Distributed Control Algorithm Based On The Alternating Direction Method Of Multipliers For Wireless Sensor Networks

Wireless sensor network integrates sensor technology, embedded technology, distributed information processing technology and communication technology, it’s one of the most popular and cutting-edge scientific research fields.It also has a very bright application prospect. Although wireless sensor network has many advantages, its development also faces many difficulties and challenges. One of the most important issues is about the energy control problem. Since the sensor nodes are typically powered by batteries, which have limited energy. The energy determines the lifetime of the network, so the research about how to effectively control the energy of sensor networks and prolong the survival circle life of the entire network has very important significance.Since the idea of the network utility maximization is presented, it has been widely applied to both wired and wireless network research. The core idea of network utility maximization is to abstract the network communication problems as a mathematical programming problem, taking the network resources and other limited conditions as constraint conditions, regarding the problem of how to achieve the network utility maximization under the constraint conditions as a target. In order to figure out the optimization problem of the network, we can design appropriate utility functions for different network environments and solve the utility functions by a variety of mathematical optimization methods.In order to facilitate the research of energy control problems in wireless sensor networks, this paper abstracts the energy control problems of sensor network as a network utility maximization problem based on the network utility maximization theory, and presents a concrete model for the utility maximization. We analyze and study the model by alternating direction method of multipliers. Alternating direction method of multipliers is a robust mathematical optimization method, which combines the advantages of limiting constraint optimization method(such as dual decomposition method and extended Lagrangian method). It divides the original problem into several sub-problems and alternately solves these sub issue to arrive at the solution of the original problem. It’s very suitable for solving the distributed optimization problems.Because of the variety of business types, the design of utility functions also varies in wireless sensor network, so this paper discusses the problem in two cases respectively. When the utility function is a concave function, we introduce a slack variable and solve the model by directly using the alternating direction method of multiplier; on the other hand, when the utility function is not a concave function, we eliminate the duality gap by the extended duality theory and deform the original question to solve it. Under the cooperation of each node in the network, this paper proposes a distributed iterative algorithm, which only requires limited information transmission but can converge to the global optimal solution. This paper gives specific topology simulation for these two cases respectively, experimental results show that the distributed algorithm is feasible and can converge to global optimal solution.