Deep learning controller for nonlinear system based on Lyapunov stability criterion

Zaki, A.; El-Nagar, Ahmad M.; El-Bardini, Mohammad; Soliman, F. A.

doi:10.1007/s00521-020-05077-1

Cited by 22 publications

(17 citation statements)

References 51 publications

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“…RBM's are networks in which probabilistic states are learned for a set of inputs suitable for unsupervised learning. A similar approach to DL control is the work in [11], where RBMs are also used for weight initialization by unsupervised training. The disadvantage of DBNs is the hardware requirement since they consist of two stages, unsupervised pre-training and supervised fine tuning.…”

Section: Output Layermentioning

confidence: 99%

Deep Learning Control for Digital Feedback Systems: Improved Performance with Robustness against Parameter Change

Alwan

Hussain

2021

Electronics

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Training data for a deep learning (DL) neural network (NN) controller are obtained from the input and output signals of a conventional digital controller that is designed to provide the suitable control signal to a specified plant within a feedback digital control system. It is found that if the DL controller is sufficiently deep (four hidden layers), it can outperform the conventional controller in terms of settling time of the system output transient response to a unit-step reference signal. That is, the DL controller introduces a damping effect. Moreover, it does not need to be retrained to operate with a reference signal of different magnitude, or under system parameter change. Such properties make the DL control more attractive for applications that may undergo parameter variation, such as sensor networks. The promising results of robustness against parameter changes are calling for future research in the direction of robust DL control.

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Section: Output Layermentioning

confidence: 99%

Deep Learning Control for Digital Feedback Systems: Improved Performance with Robustness against Parameter Change

Alwan

Hussain

2021

Electronics

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“…When the system dynamics are known, robust and certifiable control policy design can be achieved through various control-theoretic methods such as reachability analysis [13], Funnels [14,15], and Hamilton-Jacobi analysis [16,17]. Lyapunov stability criteria, Contraction Theory, and Control Barrier Functions have been extensively utilized for providing strong convergence guarantees for nonlinear dynamical systems [1,[18][19][20][21]. However, even when the dynamics are known, finding a proper Lyapunov function or a control barrier function is itself a challenging task.…”

Section: Related Workmentioning

confidence: 99%

Learning Contraction Policies from Offline Data

Rezazadeh¹,

Maxwell²,

Kia³

et al. 2021

Preprint

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This paper proposes a data-driven method for learning convergent control policies from offline data using Contraction theory. Contraction theory enables constructing a policy that makes the closed-loop system trajectories inherently convergent towards a unique trajectory. At the technical level, identifying the contraction metric, which is the distance metric with respect to which a robot's trajectories exhibit contraction is often non-trivial. We propose to jointly learn the control policy and its corresponding contraction metric while enforcing contraction. To achieve this, we learn an implicit dynamics model of the robotic system from an offline data set consisting of the robot's state and input trajectories. Using this learned dynamics model, we propose a data augmentation algorithm for learning contraction policies. We randomly generate samples in the state-space and propagate them forward in time through the learned dynamics model to generate auxiliary sample trajectories. We then learn both the control policy and the contraction metric such that the distance between the trajectories from the offline data set and our generated auxiliary sample trajectories decreases over time. We evaluate the performance of our proposed framework on simulated robotic goal-reaching tasks and demonstrate that enforcing contraction results in faster convergence and greater robustness of the learned policy.

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“…Although all these methods, the ANN demonstrated to be a robust method to handle nonlinear systems and uncertainty modeling for robust control purposes and systems identification. [15][16][17][18][19] In Reference 15, the authors presented an output-feedback control with a neural network to stochastic nonlinear strict-feedback systems. The network is applied to recompense all unknown upper bounding functions.…”

Section: Introductionmentioning

confidence: 99%

Learning‐based robust neuro‐control: A method to compute control Lyapunov functions

Rego

Araújo

2021

Intl J Robust & Nonlinear

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Nonlinear dynamical systems play a crucial role in control systems because, in practice, all the plants are nonlinear, and they are also a hopeful description of complex robot movements. To perform a control and stability analysis of a nonlinear system, usually, a Lyapunov function is used. In this article, we proposed a method to compute a control Lyapunov function (CLF) for nonlinear dynamics based on a learning robust neuro-control strategy. The procedure uses a deep neural network architecture to generate control functions supported by the Lyapunov stability theory. An estimation of the region of attraction is produced for advanced stability analysis. We implemented two numerical examples to compare the performance of the proposed technique with some existing methods.The proposed method computes a CLF that provides the stabilizability of the systems and produced better solutions to nonlinear systems in the design of stable controls without linear approximations and in the presence of disturbances.

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Deep learning controller for nonlinear system based on Lyapunov stability criterion

Cited by 22 publications

References 51 publications

Deep Learning Control for Digital Feedback Systems: Improved Performance with Robustness against Parameter Change

Deep Learning Control for Digital Feedback Systems: Improved Performance with Robustness against Parameter Change

Learning Contraction Policies from Offline Data

Learning‐based robust neuro‐control: A method to compute control Lyapunov functions

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