Competitive neural networks (CNNs) are a class of two-time-scale neural networks which can simultaneously represent fast neural activity and slow changes in synapses. In this paper, by means of the drive-response idea and inverse optimality techniques, the optimal synchronization control of two CNNs with constant time delays is solved by considering the inverse optimal synchronization control of the error system. Considering the coupling relationship between fast and slow dynamics of the error system, the control Lyapunov function (CLF) is constructed first. Then, based on the CLF, a state feedback inverse optimal synchronization controller design method is proposed to synchronize two CNNs and minimize a meaningful performance functional while avoiding solving the Hamilton-Jacobi-Bellman (HJB) equation. The designed controller is linear and easy to implement. Finally, the feasibility and superiority of the presented method is illustrated by an example.
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