  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.
