symbolic model checking for real time systems abstract we describe finite state programs over real numbered time in a guarded command language with real valued clocks or equivalently as finite automata with real valued clocks model checking answers the question which states of a real time program satisfy a branching time specification given in an extension of ctl with clock variables we develop an algorithm that computes this set of states symbolically as a fixpoint of a functional on state predicates without constructing the state space for this purpose we introduce a calculus on computation trees over real numbered time unfortunately many standard program properties such as response for all nonzeno execution sequences during which time diverges cannot be characterized by fixpoints we show that the expressiveness of the timed calculus is incomparable to the expressiveness of timed ctl fortunately this result does not impair the symbolic verification of implementable real time programs those whose safety constraints are machine closed with respect to diverging time and whose fairness constraints are restricted to finite upper bounds on clock values all timed ctl properties of such programs are shown to be computable as finitely approximable fixpoints in a simple decidable theory

robust image analysis with sparse representation on quantized visual features recent techniques based on sparse representation sr have demonstrated promising performance in high level visual recognition exemplified by the highly accurate face recognition under occlusion and other sparse corruptions most research in this area has focused on classification algorithms using raw image pixels and very few have been proposed to utilize the quantized visual features such as the popular bag of words feature abstraction in such cases besides the inherent quantization errors ambiguity associated with visual word assignment and misdetection of feature points due to factors such as visual occlusions and noises constitutes the major cause of dense corruptions of the quantized representation the dense corruptions can jeopardize the decision process by distorting the patterns of the sparse reconstruction coefficients in this paper we aim to eliminate the corruptions and achieve robust image analysis with sr toward this goal we introduce two transfer processes ambiguity transfer and mis detection transfer to account for the two major sources of corruption as discussed by reasonably assuming the rarity of the two kinds of distortion processes we augment the original sr based reconstruction objective with mmbl0 norm regularization on the transfer terms to encourage sparsity and hence discourage dense distortion transfer computationally we relax the nonconvex mmbl0 norm optimization into a convex mmbl1 norm optimization problem and employ the accelerated proximal gradient method to optimize the convergence provable updating procedure extensive experiments on four benchmark datasets caltech 101 caltech 256 corel 5k and cmu pose illumination and expression manifest the necessity of removing the quantization corruptions and the various advantages of the proposed framework

a polynomial time algorithm for checking equivalence under certain semiring congruences motivated by the state space isomorphism problem for hybrid systems this paper presents a polynomial time algorithm for equivalence under certain semiring congruences these congruences arise when studying the isomorphism of state spaces for a class of hybrid systems the area of hybrid systems concerns issues of modeling computation and control for systems which combine discrete and continuous components the subclass of piecewise linear pl systems provides one systematic approach to discrete time hybrid systems naturally blending switching mechanisms with classical linear components pl systems model arbitrary interconnections of 7nite automata and linear systems tools from automata theory logic and related areas of computer science and 7nite mathematics are used in the studyof pl sy stems in conjunction with linear algebra techniques all in the context of a pl algebra formalism pl systems are of interest as controllers as well as identi7cation models basic questions for any class of systems are those of equivalence and in particular whether state spaces are equivalent under a change of variables this paper studies this state space equivalence problem for pl systems the problem was known to be decidable but its computational complexitywas potentially exponential here it is shown to be solvable in polynomial time c 2001 elsevier science b v all rights reserved

sparsity cognizant total least squares for perturbed compressive sampling solving linear regression problems based on the total least squares tls criterion has well documented merits in various applications where perturbations appear both in the data vector as well as in the regression matrix however existing tls approaches do not account for sparsity possibly present in the unknown vector of regression coefficients on the other hand sparsity is the key attribute exploited by modern compressive sampling and variable selection approaches to linear regression which include noise in the data but do not account for perturbations in the regression matrix the present paper fills this gap by formulating and solving regularized tls optimization problems under sparsity constraints near optimum and reduced complexity suboptimum sparse s tls algorithms are developed to address the perturbed compressive sampling and the related dictionary learning challenge when there is a mismatch between the true and adopted bases over which the unknown vector is sparse the novel s tls schemes also allow for perturbations in the regression matrix of the least absolute selection and shrinkage selection operator lasso and endow tls approaches with ability to cope with sparse under determined errors in variables models interesting generalizations can further exploit prior knowledge on the perturbations to obtain novel weighted and structured s tls solvers analysis and simulations demonstrate the practical impact of s tls in calibrating the mismatch effects of contemporary grid based approaches to cognitive radio sensing and robust direction of arrival estimation using antenna arrays

