techniques, the necessary maximum principle is proved for the partially observed optimal control, where the control domain is a nonempty convex set. Under certain convexity assumptions, the author also gives the sufficient conditions of an optimal control for the aforementioned optimal optimal problem. To illustrate the theoretical result, the author also works out an example of partial information linear-quadratic optimal control, and finds an explicit expression of the corresponding optimal control by applying the necessary and sufficient maximum principle.

An Energy-Efficient Protocol Using an Objective Function & Random Search with Jumps forWSN

Wireless Sensor Networks(WSNs)have hardware and software limitations and are deployed in hostile environments.The problem of energy consumption in WSNs has become a very important axis of research.To obtain good performance in terms of the network lifetime,several routing protocols have been proposed in the literature.Hierarchical routing is considered to be the most favorable approach in terms of energy efficiency.It is based on the concept parent-child hierarchy where the child nodes forward their messages to their parent,and then the parent node forwards them,directly or via other parent nodes,to the base station(sink).In this paper,we present a new Energy-Efficient clustering protocol for WSNs using an Objective Function and Random Search with Jumps(EEOFRSJ)in order to reduce sensor energy consumption.First,the objective function is used to find an optimal cluster formation taking into account the ratio of the mean Euclidean distance of the nodes to their associated cluster heads(CH)and their residual energy.Then,we find the best path to transmit data from the CHs nodes to the base station(BS)using a random search with jumps.We simulated our proposed approach compared with the Energy-Efficient in WSNs using Fuzzy C-Means clustering(EEFCM)protocol using Matlab Simulink.Simulation results have shown that our proposed protocol excels regarding energy consumption,resulting in network lifetime extension.

Stochastic Approximate Solutions of Stochastic Differential Equations with Random Jump Magnitudes and Non-Lipschitz Coefficients

A class of stochastic differential equations with random jump magnitudes( SDEwRJMs) is investigated. Under nonLipschitz conditions,the convergence of semi-implicit Euler method for SDEwRJMs is studied. The main purpose is to prove that the semi-implicit Euler solutions converge to the true solutions in the mean-square sense. An example is given for illustration.

Reaction Subdiffusion with Random Waiting Time Depending on the Preceding Jump Length

To describe the energy-dependent characteristics of the reaction-subdiffusion process, we analyze the simple reaction A--→B under subdiffsion with waiting time depending on the preceding jump length, and derive the corresponding master equations in the Fourier Laplace space for the distribution of A and B particles in a continuous time random walk scheme. Moreover, the generalizations of the reaction-diffusion equation for the Gaussian jump length with the probability density function of waiting time being quadratically dependent on the preceding jump length are obtained by applying the derived master equations.