Compositional Synthesis of Symbolic Controllers for Attractivity Specifications

Abstract

Attractivity specifications consist in driving the state of a system to a target region and to keep it in that region afterwards. In this paper, we develop a compositional approach to symbolic controller synthesis for attractivity specifications. The approach consists in computing iteratively for each subsystem, refinements of the least-violating attractivity controller, and of the associated attractor. The controllers and attractors computed at a given iteration are used at the next iteration as control and external input constraints. The resulting fixed-point algorithm allows us to compute a decentralized attractivity controller for the interconnected system which minimizes the size of the attractor. To illustrate the effectiveness of our approach, we show an application for the temperature regulation of adjacent rooms of a building.

Abstraction Refinement for Attractivity Controllers Using Quantitative Synthesis

“…However, the construction of finite abstractions and the synthesis of controllers suffer from the so-called curse of dimensionality: the complexity grows exponentially with the dimensions of the state and input sets. This curse of dimensionality in abstractions has motivated the investigation of different approaches such as optimizing the abstraction by minimizing the number of transitions [15], [20], using of multiple refinements for designing abstractions [7], [9], [16], [19], compositional approaches for the control synthesis in [1], [2], [5], [10] and for the construction of abstractions in [14], [18]. The abstraction procedure provided in [8] can complement compositional methods by also taking advantage of sparsity within a component.…”