design of decentralized critical observers for networks of finite state machines a formal method approach abstract motivated by safety critical applications in cyber physical systems in this paper we study the notion of critical observability and design of observers for networks of finite state machines fsms critical observability corresponds to the possibility of detecting if the current state of an fsm is in a given region of interest called set of critical states a critical observer detects on line the occurrence of critical states when a large scale network of fsms is considered the construction of such an observer is prohibitive because of the large computational effort needed we propose a decentralized architecture for critical observers of networks of fsms where on line detection of critical states is performed by local critical observers each associated with an fsm of the network which do not need to interact for the efficient design of decentralized critical observers we first extend on the fly algorithms traditionally used in the community of formal methods for the verification and control design of fsms we then extend to networks of fsms bisimulation theory traditionally given in the community of formal methods for single fsms the proposed techniques provide a remarkable computational complexity reduction as discussed throughout the paper and also demonstrated by means of illustrative examples

modular strategies for recursive game graphs many problems in formal verification and program analysis can be formalized as computing winning strategies for two player games on graphs in this paper we focus on solving games in recursive game graphs which can model the control flow in sequential programs with recursive procedure calls while such games can be viewed as the pushdown games studied in the literature the natural notion of winning in our framework requires the strategies to be modular with only local memory that is resolution of choices within a module does not depend on the context in which the module is invoked but only on the history within the current invocation of the module while reachability in global pushdown games is known to be exptime complete we show reachability in modular games to be np complete we present a fixed point computation algorithm for solving modular games such that in the worst case the number of iterations is exponential in the total number of returned values from the modules if the strategy within a module does not depend on the global history but can remember the history of the past invocations of this module that is if memory is local but persistent we show that reachability becomes undecidable

decentralized supervision of petri nets this note extends previous results on the supervision of petri nets pns to the decentralized setting while focusing on the extension of supervision based on place invariants sbpi the proposed approach is more general and could be applied to other types of supervision as well we begin by introducing d admissibility as an extension to the decentralized setting of the centralized admissibility concept we define also structural d admissibility as the counterpart of the simple sufficient conditions for centralized admissibility in the context of the sbpi note that structural d admissibility is only sufficient for a specification to be enforcible with the same permissiveness as in the centralized setting with full controllability and observability however structural d admissibility can be checked with low polynomial complexity based on the d admissibility concept we propose two suboptimal methods to design decentralized supervisors the first method is to find a centralized solution and then distribute the centralized supervisory policy by means of communication the amount of communication can be minimized by means of an integer linear program ilp the second method is to transform the specification to a more restrictive d admissible specification by means of an ilp in the case of decentralized supervision with communication the ilp can be used to minimize the amount of communication required by the solution

relative observability and coobservability of timed discrete event systems we study supervisory control of timed discrete event systems tdes under partial observation and propose new observability concepts effective for supervisor synthesis first we consider monolithic centralized supervisory control and introduce timed relative observability and timed relative weak observability the former concept extends our previous work to the timed case while the latter exploits choices of forcible events to preempt the clock event tick we prove that timed relative respectively weak observability is stronger than timed respectively weak observability weaker than normality and closed under set union hence there exists the supremal relatively respectively weakly observable sublanguage of a given language

on solvability of a decentralized supervisory control problem with communication we study a decentralized control problem of discrete event systems with communication we first give a general automata theoretic formalism that enables us to handle various types of communication including delay the decentralized control problem is shown to be undecidable under this formalism next we propose a semi decision procedure for computing finite state controllers to achieve a given specification in the sense of bisimilarity between the controlled system and a given specification using this procedure we prove decidability of the problem for two special cases one is the case in which the communication behavior is given as k bounded delay communication and the other is the case in which any cycle in the state transition diagram of the system contains an event observable by all controllers we also show a method for optimizing controllers based on a graph problem

