Abstract
ABSTRACTFew results are made on non-affine non-strict feedback nonlinear systems, which is a challenging problem in the control theory. In this paper, a novel control method based on an advanced backstepping and auto disturbance rejection is presented for a class of non-affine non-strict nonlinear feedback systems. The proposed advanced backstepping controller consists of differentiator and extended state observer, which are respectively used to approach the derivative of the virtual control and estimate the unknown part of the system. The framework of the proposed controller is both systematic and simple, and the assumptions have been relaxed. Moreover, the input to state stability analysis shows that the system states can asymptotically converge to an arbitrarily small region of equilibrium point. The simulation studies proved the effectiveness of the proposed design scheme.
Highlights
In the past decade, the problem of control design for complex nonlinear systems has received considerable attention and lots of powerful control approaches have been proposed for the affine system, such as feedback linearizing control design based on differential geometric [1], adaptive backstepping control design [2] and so on
It can be noticed that the design schemes for the non-affine pure feedback nonlinear systems belong to the direct adaptive neural network control, in which the implicit function theorem is applied to illustrate the existence of an ideal controller that can achieve the control objective and neural networks are applied to construct this unknown ideal implicit controller
Each step of the advanced backstepping is combined with the idea of auto disturbance rejection (ADR)
Summary
The problem of control design for complex nonlinear systems has received considerable attention and lots of powerful control approaches have been proposed for the affine system, such as feedback linearizing control design based on differential geometric [1], adaptive backstepping control design [2] and so on. A direct adaptive neural network control is proposed for the strict feedback system with non-affine input and unknown saturation, in which a disturbance observer is developed to estimate the unknown compounded disturbance [8]. It can be noticed that the design schemes for the non-affine pure feedback nonlinear systems belong to the direct adaptive neural network control, in which the implicit function theorem is applied to illustrate the existence of an ideal controller that can achieve the control objective and neural networks are applied to construct this unknown ideal implicit controller.
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