Time-delay neural network observer-based adaptive finite-time prescribed performance control for nonlinear systems with unknown time-delay

An adaptive finite-time prescribed performance control (FTPPC) strategy is considered based on the time-delay neural network (NN) observer for the uncertain nonlinear system with unknown time-delay. Unlike previous works, a time-delay NN state observer based on the existing NN state observer is proposed, which not only solves the problem of the linear observer being unable to accurately observe the system states, but also extends the NN state observer without the time-delay to the time-delay NN state observer for the nonlinear system with state time-delay. What is more, instead of traditional Krasovskii functionals, the finite covering lemma and the RBF NN are combined to approximate unknown nonlinear time-delay functions. In addition, an adaptive FTPPC method is proposed by using the finite-time performance function (FTPF), which ensures the dynamic performance of the system while ensures the steady-state performance of the system in finite time. Among them, the stability time can be arbitrarily given, which means it does not rely on any parameter value. Finally, the electromechanical system is utilized to verify the effectiveness of the proposed strategy. • The proposed time-delay NN observer solves the problem of the linear observer ignoring the nonlinearity and the time-delay terms, resulting in more accurate observation performance. • Unlike previous nonlinear observers, the proposed time-delay NN observer is suitable for the nonlinear system with state time-delays. • What is more, instead of traditional Krasovskii functionals, the finite covering lemma and the RBF NN are combined to approximate unknown nonlinear time-delay functions. • Moreover, the use of the FTPF ensures the steady-state and dynamic performance of nonlinear time-delay systems within finite time. It is worth mentioning that the setting time does not rely on any value.