on the existence of supervisory policies that enforce liveness in discrete event dynamic systems modeled by controlled petri nets we consider discrete state plants represented by controlled petri nets ctlpns where a subset of transitions can be prevented from firing by a supervisor a transition in a ctlpn can fire at a marking if there are sufficient tokens in its input places and it is permitted to fire by the supervisor a ctlpn is live if it is possible to fire any transition from every marking that is reachable under supervision in this paper we derive a necessary and sufficient condition for the existence of a supervisory policy that enforces liveness in ctlpns we show this condition cannot be tested for an arbitrary ctlpn however for bounded ctlpns or ctlpns where each transition is individually controllable we show the existence of a supervisory policy which enforces that liveness is decidable we also show the existence of a supervisory policy that enforces liveness is necessary and sufficient for the existence of a minimally restrictive supervisory policy

effective computation of an lm g closed controllable and observable sublanguage arising in supervisory control abstract in this paper we study nonblocking supervisory control of discrete event systems under partial observation a nonblocking supervisor can be synthesized for the supremal l m g closed controllable and normal sublanguage of a given nonclosed marked language however such a supervisor may be too restrictive as a solution to the supervisory control problem we identify a subclass of observable sublanguages of a given language which has the supremal element larger than the supremal normal sublanguage by using the supremal element we present an iterative algorithm for computing an l m g closed controllable and observable sublanguage of a given marked language which is larger than the supremal l m g closed controllable and normal sublanguage

robust optimal control of regular languages this paper presents an algorithm for robust optimal control of regular languages under specified uncertainty bounds on the event cost parameters of the language measure that has been recently reported in literature the performance index for the proposed robust optimal policy is obtained by combining the measure of the supervised plant language with uncertainty the performance of a controller is represented by the language measure of the supervised plant and is minimized over the given range of event cost uncertainties synthesis of the robust optimal supervisory control policy requires at most n iterations where n is the number of states of the deterministic finite state automaton dfsa model generated from the regular language of the unsupervised plant behavior the computational complexity of the control synthesis method is polynomial in n

diagnosability of discrete event systems subject to permanent sensor failures this paper considers a failure diagnosis problem for discrete event systems subject to permanent sensor failures a notion of diagnosability subject to permanent sensor failures is introduced with respect to a certain nondeterministic observation mask for its verification an aggregated mealy automaton with a deterministic and state dependent observation mask is defined it is shown that the diagnosability of the aggregated mealy automaton is equivalent to the diagnosability of the original system subject to permanent sensor failures then a method for verifying the diagnosability of the aggregated mealy automaton is presented moreover the delay bound within which the occurrence of any failure string can be detected subject to permanent sensor failures is computed

finite element eigenvalues for the laplacian over an l shaped domain abstract the standard finite element schemes for computing eigenvalues of the laplacian converge slowly with decreasing mesh size if the domain boundary contains a re entrant corner a superelement is constructed to cover the region surrounding a corner of angle 3 2 inside the superelement the mesh is refined and the trial function constrained to fit the known analytic form of the solution in the neighborhood of the corner singularity being compatible with linear and bilinear elements the superelement is easily embodied into standard finite element programs calculations are made for an l shaped domain with various boundary conditions comparison with other calculations show that the incorporation of the superelement has neutralised the deterioration in convergence which would otherwise have taken place due to the presence of the re entrant corner

on the complexity of synthesizing a minimum weighted supervisor under partial observation abstract with full observation the problem of synthesizing a minimum weighted supervisor has been shown polynomial time solvable with partial observation the problem becomes np hard in this paper we will show that the decision version of the problem becomes np complete when the natural projection is a natural observer this np completeness result is unexpected considering that the logic supervisor synthesis problem under the same assumption becomes polynomial time solvable

boundedness analysis of finitely recursive processes ii sequential and hybrid processes part i of this paper has shown that a subclass of the finitely recursive processes frp composed without the sequential composition operator sco is bounded in this sequel it is first shown that boundedness is not guaranteed but decidable for the subclass of frp built using the sco but without the parallel composition operator pco to overcome the limitation in modeling using the sco only some bounded hybrid subclasses have been proposed where both the sco and pco can be used although in a restricted fashion finally the proposed hybrid framework is used to model a job shop and its potential in the specification and design of supervisory control systems is demonstrated

supervisory control of partially observable marked graphs this note presents a control synthesis approach for discrete event systems modeled by marked graphs with unobservable transitions it solves forbidden state problems characterized by a set of general mutual exclusion constraints we prove that for any sequence of observable transitions there exist a unique marking from which all other possible current markings can be reached unobservably this salient feature allows us to design efficient control policies based on proper separation of observation and control

linear control of live marked graphs given a linear constraint on the firing vectors of a live marked graph with uncontrollable unobservable transitions bounded or unbounded we apply linear programming techniques to compute the most liberal controller enforcing this constraint

control of discrete event systems with minimal switchings this paper studies the problem of controlling discrete event systems as formulated by ramadge and wonham 1987 an optimal d supervisor is introduced which requires a minimal number of switchings i e enabling and disabling controllable events a complete characterization of such controllers as well as a procedure for its construction is given an example to illustrate the result is also included

