Finite-Time Formation Control of Second-Order Linear Multi-Agent Systems with Relative State Constraints: A Barrier Function Sliding Mode Control Approach

The finite-time formation control of second-order linear multi-agent systems subject to constraints on both relative positions and relative velocities is studied in this paper. A novel barrier function-based sliding mode control (BFSMC) method, in which the relative state constraints are embedded through the barrier function, is proposed. The boundedness of sliding variable guarantees the satisfaction of the relative state constraints, and the convergence of the sliding variable to zero ensures that the formation will be reached in finite time. The singularity in controller is avoided. The effectiveness of the results is illustrated through a numerical example.