Adaptive Neural Network Control for a Class of Low-Triangular-Structured Nonlinear Systems

Du, Haibo; Shao, Hu; Yao, Pingjing

doi:10.1109/tnn.2005.863403

Cited by 144 publications

(91 citation statements)

References 17 publications

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“…In the following lemma, a family of discrete Nussbaum gain is proposed based on the one defined above. The continuous-time counterpart lemma is reported in [40].…”

Section: E the Discrete Nussbaum Gainmentioning

confidence: 99%

“…if others (40) where is the discrete Nussbaum gain defined in (10). Theorem 2: Consider the adaptive closed-loop system consisting of system (1) under Assumptions 1-3 or system (2) under Assumptions 4-6, NN control (28) with NN weights adaptation law (40).…”

Section: B Robust Nn Controlmentioning

confidence: 99%

“…Theorem 2: Consider the adaptive closed-loop system consisting of system (1) under Assumptions 1-3 or system (2) under Assumptions 4-6, NN control (28) with NN weights adaptation law (40). All the signals in the closed-loop system are SGUUB and the discrete Nussbaum gain will converge to a constant ultimately.…”

Section: B Robust Nn Controlmentioning

confidence: 99%

See 2 more Smart Citations

Output Feedback NN Control for Two Classes of Discrete-Time Systems With Unknown Control Directions in a Unified Approach

Yang

Chen

et al. 2008

IEEE Trans. Neural Netw.

206

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Abstract-In this paper, output feedback adaptive neural network (NN) controls are investigated for two classes of nonlinear discrete-time systems with unknown control directions: 1) nonlinear pure-feedback systems and 2) nonlinear autoregressive moving average with exogenous inputs (NARMAX) systems. To overcome the noncausal problem, which has been known to be a major obstacle in the discrete-time control design, both systems are transformed to a predictor for output feedback control design. Implicit function theorem is used to overcome the difficulty of the nonaffine appearance of the control input. The problem of lacking a priori knowledge on the control directions is solved by using discrete Nussbaum gain. The high-order neural network (HONN) is employed to approximate the unknown control. The closed-loop system achieves semiglobal uniformly-ultimately-bounded (SGUUB) stability and the output tracking error is made within a neighborhood around zero. Simulation results are presented to demonstrate the effectiveness of the proposed control.Index Terms-Discrete Nussbaum gain, discrete-time system, nonlinear autoregressive moving average with exogenous inputs (NARMAX) systems, neural networks (NNs), pure-feedback system, unknown control directions.

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“…In the following lemma, a family of discrete Nussbaum gain is proposed based on the one defined above. The continuous-time counterpart lemma is reported in [40].…”

Section: E the Discrete Nussbaum Gainmentioning

confidence: 99%

Section: B Robust Nn Controlmentioning

confidence: 99%

See 1 more Smart Citation

Output Feedback NN Control for Two Classes of Discrete-Time Systems With Unknown Control Directions in a Unified Approach

Yang

Chen

et al. 2008

IEEE Trans. Neural Netw.

206

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show abstract

“…[13,14,[31][32][33][34] Generally the adaptive NN control scheme for nonlinear uncertain discrete-time systems is on the basis of the backstepping technique and Lyapunov stability theory. [20][21][22][23] For example, in Ref.…”

Section: Introductionmentioning

confidence: 99%

Adaptive control for uncertain discrete-time systems with unknown disturbance based on RNN

Cui

Guo

Feng

et al. 2016

AIR

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A new robust adaptive control algorithm is developed for a class of uncertain discrete-time SISO systems. Different from the existing investigated systems, the concerned discrete system here is with both uncertain smooth nonlinear functions and unknown disturbance. On the basis of the idea of neural network (NN) approximation, a novel recurrent neural network (RNN) is first proposed and used to approximate a backstepping control law following the transformation of the original system into a predictor form. According to Lyapunov stability theorem, a new on-line tuning law for parameters of RNN is obtained. Meanwhile, in order to achieve satisfying robust tracking performance, a novel controller is constructed by virtue of the approximation error of RNN. It has been proved that all the concerned signals are uniformly ultimately bounded. In addition, a very small tracking error can be obtained through appropriate selection of control parameters. Finally, we give a simulation example to demonstrate the validness of the newly proposed control algorithm for the investigated systems.

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“…For the testing step, mean square error was founded to be 2.2 mg/L. Up to now, some results on feed-forward neural network for the wastewater treatment process modelling have been presented by many researchers [6][7]. Feed-forward neural networks have been successfully used to solve problems that require the computation of a static function i.e.…”

Section: Introductionmentioning

confidence: 99%

Recurrent High Order Neural Network Modeling for Wastewater Treatment Process

Qiao¹,

Yang²,

Yuan³

2011

JCP

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Abstract-Due to the multi-variable, nonlinear, large time delay and strong coupling features of the wastewater treatment process, a recurrent high-order neural network is used to model the key water quality parameters(Chemical Oxygen Demand, Biological Oxygen Demand, Suspended Solid and Ammonia Nitrogen) for the wastewater treatment process, and the neural network is trained by an filtering algorithm. Operational data of a wastewater treatment plant is employed to illustrate the efficacy of the proposed modeling method. Meanwhile, the results are compared with feed-forward neural network and the general recurrent neural network to indicate the modeling accuracy of the recurrent high-order neural network.Index Terms-wastewater treatment, recurrent high order neural network, filtering

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Adaptive Neural Network Control for a Class of Low-Triangular-Structured Nonlinear Systems

Cited by 144 publications

References 17 publications

Output Feedback NN Control for Two Classes of Discrete-Time Systems With Unknown Control Directions in a Unified Approach

Output Feedback NN Control for Two Classes of Discrete-Time Systems With Unknown Control Directions in a Unified Approach

Adaptive control for uncertain discrete-time systems with unknown disturbance based on RNN

Recurrent High Order Neural Network Modeling for Wastewater Treatment Process

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