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 a weaker notion of controllability of a language k with respect to a language l a necessary and sufficient condition for a prefix closed language k contained in sigma to be controllable with respect to another prefix closed language l contained in sigma is that k contained in l a weaker notion of controllability where it is not required that k contained in l is considered here if l is the prefix closed language generated by a plant automaton g then essentially there exists a supervisor theta that is complete with respect to g such that l theta mod g k intersection l if and only if k is weakly controllable with respect to l for an arbitrary modeling formalism it is shown that the inclusion problem is reducible to the problem of deciding the weaker notion of controllability therefore removing the requirement that k contained in l from the original definition of controllability does not help the situation from a decidability viewpoint this observation is then used to identify modeling formalisms that are not viable for supervisory control of the untimed behaviors of discrete event dynamic systems

approximately bisimilar symbolic models for nonlinear control systems control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs although these models are very powerful when dealing with physical phenomena they are less suited to describe software and hardware interfacing with the physical world for this reason there is a growing interest in describing control systems through symbolic models that are abstract descriptions of the continuous dynamics where each symbol corresponds to an aggregate of states in the continuous model since these symbolic models are of the same nature of the models used in computer science to describe software and hardware they provide a unified language to study problems of control in which software and hardware interact with the physical world furthermore the use of symbolic models enables one to leverage techniques from supervisory control and algorithms from game theory for controller synthesis purposes in this paper we show that every incrementally globally asymptotically stable nonlinear control system is approximately equivalent bisimilar to a symbolic model the approximation error is a design parameter in the construction of the symbolic model and can be rendered as small as desired furthermore if the state space of the control system is bounded the obtained symbolic model is finite for digital control systems and under the stronger assumption of incremental input to state stability symbolic models can be constructed through a suitable quantization of the inputs

bias optimality for continuous time controlled markov chains in this paper we give conditions for the existence of bias optimal policies in a class of continuous time controlled markov chains with unbounded reward and transition rates several characterizations of bias optimality are proposed we also introduce new sets of conditions ensuring uniform exponential ergodicity of continuous time controlled markov chains

a tutorial on the extended perturbation analysis abstract in this paper we explain the simple idea of infinitesimal and extended perturbation analysis the motivation of the new technique the difficulties as well as the advantages and contributions

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

the vanishing discount approach to constrained continuous time controlled markov chains we consider a denumerable state continuous time controlled markov chain cmc with possibly unbounded transition and reward rates we deal with constrained optimality that is we want to maximize a discounted reward an average reward criterion subject to a constraint on a discounted cost an average cost we give conditions ensuring that the average constrained optimal reward and policies can be obtained as the limit as the discount rate vanishes of the corresponding discounted constrained optimal reward and policies this extends to average constrained cmcs the standard results on the vanishing discount approach for the average unconstrained case we also present an example showing that the vanishing discount results for constrained problems might not hold

modular feedback logic for discrete event systems we examine a modular approach to the synthesis of state feedback controls for the problem of maintaining a predicate on the state set of a discrete dynamic system invariant dynamical systems are modeled by automata together with a mechanism for enabling and disabling a subset of state transitions the basic problem of interest is to ensure by appropriate control action that a given predicate on the state set of the process remains invariantly true whenever it is initially satisfied assuming the predicate can be decomposed into the conjunction or disjunction of component predicates we determine conditions under which it is possible to synthesize the appropriate control in a modular fashion

robust and nonblocking supervisor for discrete event systems with model uncertainty under partial observation addresses a robust and nonblocking supervisory control problem based on a framework of discrete event systems with model uncertainty under partial observation the uncertainty introduced in the paper is associated with internal and unobservable events occurring in systems the paper presents a systematic method for modeling uncertainty described as a spl delta transition representing the internal and unobservable events in particular at a state with the assigned positive integer value p a system is assumed to experience at most a p step state transition by the internal and unobservable event under the framework for model uncertainty the paper presents necessary and sufficient conditions for the existence of a robust supervisor with the nonblocking property

