Tradeoff Between Time and Energy Costs for Controlling Stochastic Coupled Neural Networks

Time cost (TC) and energy cost (EC) are two fundamental indicators for evaluating the designed protocols for controlling networked systems. Yet the relationships of which as well as their dependence on the network topology are far from clear. In this note, we explore this problem with the stochastic synchronization of coupled neural networks. A novel controller is articulated, which switches between the linear feedback control and finite-time feedback control relying on the size of system error. Sufficient criteria for achieving stochastic synchronization are derived, and the analytical estimates of TC and EC for synchronization are further obtained. Especially, we show that a reduction in TC will lead to an increase in EC, i.e., there is a tradeoff between TC and EC. Afterward, we further report that different optimal values of the steepness exponent and control strength should be taken to minimize the total costs of time and energy with the different performance indices.