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LMI-based robust iterative learning controller design for discrete linear uncertain systems. (English) Zbl 1122.93346

Summary: This paper addresses the design problem of robust iterative learning controllers for a class of linear discrete-time systems with norm-bounded parameter uncertainties. An iterative learning algorithm with current cycle feedback is proposed to achieve both robust convergence and robust stability. The synthesis problem of the proposed iterative learning control (ILC) system is reformulated as a \(\gamma\)-suboptimal \(H_\infty\) control problem via the linear fractional transformation (LFT). A sufficient condition for the convergence of the ILC algorithm is presented in terms of linear matrix inequalities (LMIs). Furthermore, the linear transfer operators of the ILC algorithm with high convergence speed are obtained by using existing convex optimization techniques. The results demonstrate the effectiveness of the proposed method.

MSC:

93B51 Design techniques (robust design, computer-aided design, etc.)
68T05 Learning and adaptive systems in artificial intelligence
93C55 Discrete-time control/observation systems
93D09 Robust stability
93C41 Control/observation systems with incomplete information
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