the complexity of mean payoff pushdown games two player games on graphs are central in many problems in formal verification and program analysis such as synthesis and verification of open systems in this work we consider solving recursive game graphs or pushdown game graphs that model the control flow of sequential programs with recursion while pushdown games have been studied before with qualitative objectives such as reachability and regular objectives in this work we study for the first time such games with the most well studied quantitative objective the mean payoff objective in pushdown games two types of strategies are relevant 1 global strategies which depend on the entire global history and 2 modular strategies which have only local memory and thus do not depend on the context of invocation but rather only on the history of the current invocation of the module our main results are as follows 1 one player pushdown games with mean payoff objectives under global strategies are decidable in polynomial time 2 two player pushdown games with mean payoff objectives under global strategies are undecidable 3 one player pushdown games with mean payoff objectives under modular strategies are np hard 4 two player pushdown games with mean payoff objectives under modular strategies can be solved in np i e both one player and two player pushdown games with mean payoff objectives under modular strategies are np complete we also establish the optimal strategy complexity by showing that global strategies for mean payoff objectives require infinite memory even in one player pushdown games and memoryless modular strategies are sufficient in two player pushdown games finally we also show that all the problems have the same complexity if the stack boundedness condition is added where along with the mean payoff objective the player must also ensure that the stack height is bounded

generalized detectability for discrete event systems in our previous work we investigated detectability of discrete event systems which is defined as the ability to determine the current and subsequent states of a system based on observation for different applications we defined four types of detectabilities weak detectability strong detectability weak periodic detectability and strong periodic detectability in this paper we extend our results in three aspects 1 we extend detectability from deterministic systems to nondeterministic systems such a generalization is necessary because there are many systems that need to be modeled as nondeterministic discrete event systems 2 we develop polynomial algorithms to check strong detectability the previous algorithms are based on observer whose construction is of exponential complexity while the new algorithms are based on a new automaton called detector 3 we extend detectability to d detectability while detectability requires determining the exact state of a system d detectability relaxes this requirement by asking only to distinguish certain pairs of states with these extensions the theory on detectability of discrete event systems becomes more applicable in solving many practical problems

an input output construction of finite state rho mu approximations for control design we consider discrete time plants that interact with their controllers via fixed discrete alphabets for this class of systems and in the absence of exogenous inputs we propose a general methodical approach for constructing a sequence of finite state approximate models starting from finite length sequences of input and output signal pairs we explicitly derive conditions under which the proposed construct used in conjunction with a particular generalized structure satisfies desirable properties of approximations thereby leading to nominal deterministic finite state machine models that can be used in certified by design controller synthesis we also show that the cardinality of the min imal disturbance alphabet that can be used in this setting equals that of the sensor output alphabet finally we show that the pro posed construct satisfies a relevant semi completeness property

feedback stabilization of some event graph models the authors introduce several notions of stability for event graph models timed or not the stability is similar to the boundedness notion for petri nets the event graph models can be controlled by an output feedback which takes information from some observable transitions and can disable some controllable transitions the controller itself is composed of an event graph in this framework the authors solve the corresponding stabilization problems i e they wonder if such a controller may prevent the explosion of the number of tokens

supervisory control of hybrid systems within a behavioural framework abstract this contribution addresses the synthesis of supervisory control for hybrid systems with discrete external signals such systems are in general neither l complete nor can they be represented by finite state machines we find an l complete approximation abstraction l for represent it by a finite state machine and investigate the control problem for the approximation if a solution exists we synthesize the maximally permissive supervisor for l we show that it also solves the control problem for the hybrid system if no solution exists approximation accuracy can be increased by computing a k complete abstraction k k l this paper is entirely set within the framework on willems behavioural systems theory

limited lookahead policies in supervisory control of discrete event systems a supervisory control scheme which is based on limited lookahead control policies is proposed using an online scheme where after the occurrence of an event the next control action is determined on the basis of an n step ahead projection of the behavior of the process represented as an n level tree this procedure then repeats after the execution of the next event different attitudes can be adopted to calculate a control action for the given n level tree in order to resolve uncertainties about the process behavior beyond n steps two such attitudes termed conservative and optimistic are studied results are presented pertaining to monotonicity and convergence properties of the optimistic and conservative n step policies in terms of n and comparison of these policies with the optimal offline solution closed form expression for the language generated by the n step conservative policy for prefix closed legal languages and lower bounds for n that guarantee that the online scheme performs as well as an offline scheme with complete information

optimal nonblocking directed control of discrete event systems for the control of discrete event systems the notion of directed control refines that of supervisory control a directed controller is one that selects at most one controllable event to be enabled at any state without disabling any uncontrollable event which is in fact how a discrete event control is implemented in contrast a supervisory controller computes a maximal allowable set of controllable events at each state leaving undecided exactly which controllable event should be enabled in previous works we developed a framework for the computation of optimal directed controllers and a polynomial synthesis algorithm for acyclic plants in this paper we present a novel synthesis approach for general plants i e plants with or without cycles thus providing a complete solution to the optimal directed control problem the complexity of the approach remains polynomial in the size of plant

