Experiment design using prior knowledge on controllability and stabilizability

TL;DR

This paper develops a method for designing input signals for unknown linear systems that leverage prior knowledge of controllability and stabilizability to optimize data collection for system identification and stabilization.

Contribution

It introduces an extended notion of universal inputs incorporating prior system-theoretic knowledge, with a full characterization and online design strategies.

Findings

Characterization of universal inputs for identification and stabilization

Design of input signals that minimize experiment duration

Extension of universal input concept to include prior knowledge

Abstract

In this paper, we consider the problem of designing input signals for an unknown linear time-invariant system in such a way that the resulting input-state data is suitable for identification or stabilization. We will take into account prior knowledge on system-theoretic properties of the system, in particular, controllability and stabilizability. For this, we extend the notion of universal inputs to incorporate prior knowledge on the system. An input is called universal for identification (resp., stabilization) if, when applied to any system complying with the prior knowledge, it results in data suitable for identification (resp., stabilization) regardless of the initial condition. We provide a full characterization of such universal inputs. In addition, we discuss online experiment design using prior knowledge, and we study cases where this approach results in the shortest possible experiment for identification and stabilization.