Many industrial control systems can be described as discrete event systems (DES), whose state space is a discrete set where event occurrences cause transitions from one state to another. Timing introduces an additional dimension to DES modeling and control. This dissertation provides two models of timed DES endowed with a single clock, namely timed finite automata (TFA) and generalized timed finite automata (GTFA). In addition, a timing function is defined to associate each transition with a time interval specifying at which clock values it may occur. While the clock of a TFA is reset to zero after each event occurs and the time semantics constrain the dwell time at each discrete state, there is an additional clock resetting function associated with a GTFA to denote whether the clock is reset to a value in a given closed time interval. We assume that the logical and time structure of a partially observable TFA/GTFA is known. The main results are summarized as follows. 1. The notion of a zone automaton is introduced as a finite automaton providing a purely discrete event description of the behaviour of a TFA/GTFA of interest. Each state of a zone automaton contains a discrete state of the timed DES and a zone that is a time interval denoting a range of possible clock values. We investigate the dynamics of a zone automaton and show that one can reduce the problem of investigating the reachability of a given timed DES to the reachability analysis of a zone automaton. 2. We present a formal approach that allows one to construct offline an observer for TFA/GTFA, i.e., a finite structure that describes the state estimation for all possible evolutions. During the online phase to estimate the current discrete state according to each measurement of an observable event, one can determine which is the state of the observer reached by the current observation and check to which interval (among a finite number of time intervals) the time elapsed since the last observed event occurrence belongs. We prove that the discrete states consistent with a timed observation and the range of clock values associated with each estimated discrete state can be inferred following a certain number of runs in the zone automaton. In particular, the state estimation of timed DES under multiple clocks can be investigated in the framework of GTFA. We model such a system as a GTFA with multiple clocks, which generalizes the timing function and the clock resetting function to multiple clocks. 3. As an application of the state estimation approach for TFA, we assume that a given TFA may be affected by a set of faults described using timed transitions and aim at diagnosing a fault behaviour based on a timed observation. The problem of fault diagnosis is solved by constructing a zone automaton of the TFA with faults and a fault recognizer as the parallel composition of the zone automaton and a fault monitor that recognizes the occurrence of faults. We conclude that the occurrence of faults can be analyzed by exploring runs in the fault recognizer that are consistent with a given timed observation. 4. We also study the problem of attack detection in the context of DESs, assuming that a system may be subject to multiple types of attacks, each described by its own attack dictionary. Furthermore, we distinguish between constant attacks, which corrupt observations using only one of the attack dictionaries, and switching attacks, which may use different attack dictionaries at different steps. The problem we address is detecting whether a system has been attacked and, if so, which attack dictionaries have been used. To solve it in the framework of untimed DES, we construct a new structure that describes the observations generated by a system under attack. We show that the attack detection problem can be transformed into a classical state estimation/diagnosis problem for these new structures.
State Estimation of Timed Discrete Event Systems and Its Applications
GAO, CHAO
20230529
Abstract
Many industrial control systems can be described as discrete event systems (DES), whose state space is a discrete set where event occurrences cause transitions from one state to another. Timing introduces an additional dimension to DES modeling and control. This dissertation provides two models of timed DES endowed with a single clock, namely timed finite automata (TFA) and generalized timed finite automata (GTFA). In addition, a timing function is defined to associate each transition with a time interval specifying at which clock values it may occur. While the clock of a TFA is reset to zero after each event occurs and the time semantics constrain the dwell time at each discrete state, there is an additional clock resetting function associated with a GTFA to denote whether the clock is reset to a value in a given closed time interval. We assume that the logical and time structure of a partially observable TFA/GTFA is known. The main results are summarized as follows. 1. The notion of a zone automaton is introduced as a finite automaton providing a purely discrete event description of the behaviour of a TFA/GTFA of interest. Each state of a zone automaton contains a discrete state of the timed DES and a zone that is a time interval denoting a range of possible clock values. We investigate the dynamics of a zone automaton and show that one can reduce the problem of investigating the reachability of a given timed DES to the reachability analysis of a zone automaton. 2. We present a formal approach that allows one to construct offline an observer for TFA/GTFA, i.e., a finite structure that describes the state estimation for all possible evolutions. During the online phase to estimate the current discrete state according to each measurement of an observable event, one can determine which is the state of the observer reached by the current observation and check to which interval (among a finite number of time intervals) the time elapsed since the last observed event occurrence belongs. We prove that the discrete states consistent with a timed observation and the range of clock values associated with each estimated discrete state can be inferred following a certain number of runs in the zone automaton. In particular, the state estimation of timed DES under multiple clocks can be investigated in the framework of GTFA. We model such a system as a GTFA with multiple clocks, which generalizes the timing function and the clock resetting function to multiple clocks. 3. As an application of the state estimation approach for TFA, we assume that a given TFA may be affected by a set of faults described using timed transitions and aim at diagnosing a fault behaviour based on a timed observation. The problem of fault diagnosis is solved by constructing a zone automaton of the TFA with faults and a fault recognizer as the parallel composition of the zone automaton and a fault monitor that recognizes the occurrence of faults. We conclude that the occurrence of faults can be analyzed by exploring runs in the fault recognizer that are consistent with a given timed observation. 4. We also study the problem of attack detection in the context of DESs, assuming that a system may be subject to multiple types of attacks, each described by its own attack dictionary. Furthermore, we distinguish between constant attacks, which corrupt observations using only one of the attack dictionaries, and switching attacks, which may use different attack dictionaries at different steps. The problem we address is detecting whether a system has been attacked and, if so, which attack dictionaries have been used. To solve it in the framework of untimed DES, we construct a new structure that describes the observations generated by a system under attack. We show that the attack detection problem can be transformed into a classical state estimation/diagnosis problem for these new structures.File  Dimensione  Formato  

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