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Convergence and the closed-loop stability property are established for a diagonal recurrent neural network (DRNN) based control system. Two DRNNs are utilized in the control system, one as an identifier called diagonal recurrent neuroidentifier (DRNI) and the other as a controller called diagonal recurrent neurocontroller (DRNC). A generalized dynamic backpropagation algorithm (DBP) is developed and used to train both DRNC and DRNI. Due to the recurrence, the DRNN can capture the dynamic behavior of a system and since it is not fully connected, the architecture is simpler than a fully connected recurrent neural network. Convergence theorems for the adaptive DBP algorithms are developed and the closed-loop stability is established for the DRNN based control system when the plant is BIBO stable.