Active Disturbance Rejection Based Adaptive Dynamic Surface Control for Nonlinear Systems

Abstract

This paper presents an adaptive dynamic surface control (DSC) method for nonlinear systems with multiple disturbances, parameter uncertainties, and unknown nonlinear dynamics, using a reduced-order extended state observer (ROESO). Compared to related methods, this proposed approach offers several distinct advantages: (i) The method does not require knowledge of the upper bound function for unknown nonlinear dynamics, allowing the controlled plant to not be bounded-input bounded-state, thus expanding the applicability of the DSC method; (ii) By utilizing known model information, an ROESO is designed to handle mismatched uncertainties and disturbances, reducing the load on the observer and enhancing its capability to suppress unknown nonlinear dynamics; (iii) This method employs an adaptive output-feedback DSC approach, which is more practical and easier to implement than state-feedback methods; and (iv) The observer gain, adaptive gain, and DSC gain are simultaneously optimized using a particle swarm optimization algorithm. Additionally, detailed stability analysis is provided, and simulations and comparative experiments are conducted on a rotational system to demonstrate the efficacy and superiority of the proposed method. Note to Practitioners—Most real systems are nonlinear and subject to a variety of matched and unmatched uncertainties and disturbances. Adaptive control is an effective method for dealing with parametric uncertainty, but requires that the uncertainty can be represented linearly in terms of unknown parameters and cannot handle exogenous disturbances. As an alternative active disturbance attenuation method, disturbance/uncertainty estimation and attenuation techniques have a two-degree-of-freedom control structure. However, for nonlinear systems, they simply estimate and compensate for the nonlinear characteristics of the system as disturbances, which, although effective, can lead to problems such as excessive inputs in the actual control, thus affecting the performance of the system. Backstepping control is one of the most powerful tools for handling nonlinear systems to deal with mismatched disturbances and has been well used in various fields, but it usually suffers from the problem of “explosion of complexity”. Thus, how to deal with various matched and unmatched uncertainties and disturbances in a nonlinear system is still a challenge. Motivated by these considerations, this paper presents an adaptive output-feedback dynamic surface control method for a class of uncertain nonlinear systems with multiple mismatched uncertainties and disturbances.