Identification of Box–Jenkins models for spatially interconnected systems in closed-loop

This paper presents an identification method for spatially interconnected distributed systems operating in closed-loop. The proposed approach makes use of refined instrumental variable method to identify spatially interconnected systems in Box–Jenkins form, where the controller is assumed to be known. The method presented here can yields statistically optimal estimates, and compared with other approaches to identify such systems under similar scenarios, takes far less time. The approach is applicable to both separable and non-separable systems and takes into account the boundary conditions. Though described only for two-dimensional systems, it is readily extendible to systems having more spatial dimensions. The effectiveness of the method is shown by a simulation example.