Distributed Synthesis of State-Dependent Switching Control

TL;DR

This paper introduces a correct-by-design, distributed control synthesis method for linear discrete-time switching systems, enabling the construction of control strategies to steer system states into desired regions using backward reachability and linear programming.

Contribution

It presents a novel distributed synthesis approach for state-dependent control of switching systems, including stability control, with practical implementation on a complex floor heating system.

Findings

Successfully synthesized control for a system with 2048 switching modes

Demonstrated the method's effectiveness in a real-world floor heating application

Provided a scalable, distributed control synthesis framework

Abstract

We present a correct-by-design method of state-dependent control synthesis for linear discrete-time switching systems. Given an objective region R of the state space, the method builds a capture set S and a control which steers any element of S into R. The method works by iterated backward reachability from R. More precisely, S is given as a parametric extension of R, and the maximum value of the parameter is solved by linear programming. The method can also be used to synthesize a stability control which maintains indefinitely within R all the states starting at R. We explain how the synthesis method can be performed in a distributed manner. The method has been implemented and successfully applied to the synthesis of a distributed control of a concrete floor heating system with 11 rooms and 2^11 = 2048 switching modes.