Predictor-based control for an uncertain Euler-Lagrange system with input delay

Sharma, Nitin; Bhasin, Shubhendu; Wang, Q.; Dixon, Warren E.

doi:10.1109/acc.2010.5531212

Cited by 18 publications

(11 citation statements)

References 67 publications

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“…Considering this factor, some other methods need to be proposed to deal with the input delay. At present, there are a few results reported on uncertain nonlinear systems with input delay . Specifically, a predictor‐based controller, which contained a finite integral of past control value, was developed in References to for a class of uncertain nonlinear systems with matching condition.…”

Section: Introductionmentioning

confidence: 99%

Adaptive neural network tracking control for uncertain nonlinear systems with input delay and saturation

Zhuang

et al. 2020

Intl J Robust & Nonlinear

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In this article, the adaptive tracking control problem is considered for a class of uncertain nonlinear systems with input delay and saturation. To compensate for the effect of the input delay and saturation, a compensation system is designed.Radial basis function neural networks are directly utilized to approximate the unknown nonlinear functions. With the aid of the backstepping method, novel adaptive neural network tracking controllers are developed, which can guarantee all the signals in the closed-loop system are semiglobally uniformly ultimately bounded, and the system output can track the desired signal with a small tracking error. In the end, a simulation example is given to illustrate the effectiveness of the proposed methods. K E Y W O R D Sinput delay, neural networks, nonlinear systems, saturation INTRODUCTIONIn recent years, adaptive control problem for nonlinear systems has attracted considerable attention and remarkable developments have been obtained in nonlinear control area. Among these results, adaptive control by using backstepping technique has received much attention because of its advantages over the conventional approaches (see References 1-5 and references therein). In addition, fuzzy logic systems and neural network have also be widely used in nonlinear control area due to their ability of approximating unknown nonlinear functions. 6-10 Although fruitful results have been obtained for nonlinear systems, there are still some challenging problems waiting to be solved. It is well known that control problem of input-delayed systems is one of the fundamental problems for time-delay systems because of its practical and theoretical significance. At present, many approaches have been proposed for system with state delay (see References 9-13). However, they all ignored the input delay. Compared with state delay, control problem of input delay is more complicated and the traditional Lyapunov-Krasovskii functional based methods are not effective to deal with the input delay. Therefore, it is noteworthy for us to investigate the systems with input delays. A basic idea in dealing with input delay is the predictor feedback. 14,15 However, traditional predictor-based methods have difficulties in practical implementation because of the distributed term. Therefore, to avoid the infinite-dimensionality of feedback laws, truncated predictor feedback was studied in References 16 to 20 to ignore the distributed term.Although fruitful results have been obtained for linear input-delay systems, the adaptive control problem for uncertain nonlinear system is still a challenging problem because nonlinear systems' states are not easy to be predicted with the existence of the nonlinearity and uncertainty. Considering this factor, some other methods need to be proposed to deal with the input delay. At present, there are a few results reported on uncertain nonlinear systems with input delay. 21-34 Specifically, Int J Robust Nonlinear Control. 2020;30:2593-2610.wileyonlinelibrary.com/journal/rnc

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Section: Introductionmentioning

confidence: 99%

Adaptive neural network tracking control for uncertain nonlinear systems with input delay and saturation

Zhuang

et al. 2020

Intl J Robust & Nonlinear

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“…Remark The previous research studies about adaptive robust control methods with input time delay focused on the CT form . In our research, we propose a novel neural network optimal control method for time‐delay DT systems instead of CT systems with time delays.…”

Section: A Novel Neural Network Optimal Control Design For Nonlinear mentioning

confidence: 99%

A novel neural network discrete‐time optimal control design for nonlinear time‐delay systems using adaptive critic designs

