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Recently, machine learning has attracted much attention, and has been applied to the design of control systems. In general, the behavior of unstable systems diverges, and the performance of control for unstable systems tends to be strongly affected by model uncertainty. Therefore, unstable systems are difficult targets to be handled by neural networks. In this study, we propose a control design strategy utilizing neural networks for a system that has both stable and unstable equilibrium points. In the strategy, we investigate the possibility of whether an inverse time response around the stable equilibrium point can be used in the learning phase of a neural network, so that the learned network may be expected to perform the behavior around the unstable equilibrium point of the target system. Numerical simulations have demonstrated this idea is available.