Optimal Learning Control Scheme for Discrete-Time Systems With Nonuniform Trials

In reality such as a rehabilitation training, a repetitive control is necessary but the operational lengths may be iteration varying due to health condition. For the issue, this article investigates an intermittent optimal learning control scheme that considers the partially available information for the learning processing. The performance index is to minimize the summation of the quadratic timewise tracking error and the amplified adjacent-iteration timewise inputs drift while the argument is assigned as the iteration-time-varying learning gain. By adopting the latest captured historical timewise input and the tracking error, the optimal learning gain is achieved. Theoretical analysis conveys that the timewise tracking error is asymptotically convergent along the iteration direction. In particular, the tracking error may vanish at some finite iteration if the amplifier is null. Numerical simulations for a permanent magnet linear motor model testify the validity and effectiveness of the proposed scheme.