Abstract
Many physical and engineered systems (e.g., smart grid, autonomous vehicles, and robotic systems) that are observed and controlled over a communication/cyber infrastructure can be efficiently modeled as stochastic hybrid systems (SHS). This paper quantifies the bias of a mode-based Kalman filter commonly used for state estimation in SHS. The main approach involves modeling the bias dynamics as a transformed switched system and the transitions across modes are abstracted via arbitrary switching signals. This general model effectively captures a wide range of SHS systems where the modes may follow deterministic, Markovian, or guard condition based transitions. By leveraging techniques developed to analyze the stability of switched systems, we derive conditions for statistical convergence of the bias in a mode-based Kalman filter in the presence of mode mismatch errors. Developed upon the foundations of Lyapunov theory, we demonstrate a linear matrix inequality condition that guarantees asymptotic stability of the corresponding autonomous switched system irrespective of the choice of mode mismatch probability. Furthermore, we obtain the range of mode mismatch probabilities that assures bounded input bounded output stability of the bias dynamics for both stable and unstable SHS. Using numerical simulations of a smart grid with network topology errors, we verify and validate the theoretical results and demonstrate the potency of using the analysis in critical infrastructures.
Highlights
Stochastic hybrid systems (SHS) represent a class of dynamical systems that experience interactions of both discrete and continuous dynamics with uncertainty
We explore the impact of discrete state estimation error on the quality of continuous state estimation derived via a mode-based Kalman filter
1.3 Contributions In this paper, we study the statistical convergence of the bias dynamics in a mode-based Kalman filter in the presence of mode mismatch errors
Summary
Stochastic hybrid systems (SHS) represent a class of dynamical systems that experience interactions of both discrete and continuous dynamics with uncertainty. The uncertainty can be modeled in continuous dynamics, discrete state transitions, or both. The evolution of continuous state is described via stochastic differential/difference equation (SDE) whereas the discrete state evolves depending on the application. Typical examples include random process (such as Markov chain) and guard conditions (i.e., the discrete state transitions depend on the continuous state). The second type of SHS, known as state-dependent SHS, finds application in flight management systems [5, 6]. For more complex systems such as a microgrid [7], the transitions of discrete state may be governed by both random processes and guard conditions
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
