Distributed Observer and Controller Design for Spatially Interconnected Systems

This paper tackles networked distributed observer and controller design problem over directed graph topology for spatially interconnected systems. Traditional centralized design methods suffer from a lack of adaptability to graph variations incurred by network reconfiguration, communication failures, and redundant sensors integration. In this paper, to handle the foregoing limitations imposed by centralized design, state observers are designed in a distributed manner facilitated by pinning control precepts. On the one hand, this novel approach adds fault tolerance with respect to communication link failures. On the other hand, the proposed approach brings flexibility of integrating additional sensors into the network. In addition, this approach affords a reduction of computational cost. A sufficient condition to guarantee stability of the closed-loop system is derived. The controllers, though in the end implemented in a distributed way, are designed in a centralized framework, where linear-quadratic-regulator theory is adopted to handle the fact that separation principle fails to hold in the networked observer and controller design. Numerical simulation results of a piezoelectric actuated smart flexible system are presented, and the effectiveness of the proposed design is thereby verified.