Constrained digital regulation of hyperbolic PDE systems: A learning control approach

Choi, Jae Young; Seo, Beom Joon; Lee, Kwang Soon

doi:10.1007/bf02706375

Cited by 31 publications

(23 citation statements)

References 6 publications

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“…In this section, with Lemma 1 and Proposition 1, we give the sufficient conditions of ILC system (15) under conditions (7) and (16). The following theorem is the main result of this paper.…”

Section: Convergence Analysis Of Ilcmentioning

confidence: 98%

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Iterative learning control for discrete parabolic distributed parameter systems

Dai

Tian

Ya-jun

2015

Int. J. Autom. Comput.

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Abstract:In this paper, iterative learning control (ILC) technique is applied to a class of discrete parabolic distributed parameter systems described by partial difference equations. A P-type learning control law is established for the system. The ILC of discrete parabolic distributed parameter systems is more complex as 3D dynamics in the time, spatial and iterative domains are involved. To overcome this difficulty, discrete Green formula and analogues discrete Gronwall inequality as well as some other basic analytic techniques are utilized. With rigorous analysis, the proposed intelligent control scheme guarantees the convergence of the tracking error. A numerical example is given to illustrate the effectiveness of the proposed method.

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Section: Convergence Analysis Of Ilcmentioning

confidence: 98%

“…In [16], ILC for the first order hyperbolic distributed parameter systems was discussed by using finite approximation. A class of second order hyperbolic elastic system was studied in [17], by using the differential difference iterative learning algorithm.…”

Section: Introductionmentioning

confidence: 99%

Iterative learning control for discrete parabolic distributed parameter systems

Dai

Tian

Ya-jun

2015

Int. J. Autom. Comput.

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“…In recent years, the application of ILC to distributed parameter systems has become a new topic [12][13][14][15]. In [12], an open-loop P-type iterative learning controller was designed for the first order hyperbolic distributed parameter system. The P-type and D-type ILC algorithms were studied in [13] for a class of parabolic distributed parameter systems.…”

Section: Introductionmentioning

confidence: 99%

ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems

Lan

Cui

2018

Algorithms

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This paper presents a second order P-type iterative learning control (ILC) scheme with initial state learning for a class of fractional order linear distributed parameter systems. First, by analyzing the control and learning processes, a discrete system for P-type ILC is established, and the ILC design problem is then converted to a stability problem for such a discrete system. Next, a sufficient condition for the convergence of the control input and the tracking errors is obtained by introducing a new norm and using the generalized Gronwall inequality, which is less conservative than the existing one. Finally, the validity of the proposed method is verified by a numerical example.

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“…Currently, the vast majority of the work reported on ILC considers finite-dimensional systems but there has been some work reported on its application to distributed parameter systems governed by Partial Differential Equations (PDEs), for example, Choi et al (2001), Moore & Chen (2006), Qu (2002), Chao et al (2009), Zhao (2005. In terms of developing ILC for PDEs, an obvious approach is to work directly with the defining equations, where, for example, Chao et al (2009) considers the design of P -Type and D-Type control laws for parabolic PDEs, such as the controlled heat equation, using semigroup theory.…”

Section: Introductionmentioning

confidence: 99%

Iterative learning control for spatio-temporal dynamics using Crank-Nicholson discretization

Cichy

Gałkowski

Rogers

2010

Multidim Syst Sign Process

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Iterative learning control is now well established for linear and nonlinear dynamics in terms of both the underlying theory and experimental application. This approach is specifically targeted at cases where the same operation is repeated over a finite duration with resetting between successive repetitions. Each repetition or pass is known as a trial and the key idea is to use information from previous trials to update the control input used on the current one with the aim of improving performance from trial-to-trial. In this paper, new results on ILC applied to systems that arise from discretization of bi-variate partial differential equations describing spatio-temporal systems or processes are developed. Theses are based on Crank-Nicholson discretization of the governing partial differential equation, resulting in an unconditionally numerically stable approximation of the dynamics. It is also shown that this setting allows the selection of a finite number of points for sensing and actuation. The resulting control laws can be computed using Linear Matrix Inequalities (LMIs). Finally, an illustrative example is given and areas for further research are discussed.

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Constrained digital regulation of hyperbolic PDE systems: A learning control approach

Cited by 31 publications

References 6 publications

Iterative learning control for discrete parabolic distributed parameter systems

Iterative learning control for discrete parabolic distributed parameter systems

ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems

Iterative learning control for spatio-temporal dynamics using Crank-Nicholson discretization

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