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

time reversal invariance for a one dimensional model of contact acoustic nonlinearity the interaction of a one dimensional 1d wave packet with a contact interface characterized by a unilateral contact law is investigated analytically and through a finite difference model it is shown that this interaction leads to the generation of higher harmonic sub harmonic and zero frequency components in the reflected wave resulting in a pulse distortion that is attributable to contact acoustic nonlinearity however the results also show that the re emission of a time reversed version of this distorted first reflection results in a healing of the distortions and a perfect recovery of the original pulse shape thereby demonstrating time reversal invariance for this type of contact acoustic nonlinearity a step by step analysis of the contact interaction provides insights into both the distortion arising from the first interaction and the subsequent healing during the second interaction these findings suggest that time reversal invariance should also apply more generally for scatterers exhibiting non dissipative contact acoustic nonlinearity

centralized and decentralized supervisory control of nondeterministic systems under partial observation in this paper we extend our earlier work on supervisory control of nondeterministic systems using prioritized synchronization as the mechanism of control and trajectory model as the modeling formalism by considering design of supervisors under partial observation we introduce the notion of observation compatible systems and show that prioritized synchronous composition psc of observation compatible systems can be used as a mechanism of control of nondeterministic systems under partial observation in presence of driven events necessary and sufficient conditions that depend on the trajectory model as opposed to the language model of the plant are obtained for the existence of centralized as well as decentralized supervision our work on centralized control shows that the results of the traditional supervisory control can be extended to the above setting provided that the supervisor is deterministic and the observation mask is projection type on the other hand our work on decentralized control is based on a new relation between controllability observability co observability and psc that we derive in this paper

deciding co observability is pspace complete in this note we reduce the deterministic finite state automata intersection problem to the problem of deciding co observability for regular languages using a polynomial time many one mapping this demonstrates that the problem of deciding co observability for languages marked by deterministic finite state automata is pspace complete we use a similar reduction to reduce the deterministic finite state automata intersection problem to deciding other versions of co observability introduced in a previous paper these results imply that the co observability of regular languages most likely cannot be decided in polynomial time unless we make further restrictions on the languages these results also show that deciding decentralized supervisor existence is pspace complete and therefore probably intractable

the verification and control of interacting similar discrete event systems this paper explore issues related to the control and verification of similar module systems in the discrete event systems framework similar module systems are distributed systems comprised of subsystem modules that exhibit isomorphic local behavior coordinated on global event occurrences when given a global model of these systems it is shown how to decompose the global model into the component subsystems in polynomial time it is also shown how to perform various verification tasks for these interacting systems while mitigating common state explosion difficulties by taking advantage of the special similar module system structure control properties of the similar module systems are also discussed it is assumed that the local modules are supervised by exactly one local controller and the controllers enforce the same local control policy necessary and sufficient conditions for achieving local and global control specifications in this setting are identified

shock structure due to stochastic forcing and the time reversal of nonlinear waves this paper is concerned with the study of the deformation of a nonlinear pulse traveling in a random medium we consider shallow water waves with a spatially random depth we demonstrate that in the presence of properly scaled stochastic forcing the solution to the nonlinear conservation law is regularized leading to a viscous shock profile this enables us to perform time reversal experiments beyond the critical time for shock formation

complexity of infimal observable superlanguages the infimal prefix closed controllable and observable superlanguage plays an essential role in the relationship between controllability observability and co observability the central notions of supervisory control theory existing algorithms for its computation are exponential and it is not known whether a polynomial algorithm exists we answer the question by studying the state complexity of this language state complexity of a language is the number of states of its minimal deterministic finite automaton dfa for a language with state complexity n we show that the upper bound state complexity on the infimal prefix closed and observable superlanguage is 2 n 1 and that this bound is asymptotically tight hence there is no algorithm computing a dfa of the infimal prefix closed and observable superlanguage in polynomial time our construction shows that such a dfa can be computed in time o 2 n the construction involves nondeterministic finite automata nfas and a computation of the supremal prefix closed sublanguage we study the computation of supremal prefix closed sublanguages and show that there is no polynomial time algorithm computing an nfa of the supremal prefix closed sublanguage of a language given as an nfa even if the language is unary

