Abstract
This article presents a novel robust iterative learning control algorithm (ILC) for linear systems in the presence of multiple time-invariant parametric uncertainties.The robust design problem is formulated as a min-max problem with a quadratic performance criterion subject to constraints of the iterative control input update. Then, we propose a new methodology to find a sub-optimal solution of the min-max problem. By finding an upper bound of the worst-case performance, the min-max problem is relaxed to be a minimisation problem. Applying Lagrangian duality to this minimisation problem leads to a dual problem which can be reformulated as a convex optimisation problem over linear matrix inequalities (LMIs). An LMI-based ILC algorithm is given afterward and the convergence of the control input as well as the system error are proved. Finally, we apply the proposed ILC to a generic example and a distillation column. The numerical results reveal the effectiveness of the LMI-based algorithm.
| Original language | English |
|---|---|
| Pages (from-to) | 2506-2518 |
| Number of pages | 13 |
| Journal | International Journal of Control |
| Volume | 83 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - Dec 1 2010 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Computer Science Applications
Cite this
Robust iterative learning control for linear systems with multiple time-invariant parametric uncertainties. / Nguyen, Hoa Dinh; Banjerdpongchai, David.
In: International Journal of Control, Vol. 83, No. 12, 01.12.2010, p. 2506-2518.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Robust iterative learning control for linear systems with multiple time-invariant parametric uncertainties
AU - Nguyen, Hoa Dinh
AU - Banjerdpongchai, David
PY - 2010/12/1
Y1 - 2010/12/1
N2 - This article presents a novel robust iterative learning control algorithm (ILC) for linear systems in the presence of multiple time-invariant parametric uncertainties.The robust design problem is formulated as a min-max problem with a quadratic performance criterion subject to constraints of the iterative control input update. Then, we propose a new methodology to find a sub-optimal solution of the min-max problem. By finding an upper bound of the worst-case performance, the min-max problem is relaxed to be a minimisation problem. Applying Lagrangian duality to this minimisation problem leads to a dual problem which can be reformulated as a convex optimisation problem over linear matrix inequalities (LMIs). An LMI-based ILC algorithm is given afterward and the convergence of the control input as well as the system error are proved. Finally, we apply the proposed ILC to a generic example and a distillation column. The numerical results reveal the effectiveness of the LMI-based algorithm.
AB - This article presents a novel robust iterative learning control algorithm (ILC) for linear systems in the presence of multiple time-invariant parametric uncertainties.The robust design problem is formulated as a min-max problem with a quadratic performance criterion subject to constraints of the iterative control input update. Then, we propose a new methodology to find a sub-optimal solution of the min-max problem. By finding an upper bound of the worst-case performance, the min-max problem is relaxed to be a minimisation problem. Applying Lagrangian duality to this minimisation problem leads to a dual problem which can be reformulated as a convex optimisation problem over linear matrix inequalities (LMIs). An LMI-based ILC algorithm is given afterward and the convergence of the control input as well as the system error are proved. Finally, we apply the proposed ILC to a generic example and a distillation column. The numerical results reveal the effectiveness of the LMI-based algorithm.
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U2 - 10.1080/00207179.2010.531398
DO - 10.1080/00207179.2010.531398
M3 - Article
VL - 83
SP - 2506
EP - 2518
JO - International Journal of Control
JF - International Journal of Control
SN - 0020-7179
IS - 12
ER -