deterministic networked control of discrete event systems with nondeterministic communication delays we continue to investigate the impacts of communication delays on networked control of discrete event systems des our previous results show that nondeterministic communication delays result in nondeterminism in the languages generated by the controlled system which makes the networked control problems more complex in this paper we investigate the language nondeterminism we define delay observability and delay controllability if the language to be synthesized is delay observable and delay controllable we can synthesize a networked supervisor to control the des such that the language generated by the controlled system is deterministic that is we can synthesize a deterministic state estimate based networked supervisor we derive algorithms to check delay controllability and delay observability if the language to be synthesized is not delay observable and or delay controllable we can find its infimal delay controllable and delay observable superlanguage and maximal delay controllable and delay observable sublanguages we develop algorithms to find these superlanguages and sublanguages all the algorithms proposed in the paper are of polynomial computational complexity

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

state estimation and detectability of probabilistic discrete event systems a probabilistic discrete event system pdes is a nondeterministic discrete event system where the probabilities of nondeterministic transitions are specified state estimation problems of pdes are more difficult than those of non probabilistic discrete event systems in our previous papers we investigated state estimation problems for non probabilistic discrete event systems we defined four types of detectabilities and derived necessary and sufficient conditions for checking these detectabilities in this paper we extend our study to state estimation problems for pdes by considering the probabilities the first step in our approach is to convert a given pdes into a nondeterministic discrete event system and find sufficient conditions for checking probabilistic detectabilities next to find necessary and sufficient conditions for checking probabilistic detectabilities we investigate the convergence of event sequences in pdes an event sequence is convergent if along this sequence it is more and more certain that the system is in a particular state we derive conditions for convergence and hence for detectabilities we focus on systems with complete event observation and no state observation for better presentation the theoretical development is illustrated by a simplified example of nephritis diagnosis

the problem of determining the weak periodic detectability of discrete event systems is pspace complete abstract in shu and lin 2011 exponential time actually polynomial space algorithms for determining the weak detectability and weak periodic detectability of nondeterministic discrete event systems dess are designed in this paper we prove that the problems of determining the weak detectability and weak periodic detectability of deterministic dess are both pspace hard hence pspace complete then as corollaries the problems of determining the weak detectability and weak periodic detectability of nondeterministic dess are also pspace hard hence pspace complete

lie algebras under constraints and non bijective canonical transformations the concept of a lie algebra under constraints is developed in connection with the theory of non bijective canonical transformations a finite dimensional vector space m carrying a faithful linear representation of a lie algebra l is mapped into a lower dimensional space m in such a manner that a subalgebra l0 of l is mapped into d l0 0 the lie algebra l under the constraint d l0 0 is the largest subalgebra l1 of l that can be represented faithfully on m if l0 is semisimple then l1 is shown to be the centraliser cent ll0 if l is semisimple and l0 is a one dimensional diagonal subalgebra of a cartan subalgebra of l then l1 is shown to be the factor algebra cent ll0 l0 the later two results are applied to non bijective canonical transformations generalising the kustaanheimo stiefel transformation

verification of detectability in probabilistic finite automata abstract in this paper we analyze state estimation in stochastic discrete event systems sdes that can be modeled as probabilistic finite automata pfas for a given pfa we obtain the necessary and sufficient conditions that guarantee exact state estimation at least asymptotically with increasing certainty as more information is acquired from observing the behavior of the given pfa by defining the notion of aa detectability and providing necessary and sufficient conditions that can be used to verify it the characterization and analysis of aa detectability is transformed to a problem of classification between two or more pfas which capture the recurrent behavior of an underlying markov process that is obtained by ignoring output behavior and focusing on state transitions in the given pfa our approach combines techniques used in classification between two or more pfas with state estimation methods used in logical discrete event systems des we prove that the proposed verification of aa detectability is of polynomial complexity with respect to the size of the state space of the given pfa

