Practical time-varying output formation tracking for high-order nonlinear strict-feedback multi-agent systems with input saturation

Abstract

Practical time-varying output formation tracking (PTVOFT) analysis and design task of high-order nonlinear strict-feedback multi-agent systems (MASs) containing control saturation is processed, in which PTVOF error is confined to a narrow range. Distinct with former achievements, agents’ model characteristics are high-order nonlinear strict-feedback form with mismatched uncertain nonlinearities and control saturation constraints while multi-follower system is required for achieving PTVOFT for a maneuvering leader. Firstly, hierarchical distributed extended state observer (DESO) is put forward which only employs information between adjacent individuals for approximating mismatched nonlinearities of followers together with mismatched nonlinearities of the leader. Secondly, the practical time-varying output formation tracking protocol can be raised. Backstepping techniques are applied in design procedures to provide primary variables for each control loop, where hierarchical DESOs are utilized for dealing with comprehensive uncertainties. Distributed auxiliary systems are designed for providing compensating signals to achieve the input saturation. Then, the design processes of PTVOFT protocol and hierarchical DESOs are summarized within three steps in an algorithm. Thirdly, the stability and the properties of the proposed protocol and algorithm are analyzed through employing graph theories and Lyapunov theories. Finally, numerical simulation results illustrate the effectiveness of achieved protocol and algorithm.