Error- and Tamper-Tolerant State Estimation for Discrete Event Systems under Cost Constraints

• Published in: IEEE transactions on automatic control Vol. 68; no. 11; pp. 1 - 8
• Main Authors: Li, Yuting, Hadjicostis, Christoforos N., Wu, Naiqi, Li, Zhiwu
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Automata; Costs; Data tampering; Discrete event systems; Discrete-event system; Information corruption; Least-cost error sequence; Measurement units; Observers; Sensor systems; Sensors; State estimation; Symbols
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2023.3239590

This paper deals with the state estimation problem in discrete-event systems modeled with nondeterministic finite automata, partially observed via a sensor measuring unit whose measurements (reported observed symbols) may be vitiated by a malicious attacker. The attacks considered in this paper include arbitrary deletions, insertions, or substitutions of observed symbols by taking into account a bounded number of attacks or, more generally, a total cost constraint (assuming that each deletion, insertion, or substitution bears a positive cost to the attacker). We provide a characterization of the sequences of symbols that match the received sequence of possibly corrupted symbols, and subsequently use them to recursively perform tamper-tolerant state estimation subject to cost constraints. Each step of the recursive state estimation procedure has complexity of <inline-formula><tex-math notation="LaTeX">O(|X||\Sigma |C)</tex-math></inline-formula>, where <inline-formula><tex-math notation="LaTeX">|X|</tex-math></inline-formula> (<inline-formula><tex-math notation="LaTeX">|\Sigma |</tex-math></inline-formula>) is the number of states (events) of the given finite automaton and <inline-formula><tex-math notation="LaTeX">C</tex-math></inline-formula> is the maximum total cost that is allowed for all deletions, insertions, and substitutions.