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

observability of place transition nets we discuss the problem of estimating the marking of a place transition p t net based on event observation we assume that the net structure is known while the initial marking is totally or partially unknown we give algorithms to compute a marking estimate that is a lower bound of the actual marking the special structure of petri nets allows us to use a simple linear algebraic formalism for estimate and error computation the error between actual marking and estimate is a monotonically nonincreasing function of the observed word length and words that lead to null error are said to be complete we define several observability properties related to the existence of complete words and show how they can be proved to prove some of them we also introduce a useful tool the observer coverability graph i e the usual coverability graph of a p t net augmented with a vector that keeps track of the estimation error on each place of the net finally we show how the estimate generated by the observer may be used to design a state feedback controller for forbidden marking specifications

observability and diagnosability of finite state systems a unifying framework abstract in this paper a general framework is proposed for the analysis and characterization of observability and diagnosability of finite state systems observability corresponds to the reconstruction of the system s discrete state while diagnosability corresponds to the possibility of determining the past occurrence of some particular states for example faulty states a unifying framework is proposed where observability and diagnosability properties are defined with respect to a critical set i e a set of discrete states representing a set of faults or more generally a set of interest these properties are characterized and the involved conditions provide an estimation of the delay required for the detection of a critical state of the precision of the delay estimation and of the duration of a possible initial transient where the diagnosis is not possible or not required our framework makes it possible to precisely compare some of the observability and diagnosability notions existing in the literature with the ones introduced in our paper and this comparison is presented

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 algorithm for calculating indistinguishable states and clusters in finite state automata with partially observable transitions this paper presents a new algorithm for efficiently calculating pairs of indistinguishable states in finite state automata with partially observable transitions the need to obtain pairs of indistinguishable states occurs in several classes of problems related to control under partial observation diagnosis or distributed control with communication for discrete event systems the algorithm obtains all indistinguishable state pairs in polynomial time in the number of states and events in the system another feature of the algorithm is the grouping of states into clusters and the identification of indistinguishable cluster pairs clusters can be employed to solve control problems for partially observed systems

opacity of discrete event systems and its applications in this paper we investigate opacity of discrete event systems we define two types of opacities strong opacity and weak opacity given a general observation mapping a language is strongly opaque if all strings in the language are confused with some strings in another language and it is weakly opaque if some strings in the language are confused with some strings in another language we show that security and privacy of computer systems and communication protocols can be investigated in terms of opacity in particular two important properties in security and privacy namely anonymity and secrecy can be studied as special cases of opacity we also show that by properly specifying the languages and the observation mapping three important properties of discrete event systems namely observability diagnosability and detectability can all be reformulated as opacity thus opacity has a wide range of applications also in this paper we provide algorithms for checking strong opacity and weak opacity for systems described by regular languages and having a generalized projection as the observation mapping

dynamical invariance algebra of the hartmann potential the accidental degeneracy occurring in the quantum mechanical treatment of the ring shaped potential v eta sigma 2r 1 1 2q eta 2 sigma 2 r sin theta 2 is explained by constructing an su 2 dynamical invariance algebra the schrodinger equation is solved in parabolic coordinates written in the framework of the kustaanheimo stiefel transformation and the hamilton jacobi equations are solved in ordinary parabolic coordinates all finite trajectories are found to be periodic

observability reconstructibility and state observers of boolean control networks the aim of this paper is to introduce and characterize observability and reconstructibility properties for boolean networks and boolean control networks described according to the algebraic approach proposed by d cheng and co authors in the series of papers 3 6 7 and in the recent monography a complete characterization of these properties based both on the boolean matrices involved in the network description and on the corresponding digraphs is provided finally the problem of state observer design for reconstructible bns and bcns is addressed and two different solutions are proposed

periodic solutions for generalized lienard neutral equation with variable parameter abstract by means of mawhin s continuation theorem existence criteria is established for the periodic solutions to a neutral equation with variable parameter it is worth stating that the coefficient c is not a constant which is different from the corresponding ones of past work

