Almost Sure Convergence of State Feedback‐Based Iterative Learning Control for Networked Nonlinear Systems With Data Dropouts

Random data dropouts, arising from bandwidth limitations or network congestion, significantly affect the tracking performance of iterative learning control (ILC) schemes for networked control systems. To address this challenge, we propose a state feedback‐based ILC scheme for a class of discrete‐time multi‐input‐multi‐output (MIMO) nonlinear systems with a feedforward term, operating in environments prone to random packet loss. More specifically, the realizability of the desired trajectory of the considered nonlinear system is first studied. When the feedforward matrix is full‐row rank, we show that any given desired trajectory is realizable. For strictly full‐column rank case, we give a necessary and sufficient condition that guarantees the realizability of the given desired trajectory. Then, using the contraction mapping method combined with matrix transformation and decomposition techniques, we investigate the almost sure convergence of tracking errors. For the full‐row rank case, we show that the spectral radius condition is necessary and sufficient for the tracking errors to converge to zero almost surely. For the strictly full‐column rank case, we illustrate that the spectral radius condition can ensure the output sequence converges to any realizable desired trajectory almost surely. Meanwhile, we show how to design the state feedback for better tracking performance. Finally, a numerical example is presented to demonstrate the effectiveness of the findings.