optimization of lyapunov invariants in verification of software systems the paper proposes a control theoretic framework for verification of numerical software systems and puts forward software verification as an important application of control and systems theory the idea is to transfer lyapunov functions and the associated computational techniques from control systems analysis and convex optimization to verification of various software safety and performance specifications these include but are not limited to absence of overflow absence of division by zero termination in finite time absence of dead code and certain user specified assertions central to this framework are lyapunov invariants these are properly constructed functions of the program variables and satisfy certain properties analogous to those of lyapunov functions along the execution trace the search for the invariants can be formulated as a convex optimization problem if the associated optimization problem is feasible the result is a certificate for the specification

bifurcations in a system of interacting fronts we show that the bifurcation scenario in a high dimensional system with interacting moving fronts can be related to the universal u sequence which is known from the symbolic analysis of iterated one dimensional maps this connection is corroborated for a model of a semiconductor superlattice which describes the complex dynamics of electron accumulation and depletion fronts by a suitable poincare section we reduce the dynamics to a low dimensional iterated map for which in the most elementary case the bifurcation points can be determined analytically

polynomial time verification of diagnosability of partially observed discrete event systems the problem of verifying the properties of diagnosability and i diagnosability is considered we present new polynomial time algorithms for deciding diagnosability and i diagnosability these algorithms are based on the construction of a nondeterministic automaton called a verifier

lyapunov theory for zeno stability zeno behavior is a dynamic phenomenon unique to hybrid systems in which an infinite number of discrete transitions occurs in a finite amount of time this behavior commonly arises in mechanical systems undergoing impacts and optimal control problems but its characterization for general hybrid systems is not completely understood the goal of this paper is to develop a stability theory for zeno hybrid systems that parallels classical lyapunov theory that is we present lyapunov like sufficient conditions for zeno behavior obtained by mapping solutions of complex hybrid systems to solutions of simpler zeno hybrid systems defined on the first quadrant of the plane these conditions are applied to lagrangian hybrid systems which model mechanical systems undergoing impacts yielding simple sufficient conditions for zeno behavior finally the results are applied to robotic bipedal walking

a method for the synthesis of controllers to handle safety liveness and real time constraints describes a synthesis method that automatically derives controllers for timed discrete event systems with nonterminating behavior modeled by timed transition graphs and specifications of control requirements expressed by metric temporal logic mtl formulas synthesis is performed by using 1 a forward chaining search that evaluates the satisfiability of mtl formulas over sequences of states generated by occurrences of actions and 2 a control directed backtracking technique that takes into consideration the controllability of actions this method has several interesting features first the issues of controllability safety liveness and real time are integrated in a single framework second the synthesis process does not require explicit storage of an entire transition structure over which formulas are checked and can be stopped at any moment giving an approximate but useful result third search and control mechanisms allow circumvention of the state explosion problem

verification of hybrid automata diagnosability by abstraction a notion of diagnosability for hybrid systems is defined which generalizes the common notion of observability we propose an abstraction procedure to translate a hybrid automaton into a timed automaton in order to verify observability and diagnosability properties we introduce a procedure to check diagnosability and show that for the system class of our abstraction namely for a subclass of timed automata the durational graphs the verification problem belongs to the complexity class p we apply our procedure to an electromagnetic valve system for camless engines

