Adaptive distributed observers for a class of linear dynamical systems

• Main Author: Heydari, Mahdi
• Other Authors: Michael A. Demetriou, Advisor
• Format: Others
• Published: Digital WPI 2015
• Subjects: Distributed unknown input observer; Distributed Kalman filter; Interconnected systems; Distributed estimation; Distributed functional observer
• Online Access: https://digitalcommons.wpi.edu/etd-dissertations/227; https://digitalcommons.wpi.edu/cgi/viewcontent.cgi?article=1226&context=etd-dissertations

The problem of distributed state estimation over a sensor network in which a set of nodes collaboratively estimates the state of continuous-time linear systems is considered. Distributed estimation strategies improve estimation and robustness of the sensors to environmental obstacles and sensor failures in a sensor network. In particular, this dissertation focuses on the benefits of weight adaptation of the interconnection gains in distributed Kalman filters, distributed unknown input observers, and distributed functional observers. To this end, an adaptation strategy is proposed with the adaptive laws derived via a Lyapunov-redesign approach. The justification for the gain adaptation stems from a desire to adapt the pairwise difference of estimates as a function of their agreement, thereby enforcing an interconnection-dependent gain. In the proposed scheme, an adaptive gain for each pairwise difference of the interconnection terms is used in order to address edge-dependent differences in the estimates. Accounting for node-specific differences, a special case of the scheme is presented where it uses a single adaptive gain in each node estimate and which uniformly penalizes all pairwise differences of estimates in the interconnection term. In the case of distributed Kalman filters, the filter gains can be designed either by standard Kalman or Luenberger observers to construct the adaptive distributed Kalman filter or adaptive distributed Luenberger observer. Stability of the schemes has been shown and it is independent of the graph topology and therefore the schemes are applicable to both directed and undirected graphs. The proposed algorithms offer a significant reduction in communication costs associated with information flow by the nodes compared to other distributed Kalman filters. Finally, numerical studies are presented to illustrate the performance and effectiveness of the proposed adaptive distributed Kalman filters, adaptive distributed unknown input observers, and adaptive distributed functional observers.