Frequency domain and dynamic game methods for actuator/sensor selection in systems with sector nonlinearities

Abstract

The purpose of this note is to provide a method for placing actuators and sensors in systems with nonlinear dynamics wherein the choices for actuator and sensor locations are such that the resulting system is rendered dissipative. The proposed method casts the problem of actuator and sensor selection as a convex optimization problem and which ensures that the resulting transfer function of the linear component becomes strictly positive real. Hence for an actuator and/or sensor whose dynamics have sector bounded nonlinearities, an application of Popov's/circle criterion with a simple static feedback would ensure absolute stability. Furthermore, the nonlinear extension is formulated using dynamic game theory under partial state information.