Augmented State Feedback for Improving Observability of Linear Systems with Nonlinear Measurements

This paper is concerned with the design of an augmented state feedback controller for finite-dimensional linear systems with nonlinear observation dynamics. Most of the theoretical results in the area of (optimal) feedback design are based on the assumption that the state is available for measurement. In this paper, we focus on finding a feedback control that avoids state trajectories with undesirable observability properties. In particular, we introduce an optimal control problem that specifically considers an index of observability in the control synthesis. The resulting cost functional is a combination of LQR-like quadratic terms and an index of observability. The main contribution of the paper is presenting a control synthesis procedure that on one hand, provides closed loop asymptotic stability, and addresses the observability of the system--as a transient performance criteria--on the other.