A practical finite-time back-stepping sliding-mode formation controller design for stochastic nonlinear multi-agent systems with time-varying weighted topology

This paper addresses a practical finite-time leader-following formation controller design for the second-order stochastic Lipchitz nonlinear systems under uncertain communication environments and external disturbances. It is desired that the orientation of the formation change according to the variations in the leader’s orientation. The time-varying weighted topology matrix is modelled as a linear combination of a finite number of constant Laplacian matrices with time-varying coefficients. The proposed back-stepping sliding-mode controller guarantees that all the signals in the closed-loop system remain bounded in probability and the norm of sliding trajectories converge almost surely in finite-time to an arbitrary small neighbourhood of origin, which can be called almost-surely practical finite-time formation. The results are then modified for solving the consensus problem as well. In the simulation section, a stochastic multi-aircraft model, as well as a numerical example, are used to illustrate the effectiveness of the proposed design methods.