Energy Supply Control of Wireless Powered Piecewise Linear Neural Network

Piecewise linear neural network (PLNN) possesses universal approximation ability for continuous functions on the compact domain, and for a PLNN in which the hidden neuron (HN) is wireless powered through wireless power transfer (WPT) technology and activated only if its energy harvest arrives at the activation threshold, the more HNs are activated, the smaller approximation error may be enjoyed, while the more energy will be consumed. Therefore, how to control the energy supply for the PLNN to reach the minimum approximation error while keeping the acceptable level of energy harvest arises as an interesting issue. To address this issue, this paper first formulates the energy-harvesting of an individual HN as a Markov decision process (MDP) to further deduce the objective function of the PLNN approximating the given continuous function, then uncovers the optimal activation probability and expected energy harvest for each HN, and finally reveals the optimal energy supply for the HNs to satisfy the optimal energy harvest. A novel algorithm based on our discovered theoretical foundations to control the energy supply to minimize the approximation error within the acceptable level of energy harvest is proposed, and the simulations and field experiments are both given to test its performance. To our best knowledge, this is the initial work towards the joint optimization of energy efficiency and universal approximation performance of the wireless powered PLNN.
Note to Practitioners
—This paper addresses the interesting issue of how to guarantee wireless powered PLNN to approximate the continuous function with the minimum approximation error under the energy constraint. Through the insightful disclosure of the optimal activation probability, optimal expected energy harvest, and optimal control of energy supply for each HN, this paper facilitates the wireless powered PLNN to operate in an energy-efficiency and universal-approximation way. Since PLNN can model the nonlinear and complex system (NCS) with arbitrary accuracy on the compact domain, our proposed solution can be applied by the NCS modeling technology to enjoy high approximation accuracy while keeping the energy consumption at the acceptable level, which we believe could inspire the development of low-power neural networks (NNs).