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

synthesis of inference based decentralized control for discrete event systems in our past work we presented a framework for the decentralized control of discrete event systems involving inferencing over ambiguities about the system state of various local decision makers using the knowledge of the self ambiguity and those of the others each local control decision is tagged with a certain ambiguity level level zero being the minimum and representing no ambiguity a global control decision is taken to be a winning local control decision i e one with a minimum ambiguity level for the existence of a decentralized supervisor so that for each controllable event the ambiguity levels of all winning disablement or enablement decisions are bounded by some number n such a supervisor is termed n inferring the notion of n inference observability was introduced when the given specification fails to satisfy the iv inference observability property an iv inferring supervisor achieving the entire specification does not exist we first show that the class of iv inference observable sublanguages is not closed under union implying that the supremal n inference observable sublanguage need not exist we next provide a technique for synthesizing an n inferring decentralized supervisor that achieves an n inference observable sublanguage of the specification the sublanguage achieved equals the specification language when the specification itself is iv inference observable a formula for the synthesized sublanguage is also presented for the special cases of n 0 and n 1 the proposed supervisor achieves the same language as those reported in 25 31 for n 0 and 32 for n 1 the synthesized supervisor is parameterized by n the parameter bounding the ambiguity level and as n is increased the supervisor becomes strictly more permissive in general thus a user can choose n based on the degree of permissiveness and the degree of computational complexity desired

stochastic differential equations with reflecting boundary conditions on resout des equations differentielles stochastiques a conditions aux limites reflechissantes par une approche directe basee sur le probleme de skorokhod

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

on skew brownian motion we consider the stochastic equation x t w t beta l x 0 t where w is a standard wiener process and l x 0 cdot is the local time at zero of the unknown process x there is a unique solution x and it is adapted to the fields of w if beta leq 1 but no solutions exist if beta 1 in the former case setting alpha beta 1 2 the unique solution x is distributed as a skew brownian motion with parameter alpha this is a diffusion obtained from standard wiener process by independently altering the signs of the excursions away from zero each excursion being positive with probability alpha and negative with probability 1 alpha finally we show that skew brownian motion is the weak limit as n rightarrow infty of n 1 2 s lbrack nt rbrack where s n is a random walk with exceptional behavior at the origin

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

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

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

brownian motion in a wedge with oblique reflection this work is concerned with the existence and uniqueness of a strong markov process that has continuous sample paths and the following additional properties i the state space is an infinite two dimensional wedge and the process behaves in the interior of the wedge like an ordinary brownian motion ii the process reflects instantaneously at the boundary of the wedge the angle of reflection being constant along each side iii the amount of time that the process spends at the comer of the wedge is zero i e the set of times for which the process is at the comer has lebesgue measure zero hereafter let be the angle of the wedge 0 2 let 1 and 2 be the angles of reflection on the two sides of the wedge measured from the inward normals the positive angles being toward the corner 1 2 and set 1 2 the question of existence and uniqueness is recast as a submartingale problem in the style used by stroock and varadhan diffusion processes with boundary conditions comm pure appl math 24 1971 pp 147 225 for diffusions on smooth domains with smooth boundary conditions it is shown that no solution exists if 2 in this case there is a unique continuous strong markov process satisfying i ii above it reaches the corner of the wedge almost surely and it remains there if 2 however then there is a unique continuous strong markov process statisfying i iii it is shown that starting away from the corner this process does not reach the corner of the wedge if 0 and does reach the corner if 0 2 the general theory of multi dimensional diffusions does not apply to the above problem because in general the boundary of the state space is not smooth and there is a discontinuity in the direction of reflection at the corner for some values of the process arises from diffusion approximations to storage systems and queueing networks i the state space is an infinite two dimensional wedge and the process behaves in the interior of the wedge like an ordinary brownian motion ii the process reflects instantaneously at the boundary of the wedge and the angle of reflection being constant along each side iii the amount of time that the process spends at the corner of the wedge is zero i e the set of times for which the process is at the corner has lebesgue measure zero

on the rate of convergence to equilibrium in one dimensional systems we determine the essential spectral radius of the perron frobenius operator for piecewise expanding transformations considered as an operator on the space of functions of bounded variation and relate the speed of convergence to equilibrium in such one dimensional systems to the greatest eigenvalues of generalized perron frobenius operators of the transformations operators which yield singular invariant measures