characterization of co observable languages and formulas for their super sublanguages we present fixed point based characterization of several classes of co observable languages that are of interest in the context of decentralized supervisory control of discrete event systems including c p spl or d a co observable languages c p co observable languages and d a co observable languages we also provide formulas for computing super sublanguages for each of these classes in cases where the class of co observable languages is not closed under intersection union we provide upper lower bound of the super sublanguage formula we present the computation of super sublanguages and also computation of their upper lower bounds has lead to the introduction of other classes of co observable languages namely strongly c p co observable languages strongly d a co observable languages locally observable languages and strongly locally observable languages fixed point based characterization of all the above language classes is also given and their closure under intersection union is investigated we also study whether the fixed point operator preserves prefix closure relative closure also called l sub m g closure and controllability

brief paper formulae relating controllability observability and co observability we present formulae relating controllability observability and co observability arising in the context of supervisory control of discrete event systems given a discrete event plant g with event set e uncontrollable event set e u i and observation mask m i of the ith supervisor we first show that the infimal prefix closed l g i e u i controllable and l g e u i m i co observable superlanguage equals the intersection taken over all i s of the infimal prefix closed l g e u i controllable and l g m i observable superlanguage next we show that the infimal prefix closed and e m observable superlanguage computation preserves e e u controllability these results can be used to compute individual supervisors in the decentralized control setting

decentralized state feedback control of discrete event systems abstract in this paper we consider decentralized state feedback control of discrete event systems with a global control specification given by a predicate in this framework instead of a global state feedback each local state feedback controls a part of the system according to local information so that global behaviors satisfy the global control specification we introduce the notion of n observability of predicates and present necessary and sufficient conditions for the existence of a decentralized state feedback which achieves the global control specification

relative observability of discrete event systems and its supremal sublanguages we identify a new observability concept called relative observability in supervisory control of discrete event systems under partial observation a fixed ambient language is given relative to which observability is tested relative observability is stronger than observability but enjoys the important property that it is preserved under set union hence there exists the supremal relatively observable sublanguage of a given language relative observability is weaker than normality and thus yields when combined with controllability a generally larger controlled behavior in particular no constraint is imposed that only observable controllable events may be disabled we design new algorithms which compute the supremal relatively observable and controllable sublanguage of a given language which is generally larger than the normal counterpart we demonstrate the new observability concept and algorithms with a guideway and an agv example

undecidability in decentralized supervision abstract it is well known that supervisor synthesis problems involving partial observations generally have high computational complexity but was only recently shown in the preliminary version of this article that the solvability of decentralized supervisor synthesis problems may be undecidable even in cases where all pertinent languages are represented as finite automata the result is established by reduction from the halting problem for turing machines alternative proofs discovered independently by other authors employ a reduction from post s correspondence problem

decentralized control of discrete event systems with bounded or unbounded delay communication we introduce problems of decentralized control with delayed communication where delays are either unbounded or bounded by a given constant k in the k bounded delay model between the transmission of a message and its reception the plant can execute at most k events in the unbounded delay model the plant can execute any number of events between transmission and reception we show that our framework yields an infinite hierarchy of control problems where the containments are strict cc is the set of control problems solvable with a single controller centralized case and dcc sub k respectively dcuc dc is the set of problems solvable with two controllers in a k bounded delay network respectively in an unbounded delay network without communication the hierarchy is a result of the following property controllers which work in a given network will also work in a less nondeterministic network this property does not hold when nonblockingness is introduced checking the existence of controllers in the unbounded delay case or in the case without communication are undecidable problems however a related decentralized observation problem with bounded delay communication is decidable

on deadlock free modular supervisory control of discrete event systems in this paper the problem of synthesizing deadlock free modular supervisors for discrete event systems is discussed by introducing the d invariant relation between a pair of supervisors it is shown that when the control objective is described in terms of intersection of two languages a necessary and sufficient condition for the modular supervisor to be deadlock free is that this pair of subsupervisors satisfies a d invariant relation a procedure for synthesizing the deadlock free modular supervisor is presented some issues concerning deadlock free modular supervisory control are also discussed

