Convergence Analysis of Saturated Iterative Learning Control Systems With Locally Lipschitz Nonlinearities

Zhang, Jingyao; Meng, Deyuan

doi:10.1109/tnnls.2019.2951752

Cited by 30 publications

(14 citation statements)

References 42 publications

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“…More recently, primitive-based control has been studied in [9][10][11][12][13], mostly as part of hierarchical learning frameworks [14][15][16][17][18]. However, the application of the Iterative Learning Control (ILC, a full list of the acronyms used in the paper is presented in abbreviations part) technique [19][20][21][22][23][24][25] over linearized feedback closed-loop control systems (CLSs) as a primer mechanism for primitive-based learning was proposed in [8]. An experiment-driven ILC (EDILC) variant was crafted in a norm-optimal tracking setting to learn reference-input controlled output pairs called primitives.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical Cognitive Control for Unknown Dynamic Systems Tracking

Rădac

Lala

2021

Mathematics

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A general control system tracking learning framework is proposed, by which an optimal learned tracking behavior called ‘primitive’ is extrapolated to new unseen trajectories without requiring relearning. This is considered intelligent behavior and strongly related to the neuro-motor cognitive control of biological (human-like) systems that deliver suboptimal executions for tasks outside of their current knowledge base, by using previously memorized experience. However, biological systems do not solve explicit mathematical equations for solving learning and prediction tasks. This stimulates the proposed hierarchical cognitive-like learning framework, based on state-of-the-art model-free control: (1) at the low-level L1, an approximated iterative Value Iteration for linearizing the closed-loop system (CLS) behavior by a linear reference model output tracking is first employed; (2) an experiment-driven Iterative Learning Control (EDILC) applied to the CLS from the reference input to the controlled output learns simple tracking tasks called ‘primitives’ in the secondary L2 level, and (3) the tertiary level L3 extrapolates the primitives’ optimal tracking behavior to new tracking tasks without trial-based relearning. The learning framework relies only on input-output system data to build a virtual state space representation of the underlying controlled system that is assumed to be observable. It has been shown to be effective by experimental validation on a representative, coupled, nonlinear, multivariable real-world system. Able to cope with new unseen scenarios in an optimal fashion, the hierarchical learning framework is an advance toward cognitive control systems.

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Section: Introductionmentioning

confidence: 99%

Hierarchical Cognitive Control for Unknown Dynamic Systems Tracking

Rădac

Lala

2021

Mathematics

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“…Actually, this assumption is not consistent with real‐world applications, such as the pick‐and‐place manipulators transport different mass, 11 and the parameters of macroscopic traffic flow may vary due to climates, holidays and epidemics 12 . Since non‐repetitive uncertainties impact system performance solidly, related works have been carried out in References 13‐16, among many others. To be specific, 13 makes full use of the upper and lower bounds of uncertainties to construct a robust iterative learning controller.…”

Section: Introductionmentioning

confidence: 99%

“…A modified initial error manner is put forward by Reference 15 to treat non‐repetitive trajectories. With the help of composite energy functions (CEF), 16 delivers a convergent condition for non‐repetitive disturbances under a locally Lipschitz restriction. Since time‐delay is unavoidable in engineering to degrade system performance or even render instability, therefore, it is meaningful to address this issue in ILC field 17 .…”

Section: Introductionmentioning

confidence: 99%

Adaptive iterative learning control for continuous systems with non‐repetitive uncertainties and unknown state delays

Park

Shen

2022

Intl J Robust & Nonlinear

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This paper is devoted to tracking control of nonlinear multiple-input multiple-output systems subject to unknown state delays and non-repetitive uncertainties. An adaptive iterative learning control scheme is proposed by integrating a P-type feedback term, an iterative updating term and an additional compensation term. Among these terms, the first one is to alleviate the ill effect caused by non-repetitive uncertainties and the third one is utilized to handle the unwell learned part. The composite energy function methodology is employed to elaborate the bounded convergence of the tracking error. The validity of the proposed method is compared with existing results via simulation studies.

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“…In particular, the linear reference model output (LRMO) tracking control setting is advantageous, ensuring indirect state-feedback linearization of control systems. Such linearity property of control systems is critical for higherlevel learning paradigms such as Iterative Learning Control [28][29][30][31][32][33][34] and primitive-based learning [34][35][36][37][38][39][40], as representative hierarchical learning control paradigms [41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Virtual State Feedback Reference Tuning and Value Iteration Reinforcement Learning for Unknown Observable Systems Control

Rădac

Borlea

2021

Energies

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In this paper, a novel Virtual State-feedback Reference Feedback Tuning (VSFRT) and Approximate Iterative Value Iteration Reinforcement Learning (AI-VIRL) are applied for learning linear reference model output (LRMO) tracking control of observable systems with unknown dynamics. For the observable system, a new state representation in terms of input/output (IO) data is derived. Consequently, the Virtual State Feedback Tuning (VRFT)-based solution is redefined to accommodate virtual state feedback control, leading to an original stability-certified Virtual State-Feedback Reference Tuning (VSFRT) concept. Both VSFRT and AI-VIRL use neural networks controllers. We find that AI-VIRL is significantly more computationally demanding and more sensitive to the exploration settings, while leading to inferior LRMO tracking performance when compared to VSFRT. It is not helped either by transfer learning the VSFRT control as initialization for AI-VIRL. State dimensionality reduction using machine learning techniques such as principal component analysis and autoencoders does not improve on the best learned tracking performance however it trades off the learning complexity. Surprisingly, unlike AI-VIRL, the VSFRT control is one-shot (non-iterative) and learns stabilizing controllers even in poorly, open-loop explored environments, proving to be superior in learning LRMO tracking control. Validation on two nonlinear coupled multivariable complex systems serves as a comprehensive case study.

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Convergence Analysis of Saturated Iterative Learning Control Systems With Locally Lipschitz Nonlinearities

Cited by 30 publications

References 42 publications

Hierarchical Cognitive Control for Unknown Dynamic Systems Tracking

Hierarchical Cognitive Control for Unknown Dynamic Systems Tracking

Adaptive iterative learning control for continuous systems with non‐repetitive uncertainties and unknown state delays

Virtual State Feedback Reference Tuning and Value Iteration Reinforcement Learning for Unknown Observable Systems Control

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