kepler orbits and the harmonic oscillator it is shown that the kustaanheimo stiefel transformation which transforms the three dimensional kepler problem into that for a four dimensional harmonic oscillator may be expressed in terms of quaternions in this form the transformation represents a continuous mapping of a triad of orthonormal vectors fixed in space into a rotating triad of orthogonal vectors where one of the unit vectors is mapped into the position vector of a moving particle the reduction of the kepler problem to that of a harmonic oscillator is straightforward and direct in the quaternion formalism the complex stereographic transformation used recently by the author in the corresponding reduction of schrodinger s equation for the hydrogen atom is shown to be closely related to the quaternion representation

on the complete symmetry group of the classical kepler system a rather strong concept of symmetry is introduced in classical mechanics in the sense that some mechanical systems can be completely characterized by the symmetry laws they obey accordingly a complete symmetry group realization in mechanics must be endowed with the following two features 1 the group acts freely and transitively on the manifold of all allowed motions of the system 2 the given equations of motion are the only ordinary differential equations that remain invariant under the specified action of the group this program is applied successfully to the classical kepler problem since the complete symmetry group for this particular system is here obtained the importance of this result for the quantum kinematic theory of the kepler system is emphasized

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

a fully automated framework for control of linear systems from temporal logic specifications we consider the following problem given a linear system and a linear temporal logic ltl formula over a set of linear predicates in its state variables find a feedback control law with polyhedral bounds and a set of initial states so that all trajectories of the closed loop system satisfy the formula our solution to this problem consists of three main steps first we partition the state space in accordance with the predicates in the formula and construct a transition system over the partition quotient which captures our capability of designing controllers second using a procedure resembling model checking we determine runs of the transition system satisfying the formula third we generate the control strategy illustrative examples are included

detectability in stochastic discrete event systems abstract a discrete event system possesses the property of detectability if it allows an observer to perfectly estimate the current state of the system after a finite number of observed symbols i e detectability captures the ability of an observer to eventually perfectly estimate the system state in this paper we analyze detectability in stochastic discrete event systems sdes that can be modeled as probabilistic finite automata more specifically we define the notion of a detectability which characterizes our ability to estimate the current state of a given sdes with increasing certainty as we observe more output symbols the notion of a detectability is differentiated from previous notions for detectability in sdes because it takes into account the probability of problematic observation sequences that do not allow us to perfectly deduce the system state whereas previous notions for detectability in sdes considered each observation sequence that can be generated by the underlying system we discuss observer based techniques that can be used to verify a detectability and provide associated necessary and sufficient conditions we also prove that a detectability is a pspace hard problem

an algorithm to relate general solutions of different bidimensional problems a sufficient condition to relate the general solutions of two different bidimensional problems both in classical and quantum mechanics is found the point transformation as well as the explicit construction of the related potentials is presented the procedure is then used in geometrical optics the vibrating membrane and other physical systems in two dimensions several examples and applications are worked out

enforcing detectability in controlled discrete event systems in this technical note we investigate supervisory control that enforces strong detectability and strongly periodic detectability in a discrete event system the goal of control is to ensure that the current state of the closed loop system can be determined forever or periodically after some finite observations for all trajectories of the system we derive necessary and sufficient conditions for the existence of supervisory control and develop algorithms to synthesize such supervisors if they exist

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

periodic solutions of neutral differential equation with multiple deviating arguments in this paper by means of an abstract continuous theorem of k set contractive operator and some analysis techniques the authors study the existence of periodic solution of the nonlinear neutral differential equation with multiple deviating argumentsddt x t cx email protected email protected i 1 email protected i t f x email protected i t email protected j 1 email protected j t g x email protected j t p t a new result is obtained

observability of finite labeled transition systems finite labeled transition systems are nondeterministic and nontotal systems with finitely many inputs states and outputs this paper provides algorithms for verifying the observability of finite labeled transition systems in the so called multiple experiment case the simple experiment case and the arbitrary experiment case respectively where these algorithms run in exponential time exponential time and quartic polynomial time respectively and are more effective than the existing algorithms in the literature

