Regret Analysis of Online Gradient Descent-based Iterative Learning Control with Model Mismatch
This work addresses control system optimization for iterative learning, but it is incremental as it applies existing online learning methods to ILC with model mismatch.
The paper tackles the problem of Iterative Learning Control (ILC) by framing it as an online learning task and analyzes an online gradient-descent scheme with inexact gradients, showing performance in terms of dynamic and static regret metrics, with numerical simulations on a benchmark problem.
In Iterative Learning Control (ILC), a sequence of feedforward control actions is generated at each iteration on the basis of partial model knowledge and past measurements with the goal of steering the system toward a desired reference trajectory. This is framed here as an online learning task, where the decision-maker takes sequential decisions by solving a sequence of optimization problems having only partial knowledge of the cost functions. Having established this connection, the performance of an online gradient-descent based scheme using inexact gradient information is analyzed in the setting of dynamic and static regret, standard measures in online learning. Fundamental limitations of the scheme and its integration with adaptation mechanisms are further investigated, followed by numerical simulations on a benchmark ILC problem.