Distributed Practical Predefined‐Time Robust Time‐Varying Formation Control for Multiple Uncertain Euler‐Lagrange Systems Under Input Saturations

Abstract

ABSTRACT This paper proposes a distributed practical predefined‐time robust time‐varying formation control (DPPTRTVFC) scheme for multiple Euler‐Lagrange systems (ELSs) subject to uncertain dynamics, input saturations, and unknown external disturbances. A new practical predefined‐time stability criterion (PPTSC) is created for nonlinear systems, where the condition inequality of our created PPTSC only contains a single fractional power term of a Lyapunov function by employing a piecewise constant function. In addition, we also create a corollary of the PPTSC. Utilizing the corollary of the PPTSC, a predefined‐time sliding‐mode disturbance observer (PTSMDO) is constructed to estimate the compound disturbances lumped by uncertain dynamics and unknown external disturbances within a predefined settling time (ST). Based on the PPTSC, a predefined‐time auxiliary dynamic system (PTADS) is constructed, which not only can be used to handle the input saturation problem but also allows the ST of the PTADS to be flexibly predefined. Further, a DPPTRTVFC law is designed by incorporating the PTSMDO and the PTADS into the dynamic surface control method. Theoretical analysis indicates that the designed control scheme can implement the time‐varying formation control within a predefined ST. Simulation results illustrate the effectiveness of the proposed DPPTRTVFC scheme.