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

TL;DR

This paper presents a novel control synthesis method for nonlinear systems that optimizes both stability and empirical observability, using a recursive algorithm to achieve closed-loop asymptotic stability and enhanced transient performance.

Contribution

It introduces a control design procedure that jointly optimizes stability and nonlinear observability, incorporating empirical Gramians and piecewise linear feedback.

Findings

Ensures closed-loop asymptotic stability.

Maximizes empirical observability during transients.

Provides a recursive algorithm for optimal control synthesis.

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.