Low-complexity observer–based output-feedback tracking control for a class of nonlinear lower-triangular systems

Abstract

The tracking control problem for a group of nonlinear lower-triangular systems with multiple uncertainties is investigated in this work. Wherein, a novel performance constraint is first constructed to guarantee the fixed-time convergence of the output tracking error. Subsequently, a linear extended high-gain observer is employed to estimate the system uncertainties including the unmeasured states and the external disturbances. Based on the observer estimations, a novel output-feedback tracking control approach is formulated via using the backstepping technique, to ensure the boundedness of the closed-loop system. Compared with the existing works, the primary advantages of the proposed design are that (1) the problem of "explosion of terms" is avoided by eliminating the need for the derivative of the virtual control signals and (2) without the use of extra auxiliary techniques, the fixed-time convergence can be guaranteed, where the convergence time is independent of the system states and initial conditions. Then, the results about system stability are proved by the theoretical analysis. Moreover, an extension of the proposed approach to multi-input multi-output systems is deduced in this paper to further present its versatility. Finally, two groups of numerical examples are performed to validate the effectiveness of the proposed controller.