D-type anticipatory iterative learning control for a class of inhomogeneous heat equations

Huang, Deqing; Xu, Jian‐Xin; Li, Xuefang; Xu, Chao; Yu, Miao

doi:10.1016/j.automatica.2013.05.005

Cited by 140 publications

(74 citation statements)

References 29 publications

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“…; 3000 with sample time DT ¼ 0:001 s. The initial state at each iteration is reset as q i ð0Þ ¼ q 0 ¼ ½0:9; 0; p=2 T . The gain matrices L 1 ðkÞ, L 2 ðkÞ, and L 3 ðkÞ in control laws (10) and (7) are set to …”

Section: Case 2: Cardioid-like Trajectorymentioning

confidence: 99%

“…In this regard, ILC is fruitful both in theoretical analysis and practical applications. [6][7][8][9][10] Widely utilized in civil and military fields, nonholonomic mobile robots (NMR) have gained significantly increasing research interests over the past few decades. The growing demands have brought in the focus on improving the autonomous motion of NMR.…”

Section: Introductionmentioning

confidence: 99%

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A novel iterative learning path-tracking control for nonholonomic mobile robots against initial shifts

Zhao

Zhou

et al. 2017

International Journal of Advanced Robotic Systems

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In this article, we propose a novel discrete-time iterative learning control framework for robust path-tracking problem of nonholonomic mobile robots. The contributions of this iterative learning control framework are threefolds: (1) With the application of a conventional feedback-aided P-type learning algorithm, the tracking error caused by a nonzero initial shift is detected. (2) By the introduction of an initial rectifying term, a novel iterative learning control scheme is proposed to improve the tracking performance. Sufficient conditions of convergence of this approach are given. (3) The convergence of the proposed algorithm for achieving the desired trajectory over a specified interval is proven theoretically. Simulation results validate the effectiveness of the proposed scheme.

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Section: Case 2: Cardioid-like Trajectorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A novel iterative learning path-tracking control for nonholonomic mobile robots against initial shifts

Zhao

Zhou

et al. 2017

International Journal of Advanced Robotic Systems

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“…When the fractional order α = 1, the fractional order distributed parameter System (1) is reduced to an integral order one, which has been widely investigated in [11,[16][17][18][19].…”

Section: Remarkmentioning

confidence: 99%

“…For uncertain nonlinear distributed parameter systems and state time-delay distributed parameter systems, the P-type ILC was investigated in [15,16], respectively. A D-type anticipatory ILC scheme was applied to the boundary control of a class of inhomogeneous heat equations in [17]. In [18], a framework in the frequency domain of ILC was designed for linear inhomogeneous 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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“…The basic objective of ILC is to overcome the imperfect knowledge of the plant using previous tracking information and to achieve output tracking through repetition [2−5] . This makes ILC schemes particularly useful in applications with repetitive tasks, such as robot manipulator [6] , tracking problem of the taking-off and landing planes [7] , freeway traffic control [8] , waste-water treatment [9] , piezoelectric positioning stage system [10] , heat flux boundary control [11] , etc. The ILC algorithm has been developed widely from classical ILC [12] , higher-order ILC [13,14] , robust ILC [15,16] , optimal ILC [17] to adaptive ILC [18−22] for the last two decades.…”

Section: Introductionmentioning

confidence: 99%

A high-order internal model based iterative learning control scheme for discrete linear time-varying systems

Zhou

Huang

2015

Int. J. Autom. Comput.

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Abstract:In this paper, an iterative learning control algorithm is proposed for discrete linear time-varying systems to track iterationvarying desired trajectories. A high-order internal model (HOIM) is utilized to describe the variation of desired trajectories in the iteration domain. In the sequel, the HOIM is incorporated into the design of learning gains. The learning convergence in the iteration axis can be guaranteed with rigorous proof. The simulation results with permanent magnet linear motors (PMLM) demonstrate that the proposed HOIM based approach yields good performance and achieves perfect tracking.

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D-type anticipatory iterative learning control for a class of inhomogeneous heat equations

Cited by 140 publications

References 29 publications

A novel iterative learning path-tracking control for nonholonomic mobile robots against initial shifts

A novel iterative learning path-tracking control for nonholonomic mobile robots against initial shifts

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

A high-order internal model based iterative learning control scheme for discrete linear time-varying systems

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