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

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

propagation of chaos and the burgers equation we establish a connection between the burgers equation and the limit of an n body problem when n to infty then we use this connection to linearize the burgers equation

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

reflected brownian motion with skew symmetric data in a polyhedral domain this paper is concerned with the characterization and invariant measures of certain reflected brownian motions rbm s in polyhedral domains the kind of rbm studied here behaves like d dimensional brownian motion with constant drift in the interior of a simple polyhedron and is instantaneously reflected at the boundary in directions that depend on the face that is hit under the assumption that the directions of reflection satisfy a certain skew symmetry condition first introduced in harrison williams 9 it is shown that such an rbm can be characterized in terms of a family of submartingales and that it reaches non smooth parts of the boundary with probability zero in 9 a purely analytic problem associated with such an rbm was solved here the exponential form solution obtained in 9 is shown to be the density of an invariant measure for the rbm furthermore if the density is integrable over the polyhedral state space then it yields the unique stationary distribution for the rbm in the proofs of these results a key role is played by a dual process for the rbm and by results in 9 for reflected brownian motions on smooth approximating domains

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 the prevalence of horseshoes in this paper the symbolic dynamics of several differentiable systems are investigated it is shown that many well known dynamical systems including axiom a systems piecewise monotonic maps of the interval the lorenz attractor and abraham smale examples have inside them subsystems conjugate to subshifts of finite type these subsystems have hyperbolic structures and hence are stable they can also be chosen to have entropy arbitrarily close to that of the ambient system let f m m be a diffeomorphism of a manifold into itself and let q f be its nonwandering set while it is usually difficult to describe completely the orbit structure of f one could look for large invariant subsets of q f on which the dynamics of f are simple to characterize this idea is due to rufus bowen who proposed that one asks the following given e 0 does there exist a hyperbolic f invariant set a c 2 f with the property that l fja is conjugate to a subshift of finite type and 2 h f iae h f e where h f is the topological entropy of f we say that f is in the sense of entropy a limit of hyperbolic subshifts of finite type if a above exists for every 0 the main result of this paper is that many dynamical systems we know are limits of this kind they include axiom a diffeomorphisms and flows piecewise monotonic maps of the interval the poincare map of the lorenz attractor 15 and certain abraham smale examples 1 perhaps this new class of systems accounts for some of the other non axiom a examples as well e g 11 17 19 23 24 28 but that remains to be decided recall the definition of a subshift of finite type let 1 n be given the discrete topology and l i 1 n the product topology let a l e be defined by ax i x i where x i denotes the ith coordinate of x let a au be annxn matrix of o s and l s let ea xel axx 1 for alliez then ai a is called a subshift of finite type if 2 l 1 n and y x e y a i 1 for all i 0 then aiya is called a one sided subshift of finite type from now on subshifts of finite type will be abbreviated as ssft received by the editors january 26 1979 ams mos subject classifications 1970 primary 58f15 secondary 28a65

