| Summary: | This paper reports the design of an iterative-learning-scheme-based fault-estimation method for interconnected nonlinear multi-flexible manipulator systems with arbitrary initial value. For state estimation, observers are employed to reconstruct the state. The proposed scheme ensures that each flexible manipulator subsystem’s states can track their desired reference signals within a finite time. In the next step, an iterative learning fault-estimation law is proposed to track the actual fault signal. In contrast to the previous literature, this approach utilizes potential information from previous iterations to enhance the accuracy of the estimation in the current iteration. Based on these efforts, the obstacle caused by the arbitrary initial value is circumvented, and addressing the fault-estimation errors of each flexible manipulator subsystem are uniformly ultimately bounded is successfully achieved. Then, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>-norm is developed to explore the convergence conditions of the presented methods. Finally, the effectiveness and feasibility of the proposed approach are verified through assessment of simulation results.
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