verification of bounded discrete horizon hybrid automata we consider the class of o minimally definable hybrid automata with a bounded discrete transition horizon we show that for every hybrid automata in this class there exists a bisimulation of finite index and that the bisimulation quotient can be effectively constructed when the underlying o minimal theory is decidable more importantly we give natural specifications for hybrid automata which ensure the boundedness of discrete transition horizons in addition we show that these specifications are reasonably tight with respect to the decidability of the models and that they can model modern day real time and embedded systems as a result the analysis of several problems for these systems admit effective algorithms we provide a representative example of a hybrid automaton in this class unlike previously examined subclasses of o minimally defined hybrid automata with decidable verification properties and extended o minimal hybrid automata we do not impose re initialization of the continuous variables in a memoryless fashion when a discrete transition is taken our class of hybrid systems has both rich continuous dynamics and strong discrete continuous coupling showing that it is not necessary to either simplify the continuous dynamics or restrict the discrete dynamics to achieve decidability

a kleene schutzenberger theorem for weighted timed automata during the last years weighted timed automata have received much interest in the real time community weighted timed automata form an extension of timed automata and allow us to assign weights costs to both locations and edges this model introduced by alur et al 2001 and behrmann et al 2001 permits the treatment of continuous consumption of resources and has led to much research on scheduling problems optimal reachability and model checking also several authors have derived kleene type characterizations of unweighted timed automata and their accepted timed languages the goal of this paper is to provide a characterization of the behaviours of weighted timed automata by rational power series we define weighted timed automata with weights taken in an arbitrary semiring resulting in a model that subsumes several weighted timed automata concepts of the literature for our main result we combine the methods of schutzenberger a recent approach for a kleene type theorem for unweighted timed automata by bouyer and petit as well as new techniques our main result also implies kleene type theorems for several subclasses of weighted timed automata investigated before e g for timed automata and timed automata with stopwatch observers

inclusion dynamics hybrid automata hybrid systems are dynamical systems with the ability to describe mixed discrete continuous evolution of a wide range of systems consequently at first glance hybrid systems appear powerful but recalcitrant neither yielding to analysis and reasoning through a purely continuous time modeling as with systems of differential equations nor open to inferential processes commonly used for discrete state transition systems such as finite state automata a convenient and popular model called hybrid automata was introduced to model them and has spurred much interest on its tractability as a tool for inference and model checking in a general setting intuitively a hybrid automaton is simply a finite state automaton with each state augmented by continuous variables which evolve according to a set of well defined continuous laws each specified separately for each state this article investigates both the notion of hybrid automaton and the model checking problem over such a structure in particular it relates first order theories and analysis results on multivalued maps and reduces the bounded reachability problem for hybrid automata whose continuous laws are expressed by inclusions x f x t to a decidability problem for first order formulaeover the reals furthermore the paper introduces a class of hybrid automata for which the reachability problem can be decided and shows that the problem of deciding whether a hybrid automaton belongs to this class can be again decided using first order formulaeover the reals despite the fact that the bisimulation quotient for this class of hybrid automata can be infinite we show that our techniques permit effective model checking for a nontrivial fragment of ctl

low dimensional hybrid systems decidable undecidable don t know even though many attempts have been made to define the boundary between decidable and undecidable hybrid systems the affair is far from being resolved more and more low dimensional systems are being shown to be undecidable with respect to reachability and many open problems in between are being discovered in this paper we present various two dimensional hybrid systems for which the reachability problem is undecidable we show their undecidability by simulating minsky machines their proximity to the decidability frontier is understood by inspecting the most parsimonious constraints necessary to make reachability over these automata decidable we also show that for other two dimensional systems the reachability question remains unanswered by proving that it is as hard as the reachability problem for piecewise affine maps on the real line which is a well known open problem

hybrid port hamiltonian systems from parameterized incidence matrices to hybrid automata abstract this paper shows how to formally design a hybrid automaton model for a wide class of dissipative physical systems with sources and switching topology this method is based on a mathematical representation of the dynamic network graph and of its dual graph using the hybrid incidence matrix and on a constructive method for analyzing admissible and constrained configurations the port hamiltonian representation associated with the set of hybrid system configurations parameterized by the discrete state of the switches is synthesized to be part of the hybrid automaton of the system this is a further step towards a generic control synthesis for physical switching systems

