Stabilisation of singularly perturbed nonlinear systems via neural network-based control and observer design

Lin, Kuo-Jung

doi:10.1080/00207721.2012.670304

Cited by 7 publications

(5 citation statements)

References 29 publications

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“…To demonstrate the potential application of the control schemes for practical systems, we consider a nonlinear circuit [35] illustrated in Fig.5. The ν c − I R characteristics of the resistor is I R = 1 5 ν 3 c − 1 5 ν c .…”

Section: B Example2mentioning

confidence: 99%

“…Due to the theoretical challenges and practical needs, some researchers pay more and more attention to singularly perturbed nonlinear systems. For instance, in [35], an H ∞ controller was presented for a class of singularly perturbed nonlinear systems to achieve H ∞ control performance via neural network-based control and observer design. Han et al [36] first indicated dynamic multi-time-scale neural networks including both fast and slow phenomena guarantee flexibility and accuracy of nonlinear system identification efficiently.…”

Section: Introductionmentioning

confidence: 99%

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Neural Network-Based Adaptive Tracking Control for a Class of Nonlinear Singularly Perturbed Systems

2019

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In this paper, the neural network-based adaptive tracking control method is addressed for a class of multi-input affine unknown nonlinear singularly perturbed systems. Based on the Lyapunov stability theorem and by utilizing the neural networks to approximate the unknown nonlinear function, an adaptive neural network controller is constructed for the singularly perturbed nonlinear systems. Meanwhile, the proposed design method can avoid ill-conditioned numerical problems that often occur in the feedback design for singularly perturbed systems. It is proved that the proposed controller can ensure that semi-global ultimately uniformly boundedness of all the signals in the closed-loop systems while the target signals converge to a small neighborhood of the desired signal. Finally, two simulation examples are given to illustrate the theoretical results. INDEX TERMS Adaptive control, neural networks, singularly perturbed systems, uncertain nonlinear.

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Section: B Example2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Neural Network-Based Adaptive Tracking Control for a Class of Nonlinear Singularly Perturbed Systems

2019

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“…For example, in [28], a differential geometric control approach has been provided to deal with the dynamics of the nodes of a power network modelled from the singular perturbation of the power flow equations. The neural network‐based control and observer design problems have been investigated in [29] for a class of singularly perturbed non‐linear (SPN) systems with guaranteed H ∞ control performance. In [30], the model predictive control problem is handled for non‐linear SPSs with application on a large‐scale non‐linear reactor‐separator process network which exhibits two‐time‐scale behaviour.…”

Section: Introductionmentioning

confidence: 99%

Decomposition approach to exponential synchronisation for a class of non‐linear singularly perturbed complex networks

Cai

Wang

et al. 2014

IET Control Theory & Applications

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This study is concerned with the globally exponential synchronisation problem for a class of non-linear singularly perturbed complex networks where all nodes possess the same structure and properties. The addressed global synchronisation problem is converted into the one for two lower-order sub-networks, namely, a non-linear slow sub-network and a linear fast sub-network, which are obtained by using the classical singular perturbation decomposition method. The network topology is directed and weighted, which means that the coupling configuration matrix is allowed to be asymmetric. By using the Lyapunov functional method and the Kronecker product technique, sufficient conditions are obtained under which the synchronisation is achieved, respectively, for the two sub-networks and the original complex network. These conditions can be easily verified by using the semi-definite programming method. A numerical example is finally simulated to validate the theoretical results and the effectiveness of the proposed synchronisation scheme.

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“…For example, in [43], the special singularly perturbed property of the classical distribution networks has been fully discussed that has led to a precise control with help from the singular perturbation approach, and the slow and the fast two-time-scale characteristics have been illustrated for a DC motor and a synchronous generator [7]. Furthermore, the neural network based control and observer design problems have been investigated in [22] for a class of singularly perturbed nonlinear systems with guaranteed H ∞ control performance. In [4], the model predictive control problem has been handled for nonlinear singularly perturbed systems with application on a large-scale nonlinear reactorseparator process network which exhibits two-time-scale behavior.…”

Section: Introductionmentioning

confidence: 99%

An Integrated Approach to Global Synchronization and State Estimation for Nonlinear Singularly Perturbed Complex Networks

Cai

Wang

et al. 2015

IEEE Trans. Cybern.

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Abstract-This paper aims to establish a unified framework to handle both the exponential synchronization and state estimation problems for a class of nonlinear singularly perturbed complex networks (SPCNs). Each node in the SPCN comprises both "slow" and "fast" dynamics that reflects the singular perturbation behavior. General sector-like nonlinear function is employed to describe the nonlinearities existing in the network. All nodes in the SPCN have the same structures and properties. By utilizing a novel Lyapunov functional and the Kronecker product, it is shown that the addressed SPCN is synchronized if certain matrix inequalities are feasible. The state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that dynamics (both "slow" and "fast") of the estimation error is guaranteed to be globally asymptotically stable. Again, a matrix inequality approach is developed for the state estimation problem. Two numerical examples are presented to verify the effectiveness and merits of the proposed synchronization scheme and state estimation formulation. It is worth mentioning that our main results are still valid even if the "slow" subsystems within the network are unstable.

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Stabilisation of singularly perturbed nonlinear systems via neural network-based control and observer design

Cited by 7 publications

References 29 publications

Neural Network-Based Adaptive Tracking Control for a Class of Nonlinear Singularly Perturbed Systems

Neural Network-Based Adaptive Tracking Control for a Class of Nonlinear Singularly Perturbed Systems

Decomposition approach to exponential synchronisation for a class of non‐linear singularly perturbed complex networks

An Integrated Approach to Global Synchronization and State Estimation for Nonlinear Singularly Perturbed Complex Networks

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