Optimal Control with Limited Sensing via Empirical Gramians and Piecewise Linear Feedback

Abstract: This paper is concerned with the design of optimal control for finite-dimensional control-affine nonlinear dynamical systems. We introduce an optimal control problem that specifically optimizes nonlinear observability in addition to ensuring stability of the closed loop system. A recursive algorithm is then proposed to obtain an optimal state feedback controller to maximize the resulting non-quadratic cost functional. The main contribution of the paper is presenting a control synthesis procedure that provides closed loop asymptotic stability, on one hand, and empirical observability of the system, as a transient performance criteria, on the other.