Adaptive consensus filters of spatially distributed systems with limited connectivity

This work is concerned with the design and optimization of distributed consensus filters for infinite dimensional systems. It is assumed that different sensors are available to provide state information of the infinite dimensional process and it is desired to design distributed filters, each of which is utilizing its own sensor, with the ultimate goal of arriving at an improved estimate of the infinite dimensional process state. The consensus filters for the infinite dimensional system are proposed and their well-posedness and convergence properties are examined for the case of limited connectivity between the agents generating the distributed filters. A modification in the form of an adaptive consensus gain is also proposed and the convergence properties are examined. Using Lyapunov-redesign methods for the infinite dimensional system, stable adaptive laws for the consensus weights are presented.