Model Free Adaptive Control for a Class of Nonlinear Systems Using Quantized Information

Abstract This paper considers the stability of model free adaptive control systems with quantized information. Two quantized model free adaptive control (QMFAC) algorithms are proposed by using different signal quantization schemes, and here the logarithmic quantizer is introduced to decode these signals with a number of quantization levels. By using the sector bound method, the stability conditions of proposed QMFAC algorithms can be given and the effect of quantization error for such systems can also be discussed. It is shown that the tracking error under the QMFAC algorithm with system output quantized signal is proved to converge to a bound, and the bound depending on quantization density and desired trajectory. Thus, the tracking error under the QMFAC algorithm with tracking error quantized signal converges to zero. Two illustrative examples are given to validate the theoretical results.