theory of extended fuzzy discrete event systems for handling ranges of knowledge uncertainties and subjectivity in 2001 we originated a theory of fuzzy discrete event systems fdess that generalized the conventional crisp discrete event systems dess vagueness and imprecision concerning states and event transitions of dess were represented by membership grades and computed via fuzzy logic our application of the fdes theory to computerized human immunodeficiency virus acquired immune deficiency syndrome treatment regimen selection although preliminarily successful suggests that a more comprehensive fdes theory is needed to address two general issues critically important not only to biomedical applications but also to real world problems in other industries first domain experts should have means other than point estimates and type 1 fuzzy sets mandated in the current framework to describe uncertainties subjectivity and imprecision in their complex knowledge and experience second when a group of experts with distinct opinions is involved they should not be forced to reach consensus for the sake of system development this is because collective consensus may not be achievable which is often the case in medicine where individual expertspsila opinions should be equally respected since the underlying ground truth is unknown most of the time the theory of extended fdes presented in this paper addresses both the problems and contains the fdes theory as a special case experts are now allowed to use interval numbers and type 1 and type 2 fuzzy sets to intuitively and quantitatively express their diverse knowledge and experience which will then be processed by the new theory to form fuzzy state vectors and fuzzy event transition matrices accordingly we have established mathematical operations that cover the computations of fuzzy states fuzzy event transitions and parallel composition numerical examples are provided

characterizing intransitive noninterference for 3 domain security policies with observability this note introduces a new algorithmic approach to the problem of checking the property of intransitive noninterference ini using discrete event systems dess tools and concepts ini property is widely used in formal verification of security problems in computer systems and protocols the approach consists of two phases first a new property called ip observability observability based on a purge function is introduced to capture ini we prove that a system satisfies ini if and only if it is ip observable second a relation between ip observability and p observability observability as used in des is established by transforming the automaton modeling a system protocol into an automaton where p observability and hence ip observability can be determined this allows us to check ini by checking p observability which can be done efficiently our approach can be used for all systems protocols with three domains or levels which is sufficient for most noninterference problems for cryptographic protocols and systems

doomsday equilibria for omega regular games abstract two player games on graphs provide the theoretical framework for many important problems such as reactive synthesis while the traditional study of two player zero sum games has been extended to multi player games with several notions of equilibria they are decidable only for perfect information games whereas several applications require imperfect information in this paper we propose a new notion of equilibria called doomsday equilibria which is a strategy profile where all players satisfy their own objective and if any coalition of players deviates and violates even one of the players objective then the objective of every player is violated we present algorithms and complexity results for deciding the existence of doomsday equilibria for various classes of regular objectives both for imperfect information games and for perfect information games we provide optimal complexity bounds for imperfect information games and in most cases for perfect information games

polynomial synthesis of supervisor for partially observed discrete event systems by allowing nondeterminism in control we study the supervisory control of discrete event systems dess under partial observation using nondeterministic supervisors we formally define a nondeterministic control policy and also a control observation compatible nondeterministic state machine and prove their equivalence the control action of a nondeterministic supervisor is chosen online nondeterministically from among a set of choices determined offline also the control action can be changed online nondeterministically prior to any new observation in accordance with choices determined offline the online choices once made can be used to affect the set of control action choices in future we show that when control is exercised using a nondeterministic supervisor the specification language is required to satisfy a weaker notion of observability which we define in terms of recognizability and achievability achievability serves as necessary and sufficient condition for the existence of a nondeterministic supervisor and it is weaker than controllability and observability combined when all events are controllable achievability reduces to recognizability we show that both existence and synthesis of nondeterministic supervisors can be determined polynomially for deterministic supervisors only existence can be determined polynomially both achievability and recognizability are preserved under union and also under intersection when restricted over prefix closed languages using the intersection closure property we derive a necessary and sufficient condition for the range control problem for the prefix closed case unlike the deterministic supervisory setting where the complexity of existence is exponential our existence condition is polynomially verifiable and also a supervisor can be polynomially synthesized

some tractable supervisory control problems for discrete event systems modeled by buchi automata discrete event systems des are modeled by buchi automata together with a means of online control in this setting the concept of a controllable language is extended to infinite strings and conditions for the existence of a supervisor controller to implement a prescribed closed loop behavior are derived the focus is on a class of des called product systems these are des composed of a finite set of asynchronous components a control problem for such a system typically requires the synthesis of an online controller so as to achieve some prescribed coordinated behavior of the component subsystems one of the principal difficulties in this task is that the size of the state space increases exponentially with the number of components it is shown that despite this fact several interesting control synthesis problems for such systems are computationally feasible and algorithms are developed for solution

