Robust iterative learning control for unstable MIMO systems

Iterative learning control (ILC) is a well-established technique to successively improve tracking accuracy for systems that repeatedly perform the same task. Most current literature imposes constraints on the nature of the system, such as requiring it to be full-rank, or inherently stable. This paper presents a generalised ILC framework that can handle non-linear, unstable, MIMO systems with rank deficiency. This involves the minimisation of a cost function that balances tracking performance and input effort, extending previous approaches to include a 'robustness filter' within the optimisation. Gap metric analysis is then applied to examine the robustness of the resulting system, with performance bounds derived for both serial and parallel ILC architectures. A design procedure is presented that allows the designer to transparently trade-off robustness and convergence properties. The design framework is illustrated via application to the inverted pendulum problem, a classic example of a highly nonlinear, unstable, and under-actuated system.