rational spaces and set constraints set constraints are inclusions between expressions denoting sets of ground terms they have been used extensively in program analysis and type inference in this paper we investigate the topological structure of the spaces of solutions to systems of set constraints we identify a family of topological spaces called rational spaces which formalize the notion of a topological space with a regular or self similar structure such as the cantor discontinuum or the space of runs of a finite automaton we develop the basic theory of rational spaces and derive generalizations and proofs from topological principles of some results in the literature on set constraints

breaking of time reversal invariance in nonlinear acoustics time reversal invariance of nonlinear acoustic wave propagation is experimentally investigated reversibility is studied for propagation shorter or longer than shock formation distance in the first case time reversal invariance holds and a sinusoid distorted by nonlinearities during forward propagation progressively recovers its initial shape after the time reversal operation in the second case reversibility is broken locally at the shock front as a time reversal operation transforms a stable compression shock into an unstable expansion shock achieving experimentally the time reversal process with a time reversal mirror made of reversible piezoelectric transducers for very broadband signals would require transducers with huge bandwidths to date such transducers remain unavailable in order to overcome this technical limitation we restricted ourselves in this study to one dimensional 1d propagation for which an experimental ersatz of a time reversal mirror can be used indeed in a 1d case the time reversal operation applied on a plane wave can be mimicked for an antisymmetric wave form by a reflection of the plane wave onto a pressure release interface

a branch and bound approach for the design of decentralized supervisors in petri net models the paper addresses the design of compact and maximally permissive decentralized supervisors for petri nets based on generalized mutual exclusion constraints decentralization constraints are formulated with respect to the net transitions instructing each local supervisor to detect and disable transitions of its own control site only a solution is characterized in terms of the states it allows and its feasibility is assessed by means of two separate tests one checking the required behavioral properties e g liveness reversibility and controllability of the induced reachability subgraph and the other ensuring the existence of a decentralized supervisor enforcing exactly the considered set of allowed states the second test employs an integer linear programming formulation maximal permissivity is ensured by efficiently exploring the solution space using a branch and bound method that operates on the reachable states particular emphasis is posed on the obtainment of the controllability property both in the structural and the behavioral interpretation

supervisory control of discrete event systems with distinguishers this paper deals with two relevant aspects of the supervisory control problem scp of discrete event systems des the degree of difficulty faced when modeling specifications to be fulfilled by the system under control and the computational complexity of the synthesis procedure the presented approach consists in refining the set of events of a des model into a new set each refinement is properly chosen to identify a particular instance of the original event in the system which may simplify the modeling of specifications a map named distinguisher is then proposed to establish the relationship between strings of the original and refined alphabets it is initially shown that using a refined set of events to solve a scp directly leads to the optimal control solution yet without providing computational advantages in synthesis with respect to the nonrefined method then we propose the use of outer approximations for the refined des model as a way to reduce the cost of synthesis while preserving controllability least restrictiveness and nonblocking of the control solution two examples of manufacturing systems illustrate our results

the hierarchical lattices of a finite machine the concept of dynamical consistency is introduced to define a high level transition function for an arbitrary partition of the state space of a finite input state machine m the existence of a dynamically consistent transition from a partition member xi to a member xj corresponds to the existence for every state x in xi of some x dependent control sequence which takes that state directly into xj this paper analyses what are termed in block controllable partition machines and between block controllable partition machines and establishes the existence of the associated in block controllable hierarchical lattice ibcp m it is shown that any partition machine in ibcp m is between block controllable if and only if the base machine m is controllable this setting allows the specification of state to state control trajectories of m to be decomposed into high level and low level components

the hierarchical control of st finite state machines this paper follows caines and wei 1995 where a new notion of state aggregation for finite machines was introduced via the concept of the dynamical consistency dc relation between the blocks of states in any given state space partition this formulation results in a definition of high level dynamics on the finite partition machine m whose states correspond to the given partition elements this paper treats the more general case of st systems where there is a preferred sense of flow from a set of source states s to a set of target states t which is to be achieved by hierarchical control a generalisation of the theory of caines and wei to st systems is given which includes the generalisation of the notions of dynamical consistency in block controllability and hierarchical feedback control on the associated hierarchical lattices

