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.

Model‐free adaptive control for a class of nonlinear systems with uniform quantizer

“…However, the analysis and design in these results all have a demand on the model information of system. In addition to our previous research in References [33,34], there has little research on the MFAC aspect about data quantization in the existing literature. In Reference [34], the system output quantization using a logarithmic quantizer is considered for unknown nonlinear systems using the MFAC method.…”

Enhancing the performance of wind energy conversion systems using unified power flow controller

“…4 is used as an online adaptive control algorithm. The parameters of the MFAC controller are set according to [42] as follows: ρ = 1, λ = 2, η = 1, μ = 1, ε = 10 −5 , and φ 1 = 0.5. Fig.…”

Model-Free Robotic Architecture with Task-Multiplexer and Discrete-Time Adaptive Control

“…Without any use of mathematical models for controlled plants, model-free adaptive controllers (MFAC) have been developed when the robots are considered as a class of unknown discrete-time systems [8][9][10]. By using only the input/output data, the design of MFAC based on the data-driven concept was established by linearization models that require the existence of a pseudo-partial derivative and a non-zero change of control effort [11,12]. Without this constraint, the control scheme for the unknown mathematical model of robotic systems for the discrete-time domain has been proposed in [13,14], by using direct IF-THEN rules and adaptive networks, but closed-loop analysis has been limited only the convergence of the tracking error.…”

“…The difficulty of acquiring analytic solutions for high-order systems has become an interesting issue. MFAC approaches in [10][11][12] have not determined the controlled plants as naturally high-order systems. Black-stepping controllers have been effectively utilized for solving high-order problems [21,22].…”

“…The resetting algorithm, which is generally required by MFAC schemes such as in [9,12], is completely neglected in this work. Therefore, the continuity of the adjustable parameter is clearly improved.…”