Computing control invariant sets of nonlinear systems: decomposition and distributed computing

TL;DR

This paper introduces a distributed graph-based method for computing control invariant sets in nonlinear cascade systems, enabling scalable analysis by decomposing systems and reconstructing overall invariants from subsystem solutions.

Contribution

The paper proposes a novel distributed framework leveraging graph algorithms to compute control invariant sets for nonlinear systems through system decomposition and subsystem analysis.

Findings

Method converges to centralized solutions

Effective for high-dimensional systems

Validated on a six-dimensional reactor model

Abstract

In this work, we present a distributed framework based on the graph algorithm for computing control invariant set for nonlinear cascade systems. The proposed algorithm exploits the structure of the interconnections within a process network. First, the overall system is decomposed into several subsystems with overlapping states. Second, the control invariant set for the subsystems are computed in a distributed manner. Finally, an approximation of the control invariant set for the overall system is reconstructed from the subsystem solutions and validated. We demonstrate the efficacy and convergence of the proposed method to the centralized graph-based algorithm using several numerical examples including a six dimensional continuous stirred tank reactor system.