A convex optimization design of robust iterative learning control for linear systems with iteration‐varying parametric uncertainties

In this paper, a new robust iterative learning control (ILC) algorithm has been proposed for linear systems in the presence of iteration‐varying parametric uncertainties. The robust ILC design is formulated as a min‐max problem using a quadratic performance criterion subject to constraints of the control input update. An upper bound of the maximization problem is derived, then, the solution of the min‐max problem is achieved by solving a minimization problem. Applying Lagrangian duality to this minimization problem results in a dual problem which can be reformulated as a convex optimization problem over linear matrix inequalities (LMIs). Next, we present an LMI‐based algorithm for the robust ILC design and prove the convergence of the control input and the error. Finally, the proposed algorithm is applied to a distillation column to demonstrate its effectiveness.