On the distributed backward reachability problem for large scale systems

TL;DR

This paper introduces a decentralized approach for backward reachability analysis in large-scale nonlinear networked systems, enabling scalable and constraint-compliant controllability assessments without conservative approximations.

Contribution

It develops a general theory that recasts large-scale nonlinear controllability problems into distributed local subproblems solved iteratively by network nodes.

Findings

Distributed algorithm guarantees global reachability solutions

Applicable to arbitrary nonlinear dynamics and constraints

No conservativeness introduced in problem reformulation

Abstract

Backward reachability (also termed controllability) has been extensively studied in control theory, and tools for a wide class of systems have been developed. Nevertheless, assessing a backward reachability analysis or synthesis remains challenging as the system dimension grows. In this paper we study the backward reachability problem for large scale networked nonlinear systems with coupled dynamics and subject to states and inputs nonlinear constraints. We propose a theory for completely general nonlinear constrained large scale controllability problems. We demonstrate that it is always possible to recast such problems for the overall large scale system into an equivalent distributed form where, without introducing any conservativeness, each node of the network iteratively solves a local reachability subproblem by exchanging information with the adjacent nodes. Although the proposed algorithm is completely decentralized, the solution of the backward reachability problem for the overall system is equivalently determined by the local ones and satisfies all the given constraints. Not being linked to any specific assumption on the system dynamics nor static constraints, the proposed results hold irrespectively of any possible analytical/numerical solver to be adopted for backward reachability computation.