observability of discrete event dynamic systems a finite state automaton is adopted as a model for discrete event dynamic systems deds observations are assumed to be a subset of the event alphabet observability is defined as having perfect knowledge of the current state at points in time separated by bounded numbers of transitions a polynomial test for observability is given it is shown that an observer may be constructed and implemented in polynomial time and space a bound on the cardinality of the observer state space is also presented a notion of resiliency is defined for observers and a test for resilient observability and a procedure for the construction of a resilient observer are presented

similarity based supervisory control of discrete event systems due to the appearance of uncontrollable events in discrete event systems one may wish to replace the behavior leading to the uncontrollability of pre specified language by some quite similar one to capture this similarity we introduce metric to traditional supervisory control theory and generalize the concept of original controllability to spl lambda controllability where spl lambda indicates the similarity degree of two languages a necessary and sufficient condition for a language to be spl lambda controllable is provided we then examine some properties of spl lambda controllable languages and present an approach to optimizing a realization

collocation on uniform grids in this paper we derive four sets of sinc like functions defined on a finite interval and obeying different boundary conditions the functions in each set are orthogonal and their nodes are uniformly distributed on the interval we have applied each set to solve a large class of eigenvalue equations with different boundary conditions both on finite intervals and on the real line showing that precise numerical results can be obtained efficiently and rapidly a comparison with results available in the literature is also performed

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

on petri net models of infinite state supervisors a class of supervisory control problems that require infinite state supervisors is considered and petri nets with inhibitor arcs pns are introduced to model the supervisors this pn based approach to supervisory control is compared to automata based approaches the primary advantage of a pn based supervisory controller is that it provides a finite representation of an infinite state supervisor for verification implementation and testing reasons a finite pn based representation of an infinite state supervisor is preferred over an automata based supervisor it is shown that this modeling advantage is accompanied by a decision disadvantage in that in general the controllability of a language that can be generated by the closed loop system is undecidable

exploiting symmetry in the synthesis of supervisors for discrete event systems we investigate a method to exploit the symmetry inherent to many discrete event systems in order to reduce the computational complexity of the supervisory control problem scp we characterize symmetry using notions of group theory and derive conditions under which there exists a quotient reduced automaton representation for a language with in general a much smaller state space than the original minimal in number of states automaton representation for the language we then propose an algorithm to synthesize a solution to the scp which is similar to the classical one but performed on reduced automata special attention is given to the particular case of systems whose models contain similar components the approach is illustrated by an example of control of a small production line

maximally permissive feedback and modular control synthesis in petri nets with external input places a necessary and sufficient condition is presented for the unique existence of a maximally permissive feedback mpf in a concurrent discrete event system modeled by a petri net the concept of the weak interaction of a predicate is introduced in addition to reviewing fundamental definitions and notations the author defines the control invariance of a predicate and an mpf a modular synthesis problem of mpf is discussed

state based decentralized diagnosis of bi fuzzy discrete event systems recently we have introduced bi fuzzy discrete event systems bfdess and established their supervisory control theory under full observations and partial observations respectively compared with the models of discrete event systems and fuzzy discrete event systems bfdess are more satisfactory models to characterize some high uncertainty systems in this paper we study the fault diagnosis problems of bfdess first the framework of state based decentralized diagnosis is introduced then the notion of state based codiagnosability is defined and a necessary and sufficient condition for state based codiagnosability is provided in particular a polynomial time algorithm for state based codiagnosability verification and an online decentralized diagnosis method are presented in addition a compact state based decentralized diagnosis framework is introduced and the notion of state based jointly diagnosability and its verification algorithm are proposed finally the implication relationships between the two diagnosabilities are investigated

supervisory control of switching control systems in this paper the problem of designing a switching policy for an adaptive switching control system is formulated as a problem of supervisory control of a discrete event system des two important problems in switching control are then addressed using the des formulation and the theory of supervisory control under partial observation first it is verified whether for a given set of controllers a switching policy satisfying a given set of constraints on the transitions among controllers exists if so then a minimally restrictive switching policy is designed next an iterative algorithm is introduced for finding a minimal set of controllers for which a switching policy satisfying the switching constraints exists it is shown that in the supervisory control problem considered in this paper limitations on event observation are the factors that essentially restrict supervisory control in other words once observation limitations are respected limitations on control will be automatically satisfied this result is used to simplify the proposed iterative algorithm for finding minimal controller sets

discrete time control for rectangular hybrid automata rectangular hybrid automata model digital control programs of analog plant environments we study rectangular hybrid automata where the plant state evolves continuously in real numbered time and the controller samples the plant state and changes the control state discretely only at the integer points in time we prove that rectangular hybrid automata have finite bisimilarity quotients when all control transitions happen at integer times even if the constraints on the derivatives of the variables vary between control states this is in contrast with the conventional model where control transitions may happen at any real time and already the reachability problem is undecidable based on the finite bisimilarity quotients we give an exponential algorithm for the symbolic sampling controller synthesis of rectangular automata we show our algorithm to be optimal by proving the problem to be exptime hard we also show that rectangular automata form a maximal class of systems for which the sampling controller synthesis problem can be solved algorithmically

