In this article, a new adaptive quantized consensus control strategy is proposed for uncertain nonlinear multi-agent systems. To achieve optimized consensus performance, the reinforcement learning algorithm is introduced, in which critic, actor, and identifier are utilized to value system performance, execute control behavior, and estimate unknown dynamics, respectively. Unlike existing reinforcement learning algorithms, the designed updating laws are simpler and facilitate more efficient training. In addition, the states and input of every agent are quantized before communication to alleviate bandwidth constraints. By integrating the command-filtered backstepping technique and substituting unquantized states with their quantized counterparts, the final controller is obtained. Different from existing quantized control studies, the virtual and final controllers contain both actor and critic neural networks, and a new lemma is accordingly established to compensate for the quantization errors.

This paper addresses the problem of beamforming (BF) design for orthogonal frequency division multiplexing (OFDM) based relay networks over frequency-selective channels. Both frequency-domain (FD) BF and time-domain (TD) BF are investigated. The later requires less feedback from the destination to perform BF. The BF vectors are designed by maximizing the minimum signal-to-noise-ratio (SNR) over all subcarriers at the destination, first under the total power constraint (TPC) and then under the per-relay power constraint (PPC). We show that both TPC and PPC BF designs lead to a quasi-convex optimization problem, which can be solved by bisection search method efficiently. Simulation results demonstrate that based on max-min SNR criterion, the performance of TD-BF rapidly approaches that of FD-BF when increasing the filter length. Moreover, it is found that for TD-BF, the minimum filter length required to achieve optimum performance under PPC is longer than that under TPC.

This letter addresses the problem of beamforming design for an amplify-and-forward (AF) based two-way relaying network (TWRN) which consists of two terminal nodes and several relay nodes. Considering a two-time-slot relaying scheme, we design the optimal beamforming coefficients to maximize the sum-rate of AF-based TWRN under total relay power constraint (TRPC). Although the optimization problem is neither convex nor concave, we show that the global optimal solution can be obtained by the branch-and-bound algorithm. To address the computational complexity concern, we also propose a low-complexity suboptimal solution which is obtained by optimizing a cost function over one real variable only. Simulation results show that the proposed optimal solution outperforms existing schemes significantly. Moreover, we show that the suboptimal solution only suffers small sum-rate losses compared to the optimal solution.