Optimal intrinsic formation using exogenous systems

This paper investigates the intrinsic formation problem of a multi-agent system using an exogenous system. The problem is formulated as an intrinsic infinite time-horizon linear quadratic optimal control problem, namely, no formation error information is incorporated in the performance index. Convergence to the formation is achieved by utilizing an exogenous system, thus expanding the steady-state formation space of the system. For the forward problem, we provide the existence condition for a nonzero steady state and characterize the steady-state space. For the inverse problem, we design both the input matrix and the exogenous system so that the desired formation can be achieved. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed results.