Adaptive Quantized Output Feedback Control of Nonlinear Systems With Mismatched Uncertainties and Sensor Failures

Digital control systems are normally characterized by quantization. It is quite challenging to exploit the celebrated backstepping control design for nonlinear systems subject to mismatched parametric uncertainties, input/output quantization, and unknown sensor failures. A major difficulty is that the output of the concerned system after quantization becomes discontinuous, and thus, nondifferentiable. As a result, the traditional recursive backstepping design method becomes infeasible because differentiation of the virtual control signals in the backstepping design no longer exists, while the control design and stability analysis processes of existing backstepping-based quantized control methods are not applicable to the underlying problem. Furthermore, the concerned problem becomes even more challenging when more general types of quantizers and more general forms of sensor failure are taken into account. In this note, we propose a novel adaptive quantized output feedback control scheme to address those difficulties and challenges. First, a state observer is constructed to generate a continuous estimate of the state and output. Then, the estimated output signal is utilized to design the virtual control signal to ensure the existence of their first-order derivatives. Meanwhile, repeated differentiation of the virtual control signals in the backstepping design is avoided by adopting dynamic filtering techniques. It is shown that all signals in the resulting closed-loop system are uniformly bounded. Finally, the effectiveness of the proposed strategy is verified and illustrated via simulation studies.