On the Optimal Design of Low Frequency Actuators

Consider a linear time-invariant dynamical system. The well-known linear quadratic regulator (LQR) provides feedback controller that stabilizes the system while minimizing a quadratic cost function in the state of the system and the magnitude of the control. The optimal actuator design problem then consists of choosing an actuator that minimizes the cost incurred by an LQR. While this procedure guarantees a low overall cost incurred, it only takes into account the magnitude of the control signals the regulator sends to the actuator. Physical actuators are, however, also limited in their ability to follow rapid change in control signals. We show in this paper how to design actuators so that the high-frequency content of the control signals is limited, while insuring stability and optimality of the resulting closed-loop system.