on the approximability of minimizing nonzero variables or unsatisfied relations in linear systems we investigate the computational complexity of two closely related classes of combinatorial optimization problems for linear systems which arise in various fields such as machine learning operations research and pattern recognition in the first class min ulr one wishes given a possibly infeasible system of linear relations to find a solution that violates as few relations as possible while satisfying all the others in the second class min rvls the linear system is supposed to be feasible and one looks for a solution with as few nonzero variables as possible for both min ulr and min rvls the four basic types of relational operators and are considered while min rvls with equations was mentioned to be np hard in garey and johnson 1979 we established in amaldi 1992 amaldi and kann 1995 that min ulr with equalities and inequalities are np hard even when restricted to homogeneous systems with bipolar coefficients the latter problems have been shown hard to approximate in arora et al 1993 in this paper we determine strong bounds on the approximability of various variants of min rvls and min ulr including constrained ones where the variables are restricted to take binary values or where some relations are mandatory while others are optional the various np hard versions turn out to have different approximability properties depending on the type of relations and the additional constraints but none of them can be approximated within any constant factor unless p np particular attention is devoted to two interesting special cases that occur in discriminant analysis and machine learning in particular we disprove a conjecture of van horn and martinez 1992 regarding the existence of a polynomial time algorithm to design linear classifiers or perceptrons that involve a close to minimum number of features

graph embedding and extensions a general framework for dimensionality reduction a large family of algorithms supervised or unsupervised stemming from statistics or geometry theory has been designed to provide different solutions to the problem of dimensionality reduction despite the different motivations of these algorithms we present in this paper a general formulation known as graph embedding to unify them within a common framework in graph embedding each algorithm can be considered as the direct graph embedding or its linear kernel tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided furthermore the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms by utilizing this framework as a tool we propose a new supervised dimensionality reduction algorithm called marginal fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class while the penalty graph connects the marginal points and characterizes the interclass separability we show that mfa effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions real face recognition experiments show the superiority of our proposed mfa in comparison to lda also for corresponding kernel and tensor extensions

probabilistic reachability for multi parameter bifurcation analysis of cardiac alternans abstract using a probabilistic reachability based approach we present a multi parameter bifurcation analysis of electrical alternans in the two current mitchell schaeffer ms cardiac cell model electrical alternans is a phenomenon characterized by a variation in successive action potential durations generated by a cardiac cell or tissue alternans are known to initiate re entrant waves and are an important physiological indicator of an impending life threatening arrhythmia such as ventricular fibrillation the multi parameter bifurcation analysis we perform identifies a bifurcation hypersurface in the ms model parameter space such that a small perturbation to this region results in a transition from highly likely alternans to highly likely non alternans behavior our approach to this problem rests on encoding alternans like behavior in the ms model as a five mode multinomial hybrid automaton to perform multi parameter bifurcation analysis of cardiac alternans we first treat the parameters in question as bounded random variables we then apply a sophisticated guided search based probabilistic reachability analysis to compute a bounded bifurcation region possibly very tight that contains the bifurcation hypersurface bh our probabilistic reachability analysis uses a technique that combines a decision procedure with statistical tests in the process of computing the bifurcation region we further partition the parameter space into two more regions such that any valuation chosen from one of the regions will either produce alternans or non alternans behavior with a probability greater than a user defined threshold

critical curves for a santalo problem in 3 space forms abstract l santalo 1956 studied in 15 the minimization of frenet first curvature dependent energies for spaces of curves constrained to lie in a surface of the euclidean 3 space in this paper we analyze an extension of that problem by considering energy functionals determined by lagrangians which depend not only on the curvature but also on the torsion acting on spaces of surface contained clamped curves of real 3 space forms

computing reachable states for nonlinear biological models in this paper we describe reachability computation for continuous and hybrid systems and its potential contribution to the process of building and debugging biological models we summarize the state of the art for linear systems and then develop a novel algorithm for computing reachable states for nonlinear systems we report experimental results obtained using a prototype implementation applied to several biological models we believe these results constitute a promising contribution to the analysis of complex models of biological systems

