Neural net robot controller with guaranteed tracking performance

Lewis, Frank L.; Liu, K.; Yeşildirek, Aydın

doi:10.1109/isic.1993.397709

Cited by 60 publications

(68 citation statements)

References 11 publications

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“…Remark 4: Therefore, by using the mean value theorem [22] and with the help of (12), (15), and (18), the smoothness of f (·) and g(·) and the activation function φ(·) can be readily used to show thatε(Y,Ẏ ) is also bounded above in , namely, ε ≤ ε m1 . Furthermore, the NN reconstruction error bounds ε m0 and ε m1 are considered to be unknown in this paper as opposed to the previous control literature [19], [20], [24], [25].…”

Section: Controller Developmentmentioning

confidence: 99%

“…(25) Remark 6: In comparison with [19], since the projection algorithm is not used, the challenging task of selecting the predefined convex set is avoided. The boundedness of NN weights are proved simultaneously along with the asymptotic convergence of the tracking error in Section III-D.…”

Section: Controller Developmentmentioning

confidence: 99%

“…Remark 8: The NN output is included inside the integral of (18), while the control input u(t), actual states, and desired trajectory are taken as the NN inputs in contrast with the traditional NN literature [18], [19], [24], [25]. Thus, the dynamics to be compensated by the robust term is bounded above in an arbitrary compact set , unlike in [19] and [20], where the bound on the unmeasurable auxiliary term is a monotonically increasing function of the tracking error.…”

Section: Stability Analysismentioning

confidence: 99%

See 2 more Smart Citations

Robust Integral of Neural Network and Error Sign Control of MIMO Nonlinear Systems

Yang

Jagannathan

Sun

2015

IEEE Trans. Neural Netw. Learning Syst.

103

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This paper presents a novel state-feedback control scheme for the tracking control of a class of multi-input multioutput continuous-time nonlinear systems with unknown dynamics and bounded disturbances. First, the control law consisting of the robust integral of a neural network (NN) output plus sign of the tracking error feedback multiplied with an adaptive gain is introduced. The NN in the control law learns the system dynamics in an online manner, while the NN residual reconstruction errors and the bounded disturbances are overcome by the error sign signal. Since both of the NN output and the error sign signal are included in the integral, the continuity of the control input is ensured. The controller structure and the NN weight update law are novel in contrast with the previous effort, and the semiglobal asymptotic tracking performance is still guaranteed by using the Lyapunov analysis. In addition, the NN weights and all other signals are proved to be bounded simultaneously. The proposed approach also relaxes the need for the upper bounds of certain terms, which are usually required in the previous designs. Finally, the theoretical results are substantiated with simulations.

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Section: Controller Developmentmentioning

confidence: 99%

Section: Controller Developmentmentioning

confidence: 99%

Section: Stability Analysismentioning

confidence: 99%

See 1 more Smart Citation

Robust Integral of Neural Network and Error Sign Control of MIMO Nonlinear Systems

Yang

Jagannathan

Sun

2015

IEEE Trans. Neural Netw. Learning Syst.

103

View full text Add to dashboard Cite

show abstract

“…These are clearly unreasonable assumptions• In the 2-layer NN case V = I (i.e. linear in the parameters), it is easy to show that, using update rule (3.26), the weights W are not generally bounded unless the hidden layer output a(x) obeys a stringent persistency of excitation (PE) condition [15]. In the 3-layer (nonlinear) case, PE conditions are not easy to derive as one is faced with the observability properties of a certain bilinear system.…”

Section: )mentioning

confidence: 99%

“…Uncertainty on how to initialize the NN weights leads to the necessity for 'preliminary off-line tuning'. Some of these problems have been addressed for the 2-layer NN, where linearity in the parameters holds [15,23,25,28,29].…”

Section: Introductionmentioning

confidence: 99%

Neural net robot controller: Structure and stability proofs

Lewis

Yeşildirek

Liu

1995

J Intell Robot Syst

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Abstract. A multilayer neural net (NN) controller for a general serial-link robot arm is developed. The structure of the NN controller is derived using a filtered error approach. It is argued that standard backpropagation tuning, when used for real-time closed-loop control, can yield unbounded NN weights if: (1) the net can not exactly reconstruct a certain required control function, (2) there are bounded unknown disturbances in the robot dynamics, or (3) the robot arm has more than one link (i.e. nonlinear case). On-line weight tuning algorithms including correction terms to backpropagation, plus an added robustifying signal, guarantee tracking as well as bounded weights. The correction terms involve a second-order forwardpropagated wave in the backprop network.

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