Data-Driven Actuator Allocation for Actuator Redundant Systems

—In this article, we consider the problem of optimally augmenting an actuator redundant system with additional actuators, so that the energy required to meet a given control objective is minimized. We study this actuator selection problem in two distinct cases; first, in the case where the control objective of the system is not known a priori, and second, in the case where the control objective is a linear state-feedback control law. In the latter scenario, knowledge of the system’s state and input matrices is required to solve the corresponding actuator selection problem. However, we relax this requirement by exploiting trajectory data gathered from the system, and using them to iteratively approximate the antistabilizing solution of an associated algebraic Riccati equation (ARE). Notably, the proposed iterative procedure is proved to be small-disturbance input-to-state stable even though the ARE associated with it entails no strictly positive-definite constant term; a result that significantly extends prior work. Finally, to further exploit the obtained trajectory data, we show that these can be used to perform online actuator fault detection without knowledge of the system’s matrices, and with complexity lower than that of existing methods. Simulations showcase the theoretical findings.