Data-based approaches to learning and control by similarity between heterogeneous systems

TL;DR

This paper introduces a similarity-based learning control framework for heterogeneous systems, enabling a host system to learn from a guest system's successful experiences using geometric similarity measures derived from sampled data.

Contribution

It defines new similarity indexes based on geometric properties and develops an efficient method for their calculation, facilitating direct transfer of control strategies between heterogeneous systems.

Findings

The framework allows host systems to replicate control tasks without trial-and-error.

Simulation results validate the effectiveness of the similarity-based control approach.

The method leverages geometric properties of admissible behaviors for similarity measurement.

Abstract

This paper proposes basic definitions of similarity and similarity indexes between admissible behaviors of heterogeneous host and guest systems and further presents a similarity-based learning control framework by exploiting the offline sampled data. By exploring helpful geometric properties of the admissible behavior and decomposing it into the subspace and offset components, the similarity indexes between two admissible behaviors are defined as the principal angles between their corresponding subspace components. By reconstructing the admissible behaviors leveraging sampled data, an efficient strategy for calculating the similarity indexes is developed, based on which a similarity-based learning control framework is proposed. It is shown that, with the application of similarity-based learning control, the host system can directly accomplish the same control tasks by utilizing the successful experience provided by the guest system, without having to undergo the trial-and-error process. All results in this paper are supported by simulation examples.