Supervisory Control and Analysis of Partially-observed Discrete Event Systems

Nowadays, a variety of real-world systems fall into discrete event systems (DES). In practical scenarios, due to facts like limited sensor technique, sensor failure, unstable network and even the intrusion of malicious agents, it might occur that some events are unobservable, multiple events are indistinguishable in observations, and observations of some events are nondeterministic. By considering various practical scenarios, increasing attention in the DES community has been paid to partially-observed DES, which in this thesis refer broadly to those DES with partial and/or unreliable observations. In this thesis, we focus on two topics of partially-observed DES, namely, supervisory control and analysis. The first topic includes two research directions in terms of system models. One is the supervisory control of DES with both unobservable and uncontrollable events, focusing on the forbidden state problem; the other is the supervisory control of DES vulnerable to sensor-reading disguising attacks (SD-attacks), which is also interpreted as DES with nondeterministic observations, addressing both the forbidden state problem and the liveness-enforcing problem. Petri nets (PN) are used as a reference formalism in this topic. First, we study the forbidden state problem in the framework of PN with both unobservable and uncontrollable transitions, assuming that unobservable transitions are uncontrollable. For ordinary PN subject to an admissible Generalized Mutual Exclusion Constraint (GMEC), an optimal on-line control policy with polynomial complexity is proposed provided that a particular subnet, called observation subnet, satisfies certain conditions in structure. It is then discussed how to obtain an optimal on-line control policy for PN subject to an arbitrary GMEC. Next, we still consider the forbidden state problem but in PN vulnerable to SD-attacks. Assuming the control specification in terms of a GMEC, we propose three methods to derive on-line control policies. The first two lead to an optimal policy but are computationally inefficient for large-size systems, while the third method computes a policy with timely response even for large-size systems but at the expense of optimality. Finally, we investigate the liveness-enforcing problem still assuming that the system is vulnerable to SD-attacks. In this problem, the plant is modelled as a bounded PN, which allows us to off-line compute a supervisor starting from constructing the reachability graph of the PN. Then, based on repeatedly computing a more restrictive liveness-enforcing supervisor under no attack and constructing a basic supervisor, an off-line method that synthesizes a liveness-enforcing supervisor tolerant to an SD-attack is proposed. In the second topic, we care about the verification of properties related to system security. Two properties are considered, i.e., fault-predictability and event-based opacity. The former is a property in the literature, characterizing the situation that the occurrence of any fault in a system is predictable, while the latter is a newly proposed property in the thesis, which describes the fact that secret events of a system cannot be revealed to an external observer within their critical horizons. In the case of fault-predictability, DES are modeled by labeled PN. A necessary and sufficient condition for fault-predictability is derived by characterizing the structure of the Predictor Graph. Furthermore, two rules are proposed to reduce the size of a PN, which allow us to analyze the fault-predictability of the original net by verifying that of the reduced net. When studying event-based opacity, we use deterministic finite-state automata as the reference formalism. Considering different scenarios, we propose four notions, namely, K-observation event-opacity, infinite-observation event-opacity, event-opacity and combinational event-opacity. Moreover, verifiers are proposed to analyze these properties

Plasmonic and Near-Field Effects in Graphene Nanostructures

We theoretically study the heat transfer mechanism between graphene and a polarsubstrate. We develop a thermodynamic theory of heat transfer between grapheneand a SiC substrate based on the master equation method. In the presence of strongcoupling between surface plasmon- and phonon-polaritons in graphene and the sub-strate, a quantum master equation can be used to describe the relaxation dynamicsof hybrid modes of our system.We explore quantization of surface plasmons in a graphene nanodisk structureand derive the response of the graphene nanodisk to an external field. Discretefrequencies and corresponding wavefunctions of localized plasmons in the graphenenanodisk are due to space quantization. The specific case of a dipole excitation isstudied to represent the near-field experiments. The approximately spherical tipof a near-field microscope is modeled as a point-dipole with an known orientation(polarization). Due to the finite(non-zero) width of plasmon resonances in the disk,the response function may allow the near-field patterns with combined angular sym-metry, obtained as a composition of modes with different angular momentum andradial quantum numbers.Furthermore, we investigate the surface plasmon hybridization between the quan-tized modes in a disk and an infinite monolayer of graphene. We also consider newmechanism for mixing of the angular plasmon modes. In the case of mismatchedlattice between the disk and the monolayer the angular momentum is not conserved.We introduce a scalar perturbation with a spatial pattern which resembles one ofa moire pattern in graphene bilayer. Such a perturbation that varies smoothlywithin the graphene nanodisk and has 3-fold symmetry modulates the conductivityof graphene. We observe coupling between plasmon modes with different angularquantum number which occurs due to perturbation. The shape of the hybrid wave-function is analyzed in terms of broken axial symmetry of the system. Responsefunction of the hybrid system is derived and near-field maps were computed

Landau-Zener-Stuckelberg interference in a multi-anticrossing system

We propose a universal analytical method to study the dynamics of a multi-anticrossing system subject to driving by one single large-amplitude triangle pulse, within its time scales smaller than the dephasing time. Our approach can explain the main features of the Landau-Zener-Stuckelberg interference patterns recently observed in a tripartite system [Nature Communications 1:51 (2010)]. In particular, we focus on the effects of the size of anticrossings on interference and compare the calculated interference patterns with numerical simulations. In addition, Fourier transform of the patterns can extract information on the energy level spectrum.Comment: 6 pages, 5 figure