process algebra for hybrid systems we propose a process algebra obtained by extending a combination of the process algebra with continuous relative timing from baeten and middelburg process algebra with timing springer berlin 2002 chapter 4 and the process algebra with propositional signals from baeten and bergstra theoret comput sci 177 1977 381 405 the proposed process algebra makes it possible to deal with the behaviour of hybrid systems i e systems in which the instantaneous state transitions caused by performing actions are alternated with continuous state evolutions this process algebra has in addition to equational axioms rules to derive equations with the help of real analysis

the algorithmic analysis of hybrid systems we present a general framework for the formal specification and algorithmic analysis of hybrid systems a hybrid system consists of a discrete program with an analog environment we model hybrid systems as finite automata equipped with variables that evolve continuously with time according to dynamical laws for verification purposes we restrict ourselves to linear hybrid systems where all variables follow piecewise linear trajectories we provide decidability and undecidability results for classes of linear hybrid systems and we show that standard program analysis techniques can be adapted to linear hybrid systems in particular we consider symbolic model checking and minimization procedures that are based on the reachability analysis of an infinite state space the procedures iteratively compute state sets that are definable as unions of convex polyhedra in multidimensional real space we also present approximation techniques for dealing with systems for which the iterative procedures do not converge

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

decidable integration graphs abstract integration graphsare a computational model developed in the attempt to identify simple hybrid systems with decidable analysis problems we start with the class ofconstant slope hybrid systems cshs in which the right hand side of all differential equations is an integer constant we refer to continuous variables whose right hand side constants are always 1 astimers all other continuous variables are calledintegrators the first result shown in the paper is that simple questions such as reachability of a given state are undecidable for even this simple class of systems to restrict the model even further we impose the requirement that no test that refers to integrators may appear within a loop in the graph this restricted class of cshs is calledintegration graphs the main results of the paper are that the reachability problem of integration graphs is decidable for two special cases the case of a single timer and the case of a single test involving integrators the expressive power of the integration graphs formalism is demonstrated by showing that some typical problems studied within the context of the calculus of durations and timed statecharts can be formulated as reachability problems for restricted integration graphs and a high fraction of these fall into the subclasses of a single timer or a single test involving integrators

symbolic reachability analysis of fifo channel systems with nonregular sets of configurations abstract we address the verification problem of fifo channel systems we apply the symbolic analysis principle to these systems we represent their sets of configurations using structures called constrained queue content decision diagrams cqdds combining finite state automata with linear arithmetical constraints on number of occurrences of symbols we show that cqdds allow forward and backward reachability analysis of systems with nonregular sets of configurations moreover we prove that cqdds allow to compute the exact effect of the repeated execution of any fixed cycle in the transition graph of a system we use this fact to define a generic reachability analysis semi algorithm parametrized by a set of cycles given a set of configurations this semi algorithm performs a least fixpoint calculation to construct the set of its successors or predecessors at each step this calculation is accelerated by considering the cycles in as additional meta transitions in the transition graph generalizing the approach of boigelot and godefroid cav 96 lecture notes in computer science vol 1102 springer berlin 1996

realization theory for linear hybrid systems the paper develops realization theory for linear hybrid systems i e hybrid systems in continuous time without guards whose continuous dynamics is determined by linear control systems and whose discrete dynamics is determined by a finite state automaton we will formulate necessary and sufficient conditions for the existence of a realization we will show that minimality is equivalent to observability and span reachability and that minimal systems are isomorphic in turn observability and span reachability can be characterized by rank conditions

numerical bifurcation analysis of the bipedal spring mass model abstract the spring mass model and its numerous extensions are currently one of the best candidates for templates of human and animal locomotion however with increasing complexity their applications can become very time consuming in this paper we present an approach that is based on the calculation of bifurcations in the bipedal spring mass model for walking since the bifurcations limit the region of stable walking locomotion can be studied by computing the corresponding boundaries originally the model was implemented as a hybrid dynamical system our new approach consists of the transformation of the series of initial value problems on different intervals into a single boundary value problem using this technique discontinuities can be avoided and sophisticated numerical methods for studying parametrized nonlinear boundary value problems can be applied thus appropriate extended systems are used to compute transcritical and period doubling bifurcation points as well as turning points we show that the resulting boundary value problems can be solved by the simple shooting method with sufficient accuracy making the application of the more extensive multiple shooting superfluous the proposed approach is fast robust to numerical perturbations and allows determining complete manifolds of periodic solutions of the original problem