optimal supervisory control of discrete event systems cyclicity and interleaving of tasks a substantial number of tasks in production systems are executed in a repetitive cyclic fashion specifically production systems run different production cycles of different products as well as different instances of the same production cycle in this paper we consider the optimal control and interleaving of such production cycles in a supervisory control framework for discrete event systems dess that is different from other approaches our work is based on a behavioral specification of each production cycle first we adapt an optimal control approach for dess in order to optimize the operation of individual production cycles second we employ the interleaving composition to design a supervisor that enables the simultaneous execution of different production cycles combining both results we can further determine the maximum number of production cycles that can be executed simultaneously on a given production system

supervisory control of nondeterministic systems with driven events via prioritized synchronization and trajectory models the supervisory control of nondeterministic discrete event dynamical systems dedss with driven events in the setting of prioritized synchronization and trajectory models introduced by heymann are studied prioritized synchronization captures the notions of controllable uncontrollable and driven events in a natural way and the authors use it for constructing supervisory controllers the trajectory model is used for characterizing the behavior of nondeterministic dedss since it is a sufficiently detailed model in contrast to the less detailed language or failures models and serves as a language congruence with respect to the operation of prioritized synchronization results concerning controllability and observability in this general setting are obtained

on closed loop liveness of discrete event systems under maximally permissive control a class of controlled discrete event systems modeled as controlled marked graphs cmgs a special case of controlled petri nets is considered liveness of controlled systems under maximally permissive feedback control policies is investigated in the cmg context closed loop liveness implies that from any reachable marking state any transition can be enabled to fire the concept of synchronic distances in petri nets is used to prove sufficient conditions under which the maximally permissive control results in a live closed loop system

output stabilizability of discrete event dynamic systems the authors investigate the problem of designing stabilizing feedback compensators for discrete event dynamic systems deds modeled as finite state automata in which some transition events are controllable and some events are observed the problem of output stabilization is defined as the construction of a compensator such that all state trajectories in the closed loop system go through a given set e infinitely often the authors also define a stronger notion of output stabilizability which requires that the state not only pass through e infinitely often but that the set of instants when the state is in e and one knows it is in e is also infinite necessary and sufficient conditions are presented for both notions the authors also introduce and characterize a notion of resiliency that corresponds to the system being able to recover from observation errors in addition they provide some general bounds for the algorithms considered and discuss several conditions under which far smaller bounds can be achieved

a note on the properties of the supremal controllable sublanguage in pushdown systems consider an event alphabet sigma the supervisory control theory of ramadge and wonham asks the question given a plant model g with language lm g sube sigma and another language k sube lm g is there a supervisor phi such that lm phi g k ramadge and wonham showed that a necessary condition for this to be true is the so called controllability of k with respect to lm g they showed that when g is a finite state automaton and k is a regular language also generated by a finite state automaton then there is a regular supremal controllable sublanguage supc k sube k that is effectively constructable from generators of k and g in this paper we show 1 there is an algorithm to compute the supremal controllable sublanguage of a prefix closed k accepted by a deterministic pushdown automaton dpda when the plant language is also prefix closed and accepted by a finite state automaton and 2 in this case we show that this supremal controllable sublanguage is also accepted by a dpda

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

robust supervisory control of a class of timed discrete event systems under partial observation this paper studies robust supervisory control of timed discrete event systems proposed by brandin and wonham given a set of possible models which includes the exact model of the plant the objective is to synthesize a robust supervisor such that it achieves legal behavior for all possible models we show that controllability for each possible model and observability for a suitably defined aggregate model are necessary and sufficient conditions for the existence of a solution to the robust supervisory control problem moreover when there does not exist a solution a maximally permissive robust supervisor is synthesized under the assumption that all controllable events are observable

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

high order eigenvalues for the helmholtz equation in complicated non tensor domains through richardson extrapolation of second order finite differences we apply second order finite differences to calculate the lowest eigenvalues of the helmholtz equation for complicated non tensor domains in the plane using different grids which sample exactly the border of the domain we show that the results obtained applying richardson and pade richardson extrapolations to a set of finite difference eigenvalues corresponding to different grids allow us to obtain extremely precise values when possible we have assessed the precision of our extrapolations comparing them with the highly precise results obtained using the method of particular solutions our empirical findings suggest an asymptotic nature of the fd series in all the cases studied we are able to report numerical results which are more precise than those available in the literature

on optimal attraction in discrete event processes abstract the concept of attraction has been shown to play a basic role in the synthesis of supervisors for stabilizing discrete event processes in this paper we define and investigate optimal attraction in the sense that the cost or distance of the convergent path is minimized with respect to some distance measure we find conditions for the existence of supervisors achieving optimal attraction and provide efficient algorithms for their synthesis

