Adaptive algorithms and stochastic approximations
Adaptive algorithms and stochastic approximations
Stochastic approximation with two time scales
Systems & Control Letters
Asynchronous Stochastic Approximations
SIAM Journal on Control and Optimization
The O.D. E. Method for Convergence of Stochastic Approximation and Reinforcement Learning
SIAM Journal on Control and Optimization
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Conserving Transmission Power in Wireless Ad Hoc Networks
ICNP '01 Proceedings of the Ninth International Conference on Network Protocols
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We propose and analyze a distributed control law that will maintain prescribed local properties of a wireless ad hoc network in the presence of node mobility, MAC layer power control and link fades. The control law uses a simple and intuitive power adaptation mechanism. We consider as an example the topology requirement of maintaining the out degrees of each node at prescribed values and keeping the in degree close to the out degree. The topology objective is achieved by adapting the transmission power based only on local information. This power adaptation algorithm is analyzed using the o.d.e. approach to stochastic approximation. Simulation results verify the analysis and demonstrate its effectiveness. We also study the ability of the proposed objective to maintain connectivity. Although many heuristics are described in the literature to maintain local topological properties, the algorithm proposed in this paper is the first one that has proven convergence properties.