On active disturbance rejection control for lower-triangular nonlinear uncertain systems with mismatched uncertainties and unknown control coefficients

Abstract

The paper investigates the control problem for a class of lower-triangular nonlinear uncertain systems with mismatched uncertainties and unknown values of control coefficients. Based on the signs of control coefficients rather than the nominal values or the approximative mathematical expressions, a new active disturbance rejection control is proposed. The design procedure can be concluded by three steps: determining the equivalent integrators chain form, constructing the extended state observer to estimate the total disturbance, and designing a dynamical system to let the actual input track the ideal input. Then under a mild assumption for mismatched uncertainties and unknown control coefficients, the paper rigorously analyzes the bounds of tracking error, estimating error and the error between the actual and ideal inputs. The presented theoretical results reveal the strong robustness of the proposed method to mismatched uncertainties and uncertain control input coefficients. Moreover, the tuning law of observer parameter and the parameter of dynamical input design is theoretically shown.