Modal consensus observers for distributed parameter systems

Abstract

This article proposes a new type of a consensus protocol for the synchronization of distributed observers in systems governed by parabolic partial differential equations. Addressing the goal of sharing useful information among distributed observers, it delves into the details governing the modal decompositions of distributed parameter systems. Assuming that two different groups of sensors are available to provide process information to the two distributed observers, the proposed modal consensus design ensures that only useful information is transmitted to the requisite modal components of each of the observers. Without any consensus protocol, the observers capture different frequency content of the spatial process in differing degrees, as it relates to the concept of modal observability. Their modal components exhibit different learning behavior toward the process state. In the extreme case, it turns out that certain modal components of the distributed observers occasionally behave as naïve observers. To ensure that, both collectively and modal componentwise, the observers agree both with the process state and with each other, a modal component consensus protocol is proposed. Such a consensus protocol is mono‐directional and provides only useful information necessary to the appropriate modal component of the distributed filters that behaves as a naïve modal observer. This protocol, when abstracted and applied to different state decompositions can be viewed as mono‐directional projections of information transmitted and received by the participating distributed observers. Detailed numerical studies of advection PDE in one and two spatial dimensions are included to elucidate the details of the proposed modal consensus observers.

Finite‐time dissipative control of fuzzy distributed parameter CPSs with quantization under cyber attacks

“…The quantized dissipative control method studied in this article provides an effective method for a class of nonlinear distributed parameter CPSs under cyber attacks. Comparisons with some existing results can be summarized as follows: In comparison with References 5,6,29‐32, the distributed parameter CPS state is transmitted through the communication channels to save the network resources and avoid network congestion. Compared with the static quantizer employed in References 18 and 19, dynamic quantizer is applied to simply the quantization rules.…”

“…In comparison with References 5,6,29‐32, the distributed parameter CPS state is transmitted through the communication channels to save the network resources and avoid network congestion. Compared with the static quantizer employed in References 18 and 19, dynamic quantizer is applied to simply the quantization rules.…”

“…3 Usually, the model of the distributed parameter CPSs can be expressed as partial differential equations (PDEs). Researches like [4][5][6] have reported numerous noteworthy results to the DPSs throughout the past few decades. However, the control of distributed parameter CPSs still faces numerous difficulties because of the complexity of nonlinear system structures, external and internal disturbances, multi-coupling of the undetermined control parameters, and the conservatism of the designed control conditions.…”

Adaptive boundary observer network design for the consensus on the estimation of a class of parabolic partial differential equation systems

“…The work in Reference 30 used a penalty of the disagreement to ensure that both state and parameter estimates remain cohesive. Reference 31 proposed modal consensus protocols to exchange information among the requisite modal components of each of the observers for PDEs.…”