Liang

Zhang

et al. 2020

Optim Control Appl Methods

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In this article, a novel neural network (NN) optimal control approach using adaptive critic designs is developed for nonlinear discrete-time (DT) systems with time delays. First, to eliminate the delay term of control input, a time-delay matrix function is developed by designing a M network. Furthermore, the cost function is approximated by the critic NN, and the control signal can be obtained directly by using the information of critic NN according to the equilibrium condition. In addition, to shorten the learning time and reduce the computational burden in the control process, a novel control strategy with less adjustable parameters for the time-delay DT nonlinear systems is proposed in this article, in which the norm of the weight estimations of critic NN is updated to generate a novel long-term performance function.The proposed control algorithm using adaptive critic designs has the advantage of reducing adaptive learning parameters and lessening calculative burden. The Lyapunov stability analysis shows that the time-delay DT controlled systems can be uniformly ultimately bounded stable. Finally, three simulations are presented to demonstrate the control performance of the developed method. K E Y W O R D Sadaptive critic designs, discrete-time systems, neural network, optimal control, time delay 1 748

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“…In (4), J ∈ ℝ n × n denotes the unknown inertia of a limb fixed in a test apparatus, C s ∈ ℝ n × n denotes the Centripetal/Coriolis matrix, M e ∈ ℝ n denotes the moment generated by the passive elastic properties of the muscles, M υ ∈ ℝ n denotes the moment generated by the passive viscous properties of the muscles, M g ∈ ℝ n denotes the gravitational torque acting on the limb, and d ( t ) ∈ ℝ n denotes any disturbances that may arise in the system. For detailed definitions of M e , M υ , and M g , see [33]. The input to the FES system, Γ s ( t ) ∈ ℝ n , is the torque produced using FES, and F e ( t ) ∈ ℝ n is the interaction force between the musculoskeletal system and environment.…”

Section: System Dynamicsmentioning

confidence: 99%

“…The force-velocity relationship is bounded by a non-zero number since it only equals zero when the muscle shortening velocity is near its maximum which is outside the range of the velocities imposed in this control problem. Note that the first time derivative of Ω is not assumed nor required to be bounded, unlike our earlier papers [17, 33]. …”

Section: Control Developmentmentioning

confidence: 99%

Bilateral control of functional electrical stimulation and robotics-based telerehabilitation

Alibeji

Dicianno

Sharma

2017

Int J Intell Robot Appl

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Currently a telerehabilitation system includes a therapist and a patient where the therapist interacts with the patient, typically via a verbal and visual communication, for assessment and supervision of rehabilitation interventions. This mechanism often fails to provide physical assistance, which is a modus operandi during physical therapy or occupational therapy. Incorporating an actuation modality such as functional electrical stimulation (FES) or a robot at the patient’s end that can be controlled by a therapist remotely, to provide therapy or to assess and measure rehabilitation outcomes can significantly transform current telerehabilitation technology. In this paper, a position-synchronization controller is derived for FES-based telerehabilitation to provide physical assistance that can be controlled remotely. The newly derived controller synchronizes an FES-driven human limb with a remote physical therapist’s robotic manipulator despite constant bilateral communication delays. The control design overcomes a major stability analysis challenge: the unknown and unstructured nonlinearities in the FES-driven musculoskeletal dynamics. To address this challenge, the nonlinear muscle model was estimated through two neural networks functions that approximated unstructured nonlinearities and an adaptive control law for structured nonlinearities with online update laws. A Lyapunov-based stability analysis was used to prove the globally uniformly ultimately bounded tracking performance. The performance of the state synchronization controller was validated through experiments on an able-bodied subject. Specifically, we demonstrated bilateral control of FES-elicited leg extension and a human operated robotic manipulator. The controller was shown to effectively synchronize the system despite unknown and different delays in the forward and backward channels.

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Predictor-based control for an uncertain Euler-Lagrange system with input delay

Cited by 18 publications

References 67 publications

Adaptive neural network tracking control for uncertain nonlinear systems with input delay and saturation

Adaptive neural network tracking control for uncertain nonlinear systems with input delay and saturation

A novel neural network discrete‐time optimal control design for nonlinear time‐delay systems using adaptive critic designs

Bilateral control of functional electrical stimulation and robotics-based telerehabilitation

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