Learning gains optimization of iterative learning control algorithms

This paper proposes a method to optimize the learning gains of the conventional first-order and second-order Proportional-type (P-type) iterative learning control algorithms so as to achieve the minimal Q
_p
factors. On the basis of subgradient and convex optimization theory, we obtain the optimal learning gains of the P-type iterative learning control algorithms of linear time-invariant (LTI) single-input-single-output (SISO) system with direct feed-through term. Inspired by the minimal Q
_p
factors of SISO system, we similarly analyze the linear time-invariant (LTI) m-input-m-output (MIMO) system with direct feed-through term and then optimize the learning gains of the P-type iterative learning control algorithms and achieve the minimal Q
_p
factors of MIMO system by applying the convex optimization theory and Lebesgue-p norm.