Iterative learning control for singular nonlinear switched systems with constant time delay and noise

This paper introduces a novel class of nonlinear singular switched systems that incorporate state delays and noise effects. A D-type iterative learning control (ILC) algorithm is developed based on the system’s structure. The study examines the effects of constant time delay and external noise on tracking performance. The findings reveal that time delay has negligible impact on learning performance when it is smaller than the dwell time. Furthermore, the output remains within an acceptable neighborhood of the desired trajectory during the entire operational interval, provided the noise stays within a finite boundary. The paper establishes sufficient conditions for the convergence of the proposed algorithm, noting that while system switching may reduce the convergence speed of the ILC algorithm, it does not affect its convergence in the iterative domain. To validate the theoretical analysis, a numerical example is presented, demonstrating and confirming the effectiveness of the D-type ILC algorithm for the considered class of switched systems.