An improved adaptive dynamic surface control approach for uncertain nonlinear systems

Abstract

Dynamic surface control (DSC) was developed to eliminate the "explosion of complexity" problem in backstepping procedure. However, as demonstrated in this paper, the obtained results by the existing DSC technique are somewhat conservative, which may pose difficulties in system debugging for realistic applications. This work addresses a modification that yields an improved adaptive DSC approach for tracking control of a class of semi-strict feedback systems. The new method introduces nonlinear adaptive filters instead of the first-order low pass ones to avoid repeatedly differentiating the virtual control signals. Meanwhile, novel flat zone introduced Lyapunov functions, which have dead zones in the prespecified neighborhood of the origin, are employed to design and analyze the improved robust adaptive control law. As a result, the developed control scheme exhibits three distinct features in comparison with the existing DSC strategy as follows: (1) global rather than semiglobal tracking is achieved even in the presence of nonlinear function nonlinearities; (2) the ultimate tracking accuracy can be exactly known before the controller is implemented; and (3) the ranges of the design parameters to guarantee the closed-loop stability and ultimate tracking accuracy can be completely determined a priori, and the design parameters can be freely chosen from the feasible ranges to improve the control performance. Finally, two examples are presented to confirm the effectiveness of the established approach.

Global fixed-time stabilization for a class of uncertain high-order nonlinear systems with dead-zone input nonlinearity

“…An important feature of such system is that the Jacobian linearization at the origin is neither controllable nor feedback linearizable, which makes the stabilization challenging. Mainly thanks to the adding a power integrator technique, a series of asymptotic stabilizing results have been obtained, for example, see the work by Gao and Wu (2014), Gao et al (2016), Liu and Wu (2015, 2018), Lin and Qian (2000, 2002a,b), Polendo and Qian (2007, 2008), Rui et al (1997), Sun et al (2016, 2014), Wu et al (2011), Xie et al (2017), Zhang and Xie (2014), Zhang et al (2018) and references therein.…”

Improved Adaptive Dynamic Surface Control for a Class of Uncertain Nonlinear Systems

“…Thirdly, it is difficult to adjust its velocity factor to a proper value. In [44], an improved adaptive DSC approach has been presented for the tracking control of a class of semi-strict feedback systems. The improved algorithm introduces nonlinear adaptive filters instead of the first-order low pass ones to avoid repeatedly differentiating the virtual control signals.…”

Adaptive double neural network control for micro-gyroscope based on dynamic surface controller

“…Adaptive dynamic surface control (DSC) approaches have been developed for nonlinear systems in the past by many researchers. [7][8][9] Tong and Li 10 proposed the adaptive fuzzy control for multiple-input multiple-output (MIMO) nonlinear systems with unknown dead-zone inputs. An adaptive DSC of microelectromechanical systems (MEMS) gyroscope was proposed using fuzzy compensator by Lei et al 11 An adaptive fuzzy DSC was introduced for uncertain discrete-time nonlinear systems in pure-feedback form by Yoshimura.…”