rotation hypersurfaces in spaces of constant curvature rotation hypersurfaces in spaces of constant curvature are defined and their principal curvatures are computed a local characterization of such hypersurfaces with dimensions greater than two is given in terms of principal curvatures some special cases of rotation hypersurfaces with constant mean curvature in hyperbolic space are studied in particular it is shown that the well known conjugation between the helicoid and the catenoid in euclidean three space extends naturally to hyperbolic three space h3 in the latter case catenoids are of three different types and the explicit correspondence is given it is also shown that there exists a family of simply connected complete embedded nontotally geodesic stable minimal surfaces in h3

a game theoretic approach to fault diagnosis and identification of hybrid systems physical systems can fail for this reason the problem of identifying and reacting to faults has received a lot of attention in the control and computer science communities in this paper we study the fault diagnosis problem for hybrid systems from a game theoretical point of view a hybrid system is a system mixing continuous and discrete behaviours that cannot be faithfully modelled neither by using a formalism with continuous dynamics only nor by a formalism including only discrete dynamics we model hybrid systems as hybrid automata and add distinguished actions to describe faults we define a fault identification game on them using two players the environment and the identifier the environment controls the evolution of the system and chooses whether and when a fault occurs the identifier observes the external behaviour of the system and announces whether a fault has occurred or not existence of a winning strategy for the identifier implies that faults can be detected correctly while computing such a winning strategy corresponds to implementing an identifier for the system we will show how to determine the existence of a winning strategy and how to compute it for all decidable classes of hybrid automata that admit a finite bisimulation quotient

extremal curves for weighted elastic energy in surfaces of 3 space forms a variational problem closely related to the bending energy of curves contained is surfaces of real 3 space forms is considered we seek curves in a surface which are critical for the elastic energy when this is weighted by the total squared normal curvature energy under two different sets of constraints clamped curves and one free end curves of constant length we start by deriving the first variation formula and the corresponding euler lagrange equations and natural boundary conditions of these energies and characterize critical geodesics we show how surfaces locally foliated by critical geodesics can be found by using the fundamental theorem of submanifolds in order to find explicit solutions we classify complete rotation surfaces in a real space form for which every parallel is critical

general subspace learning with corrupted training data via graph embedding we address the following subspace learning problem supposing we are given a set of labeled corrupted training data points how to learn the underlying subspace which contains three components an intrinsic subspace that captures certain desired properties of a data set a penalty subspace that fits the undesired properties of the data and an error container that models the gross corruptions possibly existing in the data given a set of data points these three components can be learned by solving a nuclear norm regularized optimization problem which is convex and can be efficiently solved in polynomial time using the method as a tool we propose a new discriminant analysis i e supervised subspace learning algorithm called corruptions tolerant discriminant analysis ctda in which the intrinsic subspace is used to capture the features with high within class similarity the penalty subspace takes the role of modeling the undesired features with high between class similarity and the error container takes charge of fitting the possible corruptions in the data we show that ctda can well handle the gross corruptions possibly existing in the training data whereas previous linear discriminant analysis algorithms arguably fail in such a setting extensive experiments conducted on two benchmark human face data sets and one object recognition data set show that ctda outperforms the related algorithms

toward unified analysis and controller synthesis for a class of hybrid systems abstract this work defines a new class of hybrid systems called state based switched sbs systems that have numerous important engineering applications the characterizing feature of these systems is that the discrete event dynamics are associated with the continuous time state making a specific function be equal to zero the choice of this function is application specific and for the closed loop sbs systems defined in this paper it is related to the execution of a desired set of tasks from a pre specified mission plan for this broad class of sbs systems the paper presents a unified analysis and controller synthesis methodology based on lyapunov theory depending on the details of the mission plan the closed loop hybrid system will be divided into two subclasses sequential and non sequential the controller design procedure for both subclasses consists of the same two steps finding a control law and finding a stabilizing switching rule for static state and output feedback of sequential hybrid systems the paper proposes a new hybrid sequential sliding mode controller it is proven that the control mission can be accomplished for sequential hybrid systems under static state and output feedback using this new controller a similar framework is investigated for the more complex class of nonsequential hybrid systems and a systematic procedure for designing the switching rule is presented for some specific instances of these systems