periodic solutions for some nonlinear differential equations of neutral type where f ir x ir ir is a caratheodory function f x is 2n periodic for every x ci e r and r e io 2n this problem has been studied by sadovskii in 151 by hale and mawhin in 6 in the case ial 1 to the previous one our interest is particularly motivated by the fact that represents a simple and meaningful model for a general phenomenon which often arises in the study of functional differential equations in fact as is well known in some cases a delayed differential equation can be seen as a perturbation of an ordinary differential equation in particular this occurs when the delayed term in the equation can be considered smaller than the ordinary one or dominated by it when such domination is available many good properties can be proved and several results such as those of 6 and 16 take advantage of this fact on the contrary when no domination is present the situation is much more complicated and in general very little is known in problem the delayed term can be considered dominated by the ordinary one whenever ial 1 as a matter of fact in this case one can prove the invertibility of the differential operator l x x a r ux the compactness of its inverse and even some a priori estimates for the solutions consequently one can reduce to a fixed point problem and solve it by means of some topological degree argument however when 11 1 so that the weight of the two terms x t and x t t is the same the above properties fail and moreover for some delays the kernel of the differential operator lx x a r is infinite dimensional therefore one must look for different methods problem is thus a simple but nevertheless significant example of the considerations illustrated by hale in 5 about the difficulty of undertaking a unified approach in the study of functional differential equations at the same time it provides an analogy between neutral equations and the wave equation in the line suggested by hale in 5

control of infinite behavior of finite automata a problem in the control of automata on infinite strings is defined and analyzed the key to the investigation is the development of a fixpoint characterization of the controllability subset of a deterministic rabin automaton the set of states from which the automaton can be controlled to the satisfaction of its own acceptance condition the fixpoint representation allows straightforward computation of the controllability subset and the construction of a suitable state feedback control for the automaton the results have applications to control synthesis automaton synthesis and decision procedures for logical satisfiability in particular they represent a direct efficient and natural solution to church s problem the construction of winning strategies for two player zero sum omega regular games of perfect information and the emptiness problem for automata on infinite trees

periodic solutions to a second order nonlinear neutral functional differential equation in the critical case abstract in this paper the authors study the existence of periodic solutions for a second order neutral functional differential equation x t cx t f x t x t g t x t t e t in the critical case c 1 by employing mawhin s continuation theorem and some analysis techniques sufficient conditions are given for the existence of periodic solutions

on the existence of periodic solutions for neutral functional differential equation abstract by means of mawhin s continuation theorem existence criteria are established for the periodic solutions of neutral functional differential equation

periodic solutions to a kind of neutral functional differential equation in the critical case in this paper we consider a kind of neutral functional differential equation as follows x t cx t gt xt t e t in the critical case c 1 by employing the topological degree theory and some analysis techniques we obtain some new results on the existence of periodic solutions

decentralized control of networked discrete event systems with communication delays abstract in many practical systems supervisory control is not performed by one centralized supervisor but by multiple local supervisors when communication networks are used in such a system as the medium of information transmission the communication channels between local supervisors and the system to be controlled will unavoidably result in communication delays this paper investigates how to use these local supervisors to control the system in order to satisfy given specifications even under communication delays the specifications are described by two languages a minimal required language which specifies the minimal required performance that the supervised system must have and a maximal admissible language which specifies the maximal boundary that the supervised system must be in the results show that if the control problem is solvable then there exists the minimal control policy which can be calculated based on state estimates furthermore we derive algorithms to check whether the control problem is solvable or not

fault diagnosis in discrete event systems framework and model reduction a state based approach for online passive fault diagnosis in systems modeled as finite state automata is presented in this framework the system and the diagnoser the fault detection system do not have to be initialized at the same time furthermore no information about the state or even the condition failure status of the system before the initiation of diagnosis is required the design of the fault detection system in the worst case has exponential complexity a model reduction scheme with polynomial time complexity is introduced to reduce the computational complexity of the design diagnosability of failures is studied and necessary and sufficient conditions for failure diagnosability are derived

