Approximate abstractions of control systems with an application to aggregation

TL;DR

This paper introduces an optimization-based method for creating approximate control system abstractions, allowing for flexible aggregation of agents, and demonstrates its effectiveness in a building temperature regulation application.

Contribution

It relaxes geometric and topological restrictions by using optimization to select near-satisfying abstractions, and introduces practical simulation and storage functions to quantify errors.

Findings

Effective aggregation of control agents demonstrated in building temperature regulation.

Optimization-based approach allows for flexible abstraction construction.

Quantitative error bounds provided for approximate abstractions.

Abstract

Previous approaches to constructing abstractions for control systems rely on geometric conditions or, in the case of an interconnected control system, a condition on the interconnection topology. Since these conditions are not always satisfiable, we relax the restrictions on the choice of abstractions, instead opting to select ones which nearly satisfy such conditions via optimization-based approaches. To quantify the resulting effect on the error between the abstraction and concrete control system, we introduce the notions of practical simulation functions and practical storage functions. We show that our approach facilitates the procedure of aggregation, where one creates an abstraction by partitioning agents into aggregate areas. We demonstrate the results on an application where we regulate the temperature in three separate zones of a building.