Adaptive estimation‐based TILC for the finite‐time consensus control of non‐linear discrete‐time MASs under directed graph

This work explores the consensus problems under the directed graph, variable learning gains, fast convergence and data‐driven control framework comprehensively and proposes an adaptive estimation‐based terminal iterative learning control for a nonlinear discrete‐time multi‐agent system (MAS) with a constant control input. A linear iteration‐incremental model is built by using an iterative dynamic linearisation where the unknown partial derivatives are estimated iteratively using I/O data. The learning control law is designed with both a constant learning gain and an iteration‐time‐varying learning gain. The constant one can be selected properly according to the estimation of partial derivatives and the varying one can be estimated from iteratively utilising I/O data. The result has also been extended to the nonlinear MAS with time‐varying control input and an extended adaptive estimation‐based TILC is developed by using time‐varying control input to enhance the control performance. A fast convergence of both the proposed methods is achieved by removing the unnecessary error constraints at other time instants than the endpoint. Both the proposed methods is apparently data‐driven since no model information is involved. The proposed finite time consensus control methods are confirmed to be effective under the directed graph through mathematic proof and extensive simulations.