Iterative Learning Control for Multi-Agent Systems With Finite-Leveled Sigma-Delta Quantization and Random Packet Losses

Abstract

A quantized iterative learning control (QILC) for continuous-time multi-agent systems with finite-leveled sigma-delta ( $\Sigma \Delta$ ) quantization and random packet losses is first proposed in this paper. To realize the digital communication between signals and utilize limited communication bandwidth effectively, we introduce the $\Sigma \Delta$ quantizer with limited communication data rate (quantization bits) into the control field and for the design of the QILC in this paper. In addition, the packet losses are also first considered into the QILC, which makes the controller more close to the practical engineering applications. Since the nonlinearity and randomness introduced by the quantization and packet losses, a decreasing learning gain is utilized with the help of the non-smooth analysis and mathematical expectation for the analysis of convergence. Accurate tracking in the sense of expectation can be obtained based on randomly small number of quantization bits, even merely one bit of quantization information. Numerical simulations are given to show the effectiveness of the proposed protocol.