Robust Stabilization of Extended Nonholonomic Chained‐Form Systems with Dynamic Nonlinear Uncertain Terms by Using Active Disturbance Rejection Control

Abstract

In this paper, the stabilization problem of nonholonomic chained-form systems is addressed with uncertain constants. In this paper, the active disturbance rejection control (ADRC) is designed to solve this problem. The proposed control strategy combines extended state observer (ESO) and adaptive sliding mode controller. The control of nonholonomic chained-form systems with dynamic nonlinear uncertain terms and uncertain constants is first discussed in this paper. In comparison with existing methods, the proposed method in this paper has better performance. It is proved that, with the application of the proposed control strategy, semiglobal finite-time stabilization of the systems is achieved. An example is given to illustrate the effectiveness of the proposed method.

Dynamic angular velocity turning for extremum seeking control of a two-dimensional mobile robot with external disturbances

“…For a first-order system ζ ˙ = ϒ , and we state ζ is a positive value function with respect to time, there exists a positive letter ϒ 0 , satisfying | ϒ | ≤ | ϒ 0 |. 17 For a certain number ζ ( 0 ) , there always exists a positive letter Λ , satisfying | ζ ( 0 ) | ≤ Λ . In this article, we set a Lyapunov function ϒ = − ρ sgn ( ζ ) | ζ false| δ , where ρ and ζ are constant and satisfy ρ ≤ ϒ 0 Λ δ , 0< δ < 1. So there is a finite time …”

“…Based on equation ( 23) and lemma 2, it can be proved that the sliding mode surface can converge to zero in finite time, easily confirm the disturbance observer converge to unknown disturbance in finite time by equation (17).…”

“…15 For the turning problem of dynamic angular velocity, Sanders et al have improved the classical averaging method 16 and applied it to the high-frequency oscillation closed-loop system to achieve the convergence of vehicle trajectory. Chen et al 17 proposed finite-time nonholonomic robot tracking moving targets in polar coordinates 18 based on angle turning analysis. Recent work by Matsuzaki et al 19 proposed a maneuvering target tracking filter based on constant velocity and angular velocity model, which ensures the inconsistency between the actual target and the tracking target caused by angular velocity changes.…”

Active Disturbance Rejection Attitude Control for Hypersonic Vehicle Based on Intelligent Stochastic Robust Optimization Method

“…Guo et al [16,17] have proposed the proof of MIMO ADRC stability. Chen [18] studied robust stabilization of extended nonholonomic chained-form systems with dynamic nonlinear uncertain terms by using ADRC.…”