A convex optimization approach to robust iterative learning control design for linear systems with parametric uncertainties

Abstract

Iterative learnign control (ILC) is a relatively new control stragtegy in which the control algorithms are designed for repetitively working systems so that system performance is improved after iterations. ILC drives the system output to the target trajectory at all samples in a fixed, finite time interval. Moreover, it rejects the repeated disturbances and reduces the effects due to parametric uncertainties. In this thesis, we propose robust ILC design for linear systems whose Markov matrices are affine functions of the uncertainties. In particular, three types of parametric uncertainties are considered in this thesis including time-invariant, time-varying, and iteration-varying. We develop a unified, systematic approach to design robust ILC algorithms for these types of uncertainties. First, the robust ILC design problem is formulated as a min-max problem using a quadratic performance criterion subject to constraints of the iterative control input update. Then, the min-max problem is relaxed to be a minimization problem by employing an upper-bound of the worst-case performance. Applying Lagrangian duality to this minimization problem leads to a dual problem which can be reformulated as a convex optimization problem over linear matrix inequalities. ILC algorithms are given afterward and the convergences of the control input as well as the system error are proved. Finally, we apply the proposed ILC algorithms to a flexible link system and distillation colomn in presence of parametric uncertainties. The computer simulation illustrates the effectiveness of the proposed algorithms