optimal sensor selection for discrete event systems with partial observation for discrete event systems under partial observation we study the problem of selection of an optimal set of sensors that can provide sufficient yet minimal events observation information the sufficiency of the observed information is captured as the fulfillment of a desired formal property selection of sensors can be viewed as a selection of an observation mask and also of an equivalence class of events a sensor set is called optimal if any coarser selection of the corresponding equivalence class of events results in some significant loss of the events observation information we study an optimal selection of sensors over the set of general nonprojection observation masks we show that this problem is np hard in general for mask monotonic properties we present a top down and a bottom up algorithm each of polynomial complexity we show that observerness is not mask monotonic we show that the computational complexity can be further improved if the property is preserved under the projection via an intermediary observation mask that is an observer our results are obtained in a general setting so that they can be adapted for an optimal selection of sensors for a variety of applications

control of networked discrete event systems dealing with communication delays and losses in this paper we investigate supervisory control of networked discrete event systems such systems are now widely used in practice the key feature of a networked discrete event system is communication delays and losses in observation and control without addressing communication delays and losses in networked systems no control will be effective we propose to use some special observation mappings to deal with observation delays and losses based on these mappings we define network observability we also consider control delays and losses in networked discrete event systems and define network controllability we show that these definitions capture precisely the requirements on effective supervisory control in networked discrete event systems in the sense that a networked supervisor exists if and only if both network controllability and network observability are satisfied

decentralized control of discrete event systems using prioritized composition with exclusion a necessary and sufficient condition for decentralized control of discrete event systems via prioritized composition with exclusion pcx is provided pcx was extended from prioritized synchronous composition psc in order to model various boolean modes of decision fusion by allowing the exclusivity of participation in system interactions a notion of pcx coobservability is introduced that captures the nature of pcx based decision fusion and a testing algorithm with polynomial complexity in the states of plant and specification is presented the result is extended for multiple supervisors with multiple exclusivity sets based on an extended pcx definition

think globally act locally decentralized supervisory control decentralized supervisory control is investigated by considering problem formulations that model systems whose specifications are given as global constraints but whose solution is described by local controllers a necessary and sufficient condition is given for the existence of a solution to the problem of finding decentralized supervisors that ensure that the behavior of the closed loop system lies in a given range where the range of behavior can be described by regular languages it can be effectively tested whether the decentralized control problem is solvable in this case a procedure is given to compute the associated supervisors

on the supermal controllable sublanguage of a given language the concept of controllable language has been shown to play a basic role in the existence theory of supervisory controls for discrete event processes in this paper the supremal controllable sublanguage s of a given language l is characterized as the largest fixpoint of a monotone operator omega in the case where the languages involved are regular it is shown that the fixpoint s can be computed as the limit of the finite sequence k j given by k j 1 omega k j k 0 l an effective computational algorithm is developed and three examples are provided for illustration

on conditional decomposability abstract the requirement of a language to be conditionally decomposable is imposed on a specification language in the coordination supervisory control framework of discrete event systems in this paper we present a polynomial time algorithm for verification whether a language is conditionally decomposable with respect to given alphabets moreover we also present a polynomial time algorithm to extend the common alphabet so that the language becomes conditionally decomposable a relationship of conditional decomposability to nonblockingness of modular discrete event systems in general settings is also discussed in this paper it is shown that conditional decomposability is a weaker condition than nonblockingness

the infimal prefix closed and observable superlanguage of given language abstract the supervisory control of discrete event systems under partial observation is examined in particular the condition of observability needed to solve the two main existing problems is investigated a fixed point characterization of observability is given and is shown to yield an effective test for observability where the system under consideration is specified by regular languages a formula for the infimal prefix closed observable superlanguage of a given language is presented where the system is specified by regular languages the formula for the infimal observable language is effectively computable

