Prescribed-Time Consensus Control for Nonlinear Multi-Agent Systems With Output Constraint: A Bounded Time-Varying Gain-Based Method

This paper explores the prescribed-time consensus control problem for a class of high-order strict-feedback nonlinear multi-agent systems with output state constraints. A distributed adaptive C¹ smooth control scheme is developed such that the output-constrained consensus tracking is achieved within a prescribed time regardless of any initial conditions and other design parameters, although in the presence of completely unknown control gains and uncertainties. The prescribed-time control scheme is made possible for high-order systems by constructing a hybrid time-varying gain-based prescribed-time first-order filter and using the time transformation methods. Particularly, a novel uniformly switching mechanism is introduced into the time-varying gains, where the gain function is C¹ smooth and the switching time is regardless of initial conditions, ensuring that the gains are uniformly bounded for all time and thus avoiding infinite time-varying gain problem. Finally, the benefits and effectiveness of the proposed control scheme are confirmed by a numerical simulation and its application to a 2 degree of freedom robotic manipulator.