Sufficient Condition for the Existence of the Compact Set in the RBF Neural Network Control

In this brief, sufficient conditions are proposed for the existence of the compact sets in the neural network controls. First, we point out that the existence of the compact set in a classical neural network control scheme is unsolved and its result is incomplete. Next, as a simple case, we derive the sufficient condition of the existence of the compact set for the neural network control of first-order systems. Finally, we propose the sufficient condition of the existence of the compact set for the neural-network-based backstepping control of high-order nonlinear systems. The theoretic result is illustrated through a simulation example.