An Algebraic Approach to Robust Iterative Learning Control for Linear Discrete-Time Singular System With Initial State Shifting

For a repetitive difference-algebraic singular system operated over a finite discrete-time length to track a desired trajectory, this article first lifts the output as the force-free reaction to the initial state and the response to the forced input while the initial state of the difference subsystem drops in a neighborhood of a fixed point. Then, in order to construct an iterative learning control law for mating with the dynamic–static feature, the error compensation is designed synchronous with that of the input and the gain is argued for a quadratic minimization. By extracting the lifted tracking error as nonzero and zero segments, the optimized gain is explicated by system Markov parameters and the error. Rigorously algebraic operation delivers that the tracking error is asymptotically bound for a value that is linearly relevant to the threshold of the initial states shifting, which means that the addressed optimal learning scheme is robust to the initial state uncertainties. Further inference conveys that the tracking error is asymptotically vanishing while the initial state shifting is sequentially decaying and the tracking error is linearly monotonously convergent when the initial state is settled, respectively. Numerical experiments support the clarification.