signed real measure of regular languages for discrete event supervisory control this paper reviews expands and clarifies the underlying concepts of a signed real measure of regular languages which has been used as a novel tool for synthesis of discrete event supervisory control systems the language measure is constructed upon the principles of automata theory and real analysis it allows total ordering of a set of partially ordered sublanguages of a regular language for quantitative evaluation of the supervised behaviour of deterministic finite state automata dfsa under different supervisors in the setting of the language measure a supervisor s performance is superior if the supervised plant is more likely to terminate at a good marked state and or less likely to terminate at a bad marked state the computational complexity of the language measure algorithm is polynomial in the number of dfsa states

solving the helmholtz equation for membranes of arbitrary shape numerical results i calculate the modes of vibration of membranes of arbitrary shape using a collocation approach based on little sinc functions the matrix representation of the pde obtained using this method is explicit and does not require the calculation of integrals to illustrate the virtues of this approach i have considered a large number of examples part of them are taken from the literature and part of them new when possible i have tested the accuracy of these results by comparing them with the exact results when available or with results from the literature in particular in the case of the l shaped membrane the first example discussed in the paper i show that it is possible to extrapolate the results obtained with different grid sizes to obtain highly precise results finally i also show that the present collocation technique can be easily combined with conformal mapping to provide numerical approximations to the energies which quite rapidly converge to the exact results

continuous time markov decision processes with nth bias optimality criteria in this paper we study the nth bias optimality problem for finite continuous time markov decision processes mdps with a multichain structure we first provide nth bias difference formulas for two policies and present some interesting characterizations of an nth bias optimal policy by using these difference formulas then we prove the existence of an nth bias optimal policy by using nth bias optimal policy iteration algorithms and show that such an nth bias optimal policy can be obtained in a finite number of policy iterations

on supervisory control of sequential behaviors the authors address the supervisory synthesis problem of controlling the sequential behaviors of discrete event dynamical systems dedss under complete and partial information through the use of synchronous composition of the plants and the supervisors the authors present the notion of complete languages discuss some of its algebraic properties and show its close relation to omega languages the authors prove that the supremal closed complete and controllable sublanguage of a given language exists and present an algorithm to compute it they present a closed form expression for the supremal omega controllable sublanguage of a given omega language in terms of the supremal closed complete and controllable sublanguage this closed form expression suggests that certain operations on a given omega language can alternatively be achieved by performing certain other similar operations on its prefix which is a finite language and then taking the limit to obtain the desired omega language a necessary and sufficient condition for the existence of a supervisor in case of partial observation is presented in terms of omega observability notion of omega normality is also introduced and a closed form expression for the supremal omega normal sublanguage in terms of the supremal closed complete and normal sublanguage is presented

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

a language measure for partially observed discrete event systems recent literature has introduced and validated a signed real measure of regular languages for quantitative analysis and synthesis of discrete event supervisory des control systems where all events are assumed to be observable this paper presents a modification of the language measure for supervisory control under partial observation and shows how to generalize the analysis when some of the events may not be observable at the supervisory level in the context of des control synthesis the language measure of partially observable discrete event processes is expressed in a closed form which is structurally similar to that of completely observable discrete event processes examples are provided to elucidate the concept of des control under partial observation

nonblocking supervisory control of discrete event systems modeled by mealy automata with nondeterministic output functions in the conventional supervisory control framework for discrete event systems dess with partial event observation it is assumed that for each event the corresponding output symbol is determined uniquely however this assumption does not hold in dess such as a system with sensor errors and a mobile system where an output symbol depends on not only an event but also a state at which the event occurs in this technical note we model such a des by a mealy automaton with a nondeterministic output function we consider a supervisor called the anti permissive supervisor that assigns its control action based on an anti permissive policy we introduce a notion of ap achievability to characterize a class of languages achievable by the anti permissive supervisor and discuss the existence of a nonblocking supervisor

controlled markov chains with safety upper bound in this note we introduce and study the notion of safety control of stochastic discrete event systems dess modeled as controlled markov chains for nonstochastic dess modeled by state machines or automata safety is specified as a set of forbidden states or equivalently by a binary valued vector that imposes an upper bound on the set of states permitted to be visited we generalize this notion of safety to the setting of stochastic dess by specifying it as an unit interval valued vector that imposes an upper bound on the state probability distribution vector under the assumption of complete state observation we identify 1 the set of all state feedback controllers that satisfy the safety requirement for any given safe initial state probability distribution and 2 the set of all safe initial state probability distributions for a given state feedback controller

