Zero-error convergence of iterative learning control using quantized error information

Abstract

An iterative learning control algorithm using quantized error information is proposed in this article for both linear and nonlinear systems. The actual output is first compared with the reference signal and then the corresponding error is quantized and transmitted. A logarithmic quantizer is used to guarantee an adaptive improvement for tracking performance. The tracking error under this scheme is proved to converge to zero asymptotically. Illustrative examples verify the theoretical results.

Zero‐error convergence of iterative learning control based on uniform quantisation with encoding and decoding mechanism

“…Theorem 2: Consider the system (1) and assume that A1 and A2 hold. The update law (7) is employed with an encoding-decoding mechanism (5) and (6). If the learning gain matrix L is designed such that…”

“…Remark 3: Whether the finite quantisation level situation or the infinite quantisation level situation is in effect, the transmission burden has been efficiently reduced. As we can learn from encoder equation (5) and decoder equation (6), the data that we need to transmit is just the magnified error information between the system output and the encoder estimation. If we do not introduce the encoding and decoding mechanism, then the data that we need to transmit is the real output of the system.…”

“…In particular, a lower quantisation density or a larger value of the reference trajectory leads to a larger convergent zone of the upper bound. To achieve the zero-error convergence, Xu et al proposed an error quantisation scheme to replace this output quantisation scheme [5]. In this scheme, the reference trajectory is first transmitted to the plant and compared with the real output to generate the tracking error at the local site.…”

Discrete Fourier transform based frequency characteristics of iterative learning control for linear discrete-time systems

“…Reviewing the contributions of the ILC convergence for discrete-time systems, the analytical techniques are mainly the time-and frequency-domains. In terms of convergence in a discrete-time domain, the kernel idea is to express the ILC dynamics as an algebraic input-output equation by the lift vector technique, and thus the ILC convergence is equiv-alent to the stability of the transmit matrix as shown [13][14][15][16][17][18][19][20][21][22][23][24][25][26]. The idea is innovative, and the results are progressive.…”

Iterative learning control for image feature extraction with multiple-image blends

“…However, in the face of random attacks such as Gaussian noise, the quality of the watermark we extract is poor. In order to improve the stability of the watermarking system, the literature [14,15] proposed JADE blind separation watermarking algorithm. This method used an iterative hybrid method to embed the image and used the hidden image and the carrier image as different signals.…”