Robust monotonic convergent iterative learning control design: An LMI‐based method

Abstract

This work investigates robust monotonic convergent iterative learning control (ILC) for uncertain linear systems in both time and frequency domains, and the ILC algorithm optimizing the convergence speed in terms of l2 norm of error signals is derived. First, it is shown that the robust monotonic convergence of the ILC system can be established equivalently by the positive definiteness of a matrix polynomial over some set. Then, a necessary and sufficient condition in the form of sum of squares for the positive definiteness is proposed, which is amendable to the feasibility of linear matrix inequalities. Based on such a condition, the optimal ILC algorithm that maximizes the convergence speed is obtained by solving a set of convex optimization problems. Moreover, the order of the learning function can be chosen arbitrarily so that the designers have the flexibility to decide the complexity of the learning algorithm.

Adaptive iterative learning control for continuous systems with non‐repetitive uncertainties and unknown state delays

“…ΔV 1,k (t) is utilized to offset ∫ t 0 e −s𝜏 e T k (𝜏) fk (𝜏)d𝜏 in ΔV 2,k (t) to make E k (t) decrease between neighbor iterations. Applying Newton-Leibniz formula to V 1,k (t), ∫ t 0 V1,k (𝜏)d𝜏 is obtained in (10). Meanwhile, V 1,k−1 (t) is directly removed by its positive definiteness.…”

“…1,2 Due to its practicality, it has been well applied in fields of hard disk drives, 3 ventricular assist devices, 4 high-speed trains, 5 robot manipulators, 6 micro aerial vehicles, 7 and so forth. Interesting theoretical studies have been dedicated to this scope, [8][9][10] just mentioned a few. Specially, based on a data-driven approach, 8 exploits model predictive ILC to eliminate restrictions on model uncertainty.…”

“…A sliding mode ILC is utilized by Reference 9 to alleviate noise sensitivity. An ILC convergence optimization condition in Reference 10 is presented in terms of linear matrix inequalities.…”

Iterative learning control applied to distributed‐order linear time invariant MIMO systems to achieve learnability

“…Theorem 2. If the DOLTIS presented in (16) satisfies the dissipativity criterion in lemma (2), then the P-type ILC Law given in (18), which satisfies 0…”

“…One of the most powerful tools to achieve learnability in dynamical systems is considering ILC schemes, in particular, the P-Type Law. The ILC scheme has emerged as a very important tool due to its novel theoretical development and their applications; for example, in recent years, the ILC scheme has been combined with a MPC in order to address tracking trajectory problems (see reference Liang et al [1]), and its performance has been improved using model-free disturbance observers, which are commonly used in systems that require a precise motion, thus enhancing the robustness of the system (see Su [2]). Also, in Liu et al [3], to avoid the deterioration of the classical ILC scheme due to the witticism of non-repeated trajectories and disturbances, a TIDLC scheme is proposed for improving robustness.…”