Reachability Analysis for Design Optimization

TL;DR

This paper introduces methods to approximate reachable sets for linear systems with bounded controls, providing exact characterizations for certain cases and applying these insights to aircraft design optimization.

Contribution

It offers novel approaches to approximate and exactly characterize reachable sets for linear systems with bounded controls, enhancing design optimization processes.

Findings

Exact characterization for single-input, planar systems with real, distinct eigenvalues.

L_p-norm reachable sets approximate L-infinity reachable sets effectively.

Reachability constraints improve aircraft maneuverability and safety in design.

Abstract

We present an approach to approximate reachable sets for linear systems with bounded L-infinity controls in finite time. Our first approach investigates the boundaries of these sets and reveals an exact characterization for single-input, planar systems with real, distinct eigenvalues. The second approach leverages convergence of the Lp-norms to L-infinity and uses Lp-norm reachable sets as an approximation of the L-infinity-norm reachable sets. Our optimal control results yield insights that make computational approximations of the Lp-norm reachable sets more tractable, and yield exact characterizations for L-infinity with the previous assumptions on the system. As an example, we incorporate our reachability analysis into the design optimization of a highly-maneuverable aircraft. Introducing constraints based on reachability allow us to factor physical limitations to desired flight maneuvers into the design process.