Abstract
This paper presents a novel adaptive finite-time tracking control scheme for nonlinear systems. During the design process of control scheme, the unmodeled dynamics in nonlinear systems are taken into account. The radial basis function neural networks (RBFNNs) are adopted to approximate the unknown nonlinear functions. Meanwhile, based on RBFNNs, the assumptions with respect to unmodeled dynamics are also relaxed. This paper provides a new finite-time stability criterion, making the adaptive tracking control scheme more suitable in the practice than traditional methods. Combining RBFNNs and the backstepping technique, a novel adaptive controller is designed. Under the presented controller, the desired system performance is realized in finite time. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed control method.
Highlights
IntroductionThe adaptive control of nonlinear systems has achieved remarkable breakthroughs by combining with the backstepping technology [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]
One of the breakthroughs in neural networks control is the introduction of adaptive algorithms for tuning the weighs of NNs [53]
It is well known that the applicability of the adaptive backstepping control method is limited by unmodeled dynamics existing in many practical nonlinear systems
Summary
The adaptive control of nonlinear systems has achieved remarkable breakthroughs by combining with the backstepping technology [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. It is well known that the applicability of the adaptive backstepping control method is limited by unmodeled dynamics existing in many practical nonlinear systems. In practice, the nonlinear functions are often completely unknown for the constraints of the modeling method or unknown dynamic disturbances In this case, the linear growth condition might not be satisfied. There is still some room for improvement in making the finite-time control scheme implemented more efficiently These facts motivate us to provide a new finite-time adaptive backstepping control scheme for uncertain nonlinear system with unmodeled dynamics. With the new adaptive control scheme based on the novel criterion of finite-time stability proposed in this article, the nonlinear functions can be completely unknown and they are only required to be continuous. The system performance we can expect to realize is that the solution of the system is bounded in finite time and the bound can be sufficiently small
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