Data informativity for analysis of linear systems with convex conic constraints

TL;DR

This paper investigates conditions under which data from unknown linear systems with convex conic constraints can guarantee reachability and null-controllability, enabling system analysis without full system identification.

Contribution

It formulates verifiable spectral and subspace conditions on data that ensure system properties like reachability and null-controllability for constrained systems.

Findings

Derived spectral conditions for system analysis

Established data-based criteria for reachability

Provided verifiable conditions for null-controllability

Abstract

This paper studies the informativity problem for reachability and null-controllability of constrained systems. To be precise, we will focus on an unknown linear systems with convex conic constraints from which we measure data consisting of exact state trajectories of finite length. We are interested in performing system analysis of such an unknown system on the basis of the measured data. However, from such measurements it is only possible to obtain a unique system explaining the data in very restrictive cases. This means that we can not approach this problem using system identification combined with model based analysis. As such, we will formulate conditions on the data under which any such system consistent with the measurements is guaranteed to be reachable or null-controllable. These conditions are stated in terms of spectral conditions and subspace inclusions, and therefore they are easy to verify.