fuzzy discrete event systems under fuzzy observability and a test algorithm in order to more effectively cope with the real world problems of vagueness impreciseness and subjectivity fuzzy discrete event systems fdess were proposed recently notably fdess have been applied to biomedical control for human immunodeficiency virus hiv acquired immune deficiency syndrome aids treatment planning and sensory information processing for robotic control qiu independently developed supervisory control theory of fdess we note that the controllability of events in qiu s work is fuzzy but the observability of events is crisp and the observability of events in cao and ying s work is also crisp although the controllability is not completely crisp since the controllable events can be disabled with any degrees motivated by the necessity to consider the situation that the events may be observed or controlled with some membership degrees in this paper we establish the supervisory control theory of fdess with partial observations in which both the observability and controllability of events are fuzzy instead we formalize the notions of fuzzy controllability condition and fuzzy observability condition in addition controllability and observability theorem of fdess is set up in a more generic framework in particular we present a detailed computing flow to verify whether the controllability and observability conditions hold thus this result can decide the existence of supervisors also we use this computing method to check the existence of supervisors in the controllability and observability theorem of classical discrete event systems dess which is a new method and different from classical case a number of examples are elaborated on to illustrate the presented results

the computational complexity of decentralized discrete event control problems computational complexity results are obtained for decentralized discrete event control problems these results generalize the earlier work of tsitsiklis 1989 who showed that for a special class of centralized supervisory control problems under partial observation there is an algorithm for determining in polynomial time whether or not a solution exists the negative complexity results associated with tsitsiklis work also carry over to the decentralized case so that solution existence for the more general class is not decidable in polynomial time nor does there exist a polynomial time algorithm for producing supervisor solutions when such solutions exist

decentralized supervisory control with intersection based architecture we investigate a new decentralized control architecture called intersection based architecture we propose a decentralized control protocol under this architecture called state estimator intersection based protocol sei protocol where each local supervisor sends its state estimate to the fusion sites and these sites take the intersection of these estimates in order to make a control decision the necessary and sufficient conditions for the achievability of the specification under this protocol is provided this condition is termed as state estimator intersection based coobservability sei coobservability a polynomial time algorithm for the verification of sei coobservability is provided we show that the languages that can be achieved under the sei protocol are incomparable with languages that can be achieved under existing architectures

observability and decentralized control of fuzzy discrete event systems fuzzy discrete event systems as a generalization of crisp discrete event systems have been introduced in order that it is possible to effectively represent uncertainty imprecision and vagueness arising from the dynamic of systems a fuzzy discrete event system has been modeled by a fuzzy automaton its behavior is described in terms of the fuzzy language generated by the automaton in this paper we are concerned with the supervisory control problem for fuzzy discrete event systems with partial observation observability normality and co observability of crisp languages are extended to fuzzy languages it is shown that the observability together with controllability of the desired fuzzy language is a necessary and sufficient condition for the existence of a partially observable fuzzy supervisor when a decentralized solution is desired it is proved that there exist local fuzzy supervisors if and only if the fuzzy language to be synthesized is controllable and co observable moreover the infimal controllable and observable fuzzy superlanguage and the supremal controllable and normal fuzzy sublanguage are also discussed simple examples are provided to illustrate the theoretical development

minimizing the cardinality of an events set for supervisors of discrete event dynamical systems in this paper we study sufficient observation and work spaces for supervisors of a class of discrete event dynamical systems deds we use finite state automata to model a deds the finite automata generates a formal language defined over the set of events in the deds a supervisor is a feedback system that observes a generated trace of events and dynamically disables or enables a subset of controllable events such that the closed loop system behaves as desired we model the desired behavior of the deds by a sublanguage defined over the set of events a sufficient observation space is a collection of events whose observation by a supervisor is enough to realize a given desired behavior a sufficient work space is a sufficient observation space such that the control action of the supervisor is limited to only the controllable elements of the work space we construct algorithms to evaluate a sufficient work or observation space the reduction of work or observation spaces results in reducing the number of event detectors communication and command channels between the supervisor and the plant

formulas for calculating supremal controllable and normal sublanguages abstract supremal controllable and normal sublanguages have been shown to play an important role in supervisor synthesis in this paper we discuss the computation of supremal controllable and normal sublanguages we derive formulas for both supremal controllable sublanguages and supremal normal sublanguages when the languages involved are closed as a result those languages can be computed without applying recursive algorithms we also discuss those aspects of these formulas