Learning and Control from Similarity Between Heterogeneous Systems: A Behavioral Approach

TL;DR

This paper introduces a geometric approach to defining similarity between heterogeneous linear systems and develops a control strategy that enables a host system to learn from a guest system's experience efficiently.

Contribution

It defines similarity indexes based on principal angles and proposes a novel learning control method leveraging these indexes for heterogeneous systems.

Findings

Efficient calculation of similarity indexes using geometric properties.

Successful transfer of control strategies between heterogeneous systems.

Reduction in trial-and-error learning process.

Abstract

This paper proposes basic definitions of similarity and similarity indexes between heterogeneous linear systems and presents a similarity-based learning control strategy. By exploring geometric properties of admissible behaviors of linear systems, the similarity indexes between two admissible behaviors of heterogeneous systems are defined as the principal angles between their subspace components, and an efficient strategy for calculating the similarity indexes is developed. By leveraging the similarity indexes, a similarity-based learning control strategy is proposed via projection techniques. With the application of the similarity-based learning control strategy, host system can efficiently accomplish the same tasks by leveraging the successful experience of guest system, without the necessity to repeat the trial-and-error process experienced by the guest system.