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

languages and models for hybrid automata a coalgebraic perspective abstract we study hybrid automata from a coalgebraic point of view we show that such a perspective supports a generic theory of hybrid automata with a rich palette of definitions and results this includes among other things notions of bisimulation and behaviour state minimisation techniques and regular expression languages

hybrid control synthesis for eventuality specifications using level set methods this paper is concerned with the extraction of controllers for hybrid systems with respect to eventuality specifications given a hybrid system modelled by a hybrid automaton and a target set of states the objective is to compute the maximal set of initial states together with the hybrid control policy such that all the trajectories of the controlled system reach the target in finite time due to the existence of set valued disturbance inputs the problem is studied in a game theoretic framework having shown that a least restrictive solution does not exist we propose a dynamic programming algorithm that computes the maximal initial set and a controller with the desired property to implement the algorithm reachable sets of pursuit evasion differential games need to be computed for that reason level set methods are employed where the boundary of the reachable set is characterized as the zero level set of a hamilton jacobi equation the procedure for the numerical extraction of the controller is presented in detail and examples illustrate the methodology finally to demonstrate the practical character of our results a control design problem in the benchmark system of the batch evaporator is considered as an eventuality synthesis problem and solved using the proposed methodology

on the decidability and complexity of problems for restricted hierarchical hybrid systems we study variants of a recently introduced hybrid system model called a hierarchical piecewise constant derivative hpcd these variants loosely called restricted hpcds form a class of natural models with similarities to many other well known hybrid system models in the literature such as stopwatch automata rectangular automata and pcds we study the complexity of reachability and mortality problems for variants of rhpcds and show a variety of results depending upon the allowed powers these models form a useful tool for the study of the complexity of such problems for hybrid systems due to their connections with existing models we show that the reachability problem and the mortality problem are co np hard for bounded 3 dimensional rhpcds 3 rhpcds reachability is shown to be in pspace even for n dimensional rhpcds we show that for an unbounded 3 rhpcd the reachability and mortality problems become undecidable for a nondeterministic variant of 2 rhpcds the reachability problem is shown to be pspace complete

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

efficient timed model checking for discrete time systems we consider model checking of timed temporal formulae in durational transition graphs dtgs i e kripke structures where transitions have integer durations two semantics for dtgs are presented and motivated we consider timed versions ofctl where subscripts put quantitative constraints on the time it takes before a property is satisfied we exhibit an important gap between logics where subscripts of the form c exact duration are allowed and simpler logics that only allow subscripts of the form c or c bounded duration without exact durations model checking can be done in polynomial time but with exact durations it becomes 2p complete or pspace complete depending on the considered semantics

a framework for worst case and stochastic safety verification using barrier certificates this paper presents a methodology for safety verification of continuous and hybrid systems in the worst case and stochastic settings in the worst case setting a function of state termed barrier certificate is used to certify that all trajectories of the system starting from a given initial set do not enter an unsafe region no explicit computation of reachable sets is required in the construction of barrier certificates which makes it possible to handle nonlinearity uncertainty and constraints directly within this framework in the stochastic setting our method computes an upper bound on the probability that a trajectory of the system reaches the unsafe set a bound whose validity is proven by the existence of a barrier certificate for polynomial systems barrier certificates can be constructed using convex optimization and hence the method is computationally tractable some examples are provided to illustrate the use of the method

multiresolution gray scale and rotation invariant texture classification with local binary patterns presents a theoretically very simple yet efficient multiresolution approach to gray scale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions the method is based on recognizing that certain local binary patterns termed uniform are fundamental properties of local image texture and their occurrence histogram is proven to be a very powerful texture feature we derive a generalized gray scale and rotation invariant operator presentation that allows for detecting the uniform patterns for any quantization of the angular space and for any spatial resolution and presents a method for combining multiple operators for multiresolution analysis the proposed approach is very robust in terms of gray scale variations since the operator is by definition invariant against any monotonic transformation of the gray scale another advantage is computational simplicity as the operator can be realized with a few operations in a small neighborhood and a lookup table experimental results demonstrate that good discrimination can be achieved with the occurrence statistics of simple rotation invariant local binary patterns

