Norm-optimal iterative learning control in an integer-valued control domain

Formulating a control design for integer-valued inputs might be advantageous over, for example, rounding strategies based on a real-valued solution. However, the speed of convergence, computational cost, and stability are challenges to be addressed. This is especially true for optimisation-based approaches such as the norm-optimal iterative learning control (ILC). In this contribution, the convergence properties of integer-valued ILC are derived and compared against the known real-valued ILC. After an evaluation of two recently presented solutions, a new optimal set controller synthesis method for integer-valued norm-optimal ILC is presented. The approach guarantees monotonic convergence and ensures that each iteration of the ILC will require a deterministic computational effort to find the suboptimal solution, with an upper bound for the objective function of the optimisation. This deterministic computational effort makes the setup applicable for real-time implementation. Finally, an example using the introduced new approach is given to highlight its advantages.