Adaptive Control of Uncertain Nonlinear Systems With Discontinuous Input and Time-Varying Input Delay

In this note, we investigate the adaptive quantized or event-triggered control designs for strict-feedback nonlinear systems with time-varying input delay. Because the control signal is discontinuous in the quantized control and event-triggered control, many existing methods to deal with the input delay are no longer applicable. Through constructing an auxiliary tracking error and an auxiliary system, the input-quantized control is implemented for nonlinear systems with unknown control gain and unknown input delay. With the well-designed Lyapunov-Krasovskii functionals and the linear growth condition of input delay, the stability analysis is achieved. The studied method is also applicable to the event-triggered control for systems possessing unknown input delay. The stability analysis shows that all the signals are semiglobally uniformly ultimately bounded (SGUUB). The use of dynamic surface control (DSC) effectively simplifies the controller structure. The quantized and event-triggered control simulations illustrate that the proposed schemes are effective.