Stable adaptive neural control of nonlinear systems

Polycarpou, Marios M.; Weaver, S.E.

doi:10.1109/acc.1995.529368

Cited by 16 publications

(8 citation statements)

References 9 publications

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“…Moreover, the introduction of the term g 1 (x 1 )z 1 does not add any new variable in the function h 2 (Z 2 ), which makes the existing NN approximation results still valid in this paper. Therefore, employing the RBF NN to approximate h 2 (Z 2 ), we have 2 is the approximation error and satisfies | 2 | ≤ * 2 , and W * 2 is an unknown ideal weight vector. LetŴ 2 be the estimate of W * 2 , andW 2 =Ŵ 2 − W * 2 be the estimate error.…”

Section: Iss-modular Direct Ancmentioning

confidence: 99%

“…Theorem 4: Consider the closed-loop system consisting of the strict-feedback system (1), the reference model (2), and the neural learning controller (34) with the virtual control laws (35) and the learned neural weights given by (23). For initial conditions x di (0) of the reference model which generates the same recurrent orbit ϕ d i (Z d i (0)) as in Theorem 3, and with the corresponding initial conditions x i (0) of (1) in a close vicinity of ϕ d i (Z d i (0)), we have that all signals in the closedloop system remain bounded, and the tracking error converges exponentially to a small neighborhood around zero.…”

Section: Learning Control Using Experiencesmentioning

confidence: 99%

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Learning From ISS-Modular Adaptive NN Control of Nonlinear Strict-Feedback Systems

Wang

Liu

et al. 2012

IEEE Trans. Neural Netw. Learning Syst.

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This paper studies learning from adaptive neural control (ANC) for a class of nonlinear strict-feedback systems with unknown affine terms. To achieve the purpose of learning, a simple input-to-state stability (ISS) modular ANC method is first presented to ensure the boundedness of all the signals in the closed-loop system and the convergence of tracking errors in finite time. Subsequently, it is proven that learning with the proposed stable ISS-modular ANC can be achieved. The cascade structure and unknown affine terms of the considered systems make it very difficult to achieve learning using existing methods. To overcome these difficulties, the stable closed-loop system in the control process is decomposed into a series of linear time-varying (LTV) perturbed subsystems with the appropriate state transformation. Using a recursive design, the partial persistent excitation condition for the radial basis function neural network (NN) is established, which guarantees exponential stability of LTV perturbed subsystems. Consequently, accurate approximation of the closed-loop system dynamics is achieved in a local region along recurrent orbits of closed-loop signals, and learning is implemented during a closed-loop feedback control process. The learned knowledge is reused to achieve stability and an improved performance, thereby avoiding the tremendous repeated training process of NNs. Simulation studies are given to demonstrate the effectiveness of the proposed method.

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Section: Iss-modular Direct Ancmentioning

confidence: 99%

Section: Learning Control Using Experiencesmentioning

confidence: 99%

Learning From ISS-Modular Adaptive NN Control of Nonlinear Strict-Feedback Systems

Wang

Liu

et al. 2012

IEEE Trans. Neural Netw. Learning Syst.

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“…The initial condition is [ (25) have to be shifted simultaneously. The control gains are k z1 = 10.0, k z2 = 10.0,, and the remaining numerical parameters are identical to those in Example 1.…”

Section: Simulationmentioning

confidence: 99%

Global adaptive neural dynamic surface control of strict-feedback systems

Huang

2015

Neurocomputing

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“…Theorem 3: (Learning) Consider the closed-loop system consisting of the strict-feedback plant (1) with the unknown affine terms , the reference model (2), the controller (13), and the NN weight updating laws (17). For any recurrent orbit ϕ d (x d (0)), and with initial conditions x(0) ∈ Ω 0 (where Ω 0 is an appropriately chosen compact set) and W i (0) = 0, we have that the neural-weight estimates W i converge to small neighborhoods of optimal values W * i , the locally-accurate approximation of controller dynamics…”

Section: Learning From Iss-modular Direct Ancmentioning

confidence: 99%

Deterministic learning from ISS-modular adaptive NN control of nonlinear strict-feedback systems

Wang

2011

2011 IEEE 5th International Conference on Cybernetics and Intelligent Systems (CIS)

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This paper studies deterministic learning from adaptive neural control for a class of strict-feedback nonlinear systems with unknown affine terms. Firstly, an ISS-modular approach is presented to ensure uniformly ultimate boundedness of all the signals in the closed-loop system and the convergence of tracking errors in a finite time. The proposed ISS-modular approach avoids the possible control singularity without the restriction of the derivative of affine terms. Secondly, it will be shown the proposed stable ISS-modular adaptive neural controller is able to learn closed-loop system dynamics. The cascade structure and unknown affine terms of the considered systems make it very difficult to achieve learning using previous methods. To overcome these difficulties, the stable closedloop system in control process is decomposed into a series of linear time-varying (LTV) perturbed subsystems with the appropriate state transformation. Using a recursive design, the partial persistent excitation (PE) condition for radial basis function (RBF) neural networks (NN) is established, which guarantees exponential stability of LTV perturbed subsystems. Consequently, accurate approximation of the closed-loop control system dynamics is achieved in a local region along a recurrent orbit of closed-loop signals, and a learning ability is implemented during a closed-loop feedback control process. The learned knowledge can be reused in the same or similar control tasks, and avoid the tremendous repeated training process of NNs.

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Stable adaptive neural control of nonlinear systems

Cited by 16 publications

References 9 publications

Learning From ISS-Modular Adaptive NN Control of Nonlinear Strict-Feedback Systems

Learning From ISS-Modular Adaptive NN Control of Nonlinear Strict-Feedback Systems

Global adaptive neural dynamic surface control of strict-feedback systems

Deterministic learning from ISS-modular adaptive NN control of nonlinear strict-feedback systems

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