Data-Driven Control Allocation for Overactuated LTI Systems by Exploiting Sparsity

Abstract This paper proposes a data-driven control allocation scheme for input redundant linear time-invariant systems. Contrary to the existing literature, the present work is built on a static state feedback controller with row-sparse structure that generates a virtual stabilizing input for control allocation problem. It is emphasized that a stabilizing row-sparse static state feedback controller always exists if the system is controllable and has input redundancy. With a set of available input-state data, a stabilizing controller is designed in linear matrix inequality framework. The system matrix A and the input matrix B are assumed to be unknown. For control allocation, however, we have assumed that the linear dependence information of actuators is available. Both the continuous-time and the discrete-time systems have been considered. The pole placement technique has also been included in data-driven design framework to ensure certain closed-loop performances. To demonstrate the effectiveness of the methodology, the proposed allocation approach is applied to two systems: a satellite launch vehicle model and an innovative control effector aircraft model.