A General Equilibrium Analysis of Predefined-Time Control and Energy Consumption for Neural Networks With Time-Varying Delays

This paper mainly focuses on the equilibrium problem of predefined-time stability and control energy consumption in nonlinear neural networks with time-varying delays. A new criterion for one global composite switching controller to assure predefined-time stability is provided by employing inequality technologies and Lyapunov stability theorem. Under the constructed controller, it is proved that the system is predefined-time stable when the initial conditions are inside and outside the unit sphere. Then, the energy consumption required for the system to reach the control target is estimated, which is related to the preset control time. Moreover, the equilibrium problem of the control energy consumption and the settling time is investigated by constructing an evaluation index function, and the optimal preset control time is obtained. The results show that a suitable preset control time can better balance the energy consumed by the controller, which has practical implications. Finally, a simulation example has clearly verified the theoretical results.