An LMI approach for robust iterative learning control with quadratic performance criterion

Nguyễn, Đình Hòa; Banjerdpongchai, David

doi:10.1016/j.jprocont.2008.12.004

Cited by 30 publications

(16 citation statements)

References 16 publications

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“…From dynamic equation (16) we conclude that, in order for the presented ILC to be convergent, all eigenvalues of G c must lie within the unit circle. That is:…”

Section: Monotonic Convergence Analysismentioning

confidence: 94%

“…An ILC for a class of SISO nonlinear systems which are partially linearizable by state feedback was studied in [15]. A design method for ILC, based on the quadratic performance criterion (Q-ILC), was presented in [16] for linear systems subject to additive uncertainty. A new concept of stability for discrete linear repetitive processes has been developed from physical motivations by [17].…”

Section: Introductionmentioning

confidence: 99%

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A guaranteed monotonically convergent iterative learning control

Madady¹,

Reza-Alikhani²

2011

Asian Journal of Control

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This paper presents a new iterative learning control (ILC) scheme for linear discrete time systems. In this scheme, the input of the controlled system is modified by applying a semi-sliding window algorithm, with a maximum length of n +1, on the tracking errors obtained from the previous iteration (n is the order of the controlled system). The convergence of the presented ILC is analyzed. It is shown that, if its learning gains are chosen proportional to the denominator coefficients of the system transfer function, then its monotonic convergence condition is independent of the time duration of the iterations and depends only on the numerator coefficients of the system transfer function. The application of the presented ILC to control second-order systems is described in detail. Numerical examples are added to illustrate the results.

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“…From dynamic equation (16) we conclude that, in order for the presented ILC to be convergent, all eigenvalues of G c must lie within the unit circle. That is:…”

Section: Monotonic Convergence Analysismentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

A guaranteed monotonically convergent iterative learning control

Madady¹,

Reza-Alikhani²

2011

Asian Journal of Control

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“…Recently robust ILC has been actively explored using Q-filter (Bristow and Alleyne 2008), H 1 approach (Moore, Ahn, and Chen 2008) or LMI (Nguyen and Banjerdpongchai 2009). In the past few years dozens of papers were dedicated to robust ILC, but unanimously for linear systems.…”

Section: Remarkmentioning

confidence: 99%

A survey on iterative learning control for nonlinear systems

2011

International Journal of Control

374

173

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“…After obtaining the nominal Markov matrix as well as the uncertainty matrices from the above procedure, the Markov matrix of the system (1) has the following form, (9) where G 0 represents the nominal system, G 1 , . .…”

Section: Step 1 Determine the Nominal Impulse Responsesmentioning

confidence: 99%

“…Next, we derive a dual problem of the minimization problem and reformulate it as a convex optimization over linear matrix inequalities (LMIs). In our previous work [9], the robust ILC is designed for linear systems with the time-invariant parametric uncertainty, whereas in this paper, the parametric uncertainties are iteration-varying. Thus, our results yield a unified approach to the robust ILC designs for linear systems with iteration-varying parametric uncertainties and time-invariant parametric uncertainties.…”

Section: Introductionmentioning

confidence: 99%

A convex optimization design of robust iterative learning control for linear systems with iteration‐varying parametric uncertainties

Nguyễn

Banjerdpongchai

2011

Asian Journal of Control

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In this paper, a new robust iterative learning control (ILC) algorithm has been proposed for linear systems in the presence of iteration-varying parametric uncertainties. The robust ILC design is formulated as a min-max problem using a quadratic performance criterion subject to constraints of the control input update. An upper bound of the maximization problem is derived, then, the solution of the min-max problem is achieved by solving a minimization problem. Applying Lagrangian duality to this minimization problem results in a dual problem which can be reformulated as a convex optimization problem over linear matrix inequalities (LMIs). Next, we present an LMIbased algorithm for the robust ILC design and prove the convergence of the control input and the error. Finally, the proposed algorithm is applied to a distillation column to demonstrate its effectiveness.

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An LMI approach for robust iterative learning control with quadratic performance criterion

Cited by 30 publications

References 16 publications

A guaranteed monotonically convergent iterative learning control

A guaranteed monotonically convergent iterative learning control

A survey on iterative learning control for nonlinear systems

A convex optimization design of robust iterative learning control for linear systems with iteration‐varying parametric uncertainties

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