Kalman filtering for linear singular systems subject to round-robin protocol

• Published in: Control theory and technology Vol. 22; no. 4; pp. 543 - 551
• Main Authors: Goel, Ashna, Bhaumik, Shovan, Tomar, Nutan Kumar
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2024; Springer Nature B.V
• Subjects: Algorithms; Bandwidths; Complexity; Computational Intelligence; Control; Control and Systems Theory; Covariance; Data transmission; Design of experiments; Discrete time systems; Engineering; Error analysis; Kalman filters; Mechatronics; Optimization; Research Article; Resource allocation; Riccati equation; Robotics; Scheduling; State estimation; Systems Theory; Upper bounds; Networked control systems; Filtering; Round-robin protocol; Singular systems; Communication constraints
• ISSN: 2095-6983; 2198-0942
• DOI: 10.1007/s11768-024-00205-x

This paper introduces a Kalman-type recursive state estimator for a class of discrete-time stochastic linear singular systems where the measurements are carried part by part periodically following a scheduling algorithm. We consider that the system is in a network with limited allotted bandwidth, which refers to a situation where the total available bandwidth for data transmission through the network is limited. This limitation can occur for various reasons, such as network congestion, resource allocation policies, or bandwidth limitations imposed by network administrators. In such networks, the entire measurement vector cannot be transmitted to the estimator instantly. Thus, managing a network with a limited allotted bandwidth requires careful planning, monitoring, and implementing some scheduling strategies to optimize the use of measured data while estimating the system states. We show that a scheduling method, namely, round-robin protocol, is suitable for singular systems to deal with such a scenario. The upper bound of the prior error covariance is studied via a periodic Riccati equation (PRE). To retain the boundedness of prior error covariance, the stability of the PRE is examined by the observability properties of the round-robin-induced system. Finally, a simulation example is presented to show the effectiveness of the designed filtering scheme.