periodic solutions of impulsive systems with a small delay for an impulsive system with delay it is proved that if the corresponding system without delay has an isolated omega periodic solution then in any neighbourhood of this orbit the system considered also has an omega periodic solution if the delay is small enough

testing finite state machines state identification and verification we study the complexity of two fundamental problems in the testing of finite state machines 1 distinguishing sequences state identification we show that it is pspace complete to determine whether a finite state machine has a preset distinguishing sequence there are machines that have distinguishing sequences but only of exponential length we give a polynomial time algorithm that determines whether a finite state machine has an adaptive distinguishing sequence the previous classical algorithms take exponential time furthermore if there is an adaptive distinguishing sequence then we give an efficient algorithm that constructs such a sequence of length at most n n spl minus 1 2 which is the best possible where n is the number of states 2 unique input output sequences state verification it is pspace complete to determine whether a state of a machine has a unique input output sequence there are machines whose states have unique input output sequences but only of exponential length

new algorithms for verification of relative observability and computation of supremal relatively observable sublanguage in this technical note we present a new property of relative observability and based on this property we propose two algorithms the first one that has polynomial complexity verifies if a regular language is relatively observable the second algorithm computes the supremal relatively observable sublanguage of a given regular language although the latter has exponential complexity it is more efficient than a recently proposed algorithm which has double exponential complexity moreover the algorithm proposed here has polynomial complexity when the automaton that marks the specification language is state partition

detectability of discrete event systems in this note we investigate the detectability problem in discrete event systems we assume that we do not know initially which state the system is in the problem is to determine the current and subsequent states of the system based on a sequence of observations the observation includes partial event observation and or partial state observation which leads to four possible cases we further define four types of detectabilities strong detectability weak detectability strong periodic detectability and weak periodic detectability we derive necessary and sufficient conditions for these detectabilities these conditions can be checked by constructing an observer which models the estimation of states under different observations the theory developed in this note can be used in feedback control and diagnosis if the system is detectable then the observer can be used as a diagnoser to diagnose the failure states of the system

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

delayed detectability of discrete event systems in this paper we extend detectability to delayed detectability in order to answer the following question after observing k1 k2 observable events can we determine the state of a system at the time when the k1th event was observed if the answer is yes we say that the system is delayed detectable it involves two delays the prior delay k1 before the estimation is attempted and the post delay k2 after which the estimation is completed we investigate various properties of delayed detectability we also provide polynomial algorithms to check delayed detectability the usefulness of delayed detectability is not only evident by the state estimation problems it solves which include current state estimation problem and initial state estimation problem but also evident by the fact that two important properties in discrete event systems namely observability and diagnosability can both be shown to be special cases of delayed detectability

verification complexity of a class of observational properties for modular discrete events systems abstract a modular discrete event system is modeled by a set of module automata running synchronously in this paper we investigate the complexity of the verification problems of three different properties diagnosability predictability and detectability for partially observed modular discrete event systems we first show that deciding diagnosability for modular discrete event systems is pspace complete when the number of modules is unbounded then we show that deciding predictability and detectability for modular discrete event systems are both pspace hard problems these results reveal that in order to verify these properties for the complete system exploring the state space of the monolithic model may be unavoidable in the worst case

periodic solutions for a kind of second order neutral functional differential equations in this paper criteria are established for the existence of periodic solutions to a second order sublinear neutral differential equation our method is based on careful a priori estimation and continuation theorem and our sublinear condition is an improvement of the boundedness condition in some recent results

observability of boolean control networks a unified approach based on finite automata the problem on how to determine the observability of boolean control networks bcns has been open for five years already in this technical note we propose a unified approach to determine all the four types of observability of bcns in the literature we define the concept of weighted pair graphs for bcns in the sense of each observability we use the so called weighted pair graph to transform a bcn to a finite automaton and then we use the automaton to determine observability in particular the two types of observability that rely on initial states and inputs in the literature are determined finally we show that no pairs of the four types of observability are equivalent which reveals the essence of nonlinearity of bcns