In this paper, we study a general class of strict feedback nonlinear systems, where the input signal takes quantized values. We consider a stabilization problem for nonlinear uncertain systems via adaptive backstepping approach. The control design is achieved by introducing a hysteretic quantizer to avoid chattering and using backstepping technique. A guideline is derived to select the parameters of the quantizer. The designed controller together with the quantizer ensures the stability of the closed loop system in the sense of signal boundedness.

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Summary This paper proposes a novel adaptive backstepping control method for parametric strict‐feedback nonlinear systems with event‐sampled state and input vectors via impulsive dynamical systems tools. In the design procedure, both the parameter estimator and the controller are aperiodically updated only at the event‐sampled instants. An adaptive event sampling condition is designed to determine the event sampling instants. A positive lower bound on the minimal intersample time is provided to avoid Zeno behavior. The closed‐loop stability of the adaptive event‐triggered control system is rigorously proved via Lyapunov analysis for both the continuous and jump dynamics. Compared with the periodic updates in the traditional adaptive backstepping design, the proposed method can reduce the computation and the transmission cost. The effectiveness of the proposed method is illustrated using 2 simulation examples.

This paper investigates the event-triggered adaptive output feedback control problem for a class of uncertain nonlinear systems in the presence of actuator failures and unknown control direction. By utilizing the adaptive backstepping technique, an event-based output feedback controller is developed together with a time-variant event-triggered rule. In this design, the radial basis function neural network algorithms are first introduced to identify the unknown terms of the systems. Then, a new state observer with adaptive compensation is designed to estimate the state vector. The overall control strategy guarantees that the output signal tracks the reference signal and all the signals of the closed-loop systems are bounded. Unlike the existing methods, the proposed control scheme can handle the coupling term incurred by the loss of effectiveness fault of the actuator, the event-triggered rule, and unknown control direction. Finally, an example is performed to demonstrate the validity of the proposed strategy.