Practical Prescribed-Time Consensus Tracking Control for Nonlinear Heterogeneous MASs With Bounded Time-Varying Gain Under Mismatching and Non-Vanishing Uncertainties

This paper investigates the practical prescribed-time trajectory tracking consensus control problem for nonlinear heterogeneous multi-agent systems subject to mismatched uncertainties and non-vanishing disturbances, which cannot be directly compensated through control inputs. A time-varying scaling function defined by piecewise power functions is adopted, and a distributed controller is designed using the adaptive backstepping method. The study proposes a practical prescribed-time trajectory tracking consensus algorithm for heterogeneous multi-agent systems that avoids the use of infinite control gains. Unlike prescribed-time consensus tracking methods for heterogeneous multi-agent systems based on control switching, which involve discontinuities at switching points due to infinite control gains, the proposed control scheme incorporates softening units to ensure continuous control actions at segment points. Furthermore, the proposed control approach is effective over the entire time interval without requiring prior knowledge of the upper or lower bounds of $g_{i,m}$ , thereby broadening its applicability. Finally, theoretical analysis and simulation experiments validate the rationality and effectiveness of the proposed method.