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

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

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

dynamical analysis of a repeated game with incomplete information we study a two player repeated zero sum game with asymmetric information introduced by renault in which the underlying state of the game undergoes markov evolution parameterized by a transition probability p in the range 12 to 1 horner rosenberg solan and vieille identified an optimal strategy for the informed player for p in the range 12 23 we extend the range on which is proved to be optimal to about 12 0 719 and prove that it fails to be optimal at a value around 0 7328 our techniques make use of tools from dynamical systems specifically the notion of pressure introduced by d ruelle

topological entropy of standard type monotone twist maps we study invariant measures of families of monotone twist maps s q p 2q p v q q with periodic morse potential v we prove that there exist a constant c c v such that the topological entropy satisfies htop s log c 3 in particular htop s for we show also that there exist arbitrary large such that s has nonuniformly hyperbolic invariant measures with positive metric entropy for large the measures are hyperbolic and for a class of potentials which includes v q sin q the lyapunov exponent of the map s with invariant measure grows monotonically with

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

inference based ambiguity management in decentralized decision making decentralized control of discrete event systems decentralized decision making requires the interaction of various local decision makers in order to arrive at a global decision limited sensing capabilities at each local site can create ambiguities in a decision making process at each local site we argue that such ambiguities are of differing gradations we propose a framework for decentralized decision making applied to decentralized control in particular that allows computation of such ambiguity gradations and utilizes their knowledge in arriving at a global decision each local decision is tagged with a certain grade or level of ambiguity with zero being the minimum ambiguity level a global decision is taken to be the same as a ldquowinningrdquo local decision i e one having the minimum level of ambiguity the computation of an ambiguity level for a local decision requires an assessment of the self ambiguities as well as the ambiguities of the others and an inference based upon such knowledge for the existence of a decentralized supervisor so that for each controllable event the ambiguity levels of all winning disablement or enablement decisions are bounded by some number n such a supervisor is termed n inferring the notion of n inference observability is introduced we show that the conjunctive and permissive c p v disjunctive and antipermissive d a co observability is the same as the zero inference observability whereas the conditional c p v d a co observability is the same as the unity inference observability we also present examples of higher order inference observable languages our framework does not require the existence of any a priori partition of the controllable events into permissive antipermissive sets nor does it require a global control computation based on conjunction disjunction of local decisions exhibiting that our ambiguity based approach is more efficient

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

brownian motion in a wedge with variable skew reflection does planar brownian motion confined to a wedge by skew reflection on the sides approach the vertex of the wedge this question has been answered by varadhan and williams in the case where the direction of reflection is constant on each of the sides but here we address the question when the direction reflected is allowed to vary a necessary condition and a sufficient condition are obtained for the vertex to be reached the conditions are of a geometric nature and the gap between them is quite small

on the existence of solutions of stochastic differential equations with singular drifts on montre l existence de solutions pour une equation differentielle stochastique dans ir lorsque la derive et le terme de diffusion sont dependant d une maniere specifique du temps local de la deme coordonnee du processus a construire

nonblocking supervisory control of nondeterministic systems via prioritized synchronization shayman and kumar 1995 showed that supervisory control of nondeterministic discrete event systems in the presence of driven events can be achieved using prioritized synchronous composition as a mechanism of control and trajectory models as a modeling formalism first introduced by heymann 1990 the specifications considered in this earlier work were given by prefix closed languages in this paper we extend this work to include markings so that nonclosed specifications and issues such as blocking can be addressed it is shown that the usual notion of nonblocking called language model nonblocking may not be adequate in the setting of nondeterministic systems and a stronger notion called trajectory model nonblocking is introduced necessary and sufficient conditions for the existence of language model nonblocking as well as trajectory model nonblocking supervisors are obtained for nondeterministic systems in the presence of driven events in terms of extended controllability and relative closure conditions and a new condition called the trajectory closure condition

general change of variable formulas for semimartingales in one and finite dimensions a general one dimensional change of variables formula is established for continuous semimartingales which extends the famous meyer tanaka formula the inspiration comes from an application arising in stochastic finance theory for functions mapping n to a general change of variables formula is established for arbitrary semimartingales where the usualc2 hypothesis is relaxed

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

a multidimensional process involving local time on presente une approche probabiliste a un probleme pose par mckean 1967 pour la construction d un systeme de n particules sur r avec un generateur formel