Abstract
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.
Highlights
The many industrial systems, such as power systems, motor control systems, electronic circuit systems, robotics systems, have ‘‘slow’’ and ‘‘fast’’ dynamics due to the presence of some small parameters such as capacitances, resistances, inductances, moments of inertia, and so on [1]–[5]
It is worth mentioning that adaptive tracking control approach is not considered in the existing works on unknown singularly perturbed systems
Compared with the published literature on singularly perturbed systems, the main works of this paper are as follows: 1) The neural network is used to approximate unknown nonlinear continuous-time functions, and ε-dependent adaptive laws are constructed to alleviate the ill-conditioned numerical problem which usually occur in the analysis and design of singularly perturbed systems
Summary
The many industrial systems, such as power systems, motor control systems, electronic circuit systems, robotics systems, have ‘‘slow’’ and ‘‘fast’’ dynamics due to the presence of some small parameters such as capacitances, resistances, inductances, moments of inertia, and so on [1]–[5]. H. Wang et al.: Neural Network-Based Adaptive Tracking Control for a Class of Nonlinear Singularly Perturbed Systems systems with unknown functions was studied in [30], [31]. Adaptive tracking control problem for a class of singularly perturbed nonlinear systems with unknown functions will be addressed. Compared with the published literature on singularly perturbed systems, the main works of this paper are as follows: 1) The neural network is used to approximate unknown nonlinear continuous-time functions, and ε-dependent adaptive laws are constructed to alleviate the ill-conditioned numerical problem which usually occur in the analysis and design of singularly perturbed systems. 2) An adaptive neural network trajectory tracking controller for a class of unknown multi-input affine singularly perturbed nonlinear systems with unknown functions is designed. Remark 2: The above assumptions are common assumptions in the literature and easy to be satisfied in applications [26], [33], [34]
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