  This paper studies the problem of distributed optimal coordination (DOC) for
a class of nonlinear large-scale cyber-physical systems (CPSs) in the presence
of cyber attacks. A secure DOC architecture with attack diagnosis is proposed
that guarantees the attack-free subsystems to achieve the output consensus
which minimizes the sum of their objective functions, while the attacked
subsystems converge to preset secure states. A two-layer DOC structure is
established with emphasis on the interactions between cyber and physical
layers, where a command-driven control law is designed that generates provable
optimal output consensus. Differing from the existing fault diagnosis methods
which are generally applicable to given failure types, the focus of the attack
diagnosis is to achieve detection and isolation for arbitrary malicious
behaviors. To this end, double coupling residuals are generated by a
carefully-designed distributed filter. The adaptive thresholds with prescribed
performance are designed to enhance the detectability and isolability. It is
theoretically guaranteed that any attack signal cannot bypass the designed
attack diagnosis methodology to destroy the convergence of the DOC algorithm,
and the locally-occurring detectable attack can be isolated from the
propagating attacks from neighboring subsystems. Simulation results for the
motion coordination of multiple remotely operated underwater vehicles
illustrate the effectiveness of the proposed architecture.