verification of initial state opacity in security applications of discrete event systems in this paper we formulate and analyze methodologies for verifying the notion of initial state opacity in discrete event systems that are modeled as non deterministic finite automata with partial observation on their transitions a system is initial state opaque if the membership of its true initial state to a set of secret states remains opaque i e uncertain to an intruder who observes system activity through some projection map initial state opacity can be used to characterize security requirements in a variety of applications including tracking problems in sensor networks in order to model and analyze the intruder capabilities regarding initial state opacity we first address the initial state estimation problem in a non deterministic finite automaton via the construction of an initial state estimator we analyze the properties and complexity of the initial state estimator and show how the complexity of the verification method can be greatly reduced in the special case when the set of secret states is invariant we also establish that the verification of initial state opacity is a pspace complete problem

control of discrete event systems modeled as hierarchical state machines discrete event systems dess are systems in which state changes take place in response to events that occur discretely asynchronously and often nondeterministically a class of dess modeled as hierarchical state machines hsms a special case of the statecharts formalism introduced recently is considered an efficient algorithm is provided for solving reachability problems in the hsm framework it utilizes the hierarchical structure of hsms this efficient solution is used extensively in control applications where controllers achieving a desired behavior are synthesized online

on controllability and normality of discrete event dynamical systems abstract this paper studies the supervisor synthesis problem of discrete event dynamical systems deds s through the use of synchronous composition of the plant and the supervisor and discusses some of the simplifications achieved by using the synchronous composition to model supervisory control an alternate definition of controllability is presented this definition of controllability is then used to derive an algorithm that is computationally more efficient than previously existing ones for the construction of the supremal controllable sublanguage the algorithm is also shown to be optimal the observability and normality issues arising due to the partial observation of the system dynamics under an arbitrary mask are then investigated closed form representations of the supremal normal and supremal closd and normal sublanguages are derived in the more general setting of arbitrary mask and nonclosed languages thus extending earlier results of the authors and others

a framework for state attraction of discrete event systems under partial observation state attraction for discrete event systems des addresses the problem of reaching a desired subset of the plant state space after a bounded number of event occurrences the problem of state attraction arises for example in fault tolerant supervisory control or in the control of reconfigurable manufacturing systems and is also applicable to systems biological problems such as the control of gene regulatory networks state attraction is investigated with the assumption of full event observation in the existing literature this paper extends the concept of state attraction to the case of partial observation the notion of weak attraction under partial observation wapo is introduced and necessary and sufficient conditions for the existence of a supervisor under partial observation that achieves wapo are derived furthermore a solution algorithm is proposed that finds such supervisor whenever it exists it is shown that such supervisor can always be realized as a subautomaton of the observer automaton of the des plant an application example from systems biology illustrates the obtained results

on the notion of uncontrollable marking in supervisory control of petri nets we show that the notion of uncontrollable marking commonly used in the literature on supervisory control theory of petri nets is not sound by means of a counter example we also show how the definition can be corrected and provide an adaptation of a decidability proof for the problem of checking controllability for specifications expressed as deterministic petri net languages

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

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

approximating ergodic average reward continuous time controlled markov chains we study the approximation of an ergodic average reward continuous time denumerable state markov decision process mdp by means of a sequence of mdps our results include the convergence of the corresponding optimal policies and the optimal gains for a controlled upwardly skip free process we show some computational results to illustrate the convergence theorems

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

structural optimal control for safe petri nets this article addresses the problem of forbidden states in both conservative and non conservative safe petri net pn models the property of conservativeness is discussed and its implications are analysed the construction and formulation of control conditions in the context of safe and non conservative pn models is investigated emphasising the problem of control optimality the fundamental issue studied is that of the equivalence between a forbidden state and its associated constraint a new fashion of writing control conditions is proposed and used in conjunction with the place invariant synthesis method for the generation of a control solution the final controlled model obtained is a pn similar in size to the initial model finally the approach is illustrated via a simple example

on the existence of finite state supervisors for arbitrary supervisory control problems given two prefix closed languages k l spl sube spl sigma where k spl sube l represents the desired closed loop behavior and l is the open loop behavior there exists a finite state supervisor that enforces k in the closed loop if and only if there is a regular prefix closed language m spl sube spl sigma such that 1 m spl sigma sub u spl cup l spl sube m and 2 m spl cup l k in this paper we show that this is equivalent to 1 the controllability of sup spl lcub p spl sube k spl cup l spl macr spl verbar pr p p spl rcub with respect to spl sigma and 2 the regularity of sup spl lcub p spl sube k spl cup l spl macr spl verbar pr p p spl rcub where l spl macr spl sigma spl minus l and pr spl middot is the set of prefixes of strings in the language argument we use this property to investigate the issue of deciding the existence of a finite state supervisor for different representations we also present some properties of the language sup spl lcub p spl sube k spl cup l spl macr spl verbar pr p p spl rcub along with implications to the synthesis of solutions to the supervisory control problem with the fewest states