sparse representation for color image restoration sparse representations of signals have drawn considerable interest in recent years the assumption that natural signals such as images admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data in particular the design of well adapted dictionaries for images has been a major challenge the k svd has been recently proposed for this task and shown to perform very well for various grayscale image processing tasks in this paper we address the problem of learning dictionaries for color images and extend the k svd based grayscale image denoising algorithm that appears in this work puts forward ways for handling nonhomogeneous noise and missing information paving the way to state of the art results in applications such as color image denoising demosaicing and inpainting as demonstrated in this paper

on time optimal control of integrator switched systems with state constraints abstract in this paper time optimal control problems of a class of integrator switched systems with polyhedral state constraint subsets are studied we first develop a directed graph representation of the system discrete structure based on the graph representation we generate candidate solution paths and propose an algorithm for seeking the optimal solution a linear programming method for finding the optimal timing information for each path is then proposed finally we report preliminary results on some sufficient conditions and techniques which help reduce the number of candidate paths

algorithmic analysis of polygonal hybrid systems part i reachability in this work we are concerned with the formal verification of two dimensional non deterministic hybrid systems namely polygonal differential inclusion systems spdis spdis are a class of non deterministic systems that correspond to piecewise constant differential inclusions on the plane for which we study the reachability problem our contribution is the development of an algorithm for solving exactly the reachability problem of spdis we extend the geometric approach due to maler and pnueli o maler a pnueli reachability analysis of planar multi linear systems in c courcoubetis ed cav 93 in lncs vol 697 springer verlag 1993 pp 194 209 to non deterministic systems based on the combination of three techniques the representation of the two dimensional continuous time dynamics as a one dimensional discrete time system using poincare maps the characterization of the set of qualitative behaviors of the latter as a finite set of types of signatures and acceleration used to explore reachability according to each of these types

verification of hybrid automata diagnosability with measurement uncertainty the problem of system diagnosability verification is concerned with whether a fault in the system operation can be diagnosed by using the system model and observations of the system output in this paper we investigate the delta d delta m diagnosability of hybrid automata which characterizes the maximum delay for diagnosing faults since their first occurrence given the measurement uncertainty in observing the system output

achilles and the tortoise climbing up the hyper arithmetical hierarchy abstract in this paper we characterize the computational power of dynamical systems with piecewise constant derivatives pcd considered as computational machines working on a continuous real space with a continuous real time we prove that piecewise constant derivative systems recognize precisely the languages of the kth respectively k 1 th level of the hyper arithmetical hierarchy in dimension d 2k 3 respectively d 2k 4 k 0 hence we prove that the reachability problem for pcd systems of dimension d 2k 3 resp d 2k 4 k 1 is hyper arithmetical and is k complete resp k complete

a decidable class of planar linear hybrid systems abstract in this paper we show the decidability of a new subclass of linear hybrid automata these automata are planar that is consist of two state variables monotonic along some direction in the plane and have identity resets that is the values of the continuous variables are not reset to a different value on a discrete transition our proof uses a combination of a tree construction capturing the edge to edge reachability and a finite bisimulation construction our class strictly contains the class of two dimensional piecewise constant derivative systems for which decidability of the reachability problem is known

deciding stability and mortality of piecewise affine dynamical systems in this paper we study problems such as given a discrete time dynamical system of the form x t 1 f x t where f r n r n is a piecewise affine function decide whether all trajectories converge to 0 we show in our main theorem that this attractivity problem is undecidable as soon as n greater than or equal to2 the same is true of two related problems stability is the dynamical system globally asymptotically stable and mortality do all trajectories go through 0 we then show that am activity and stability become decidable in dimension 1 for continuous functions c 2001 elsevier science b v all rights reserved

a hybrid bounding method for computing an over approximation for the reachable set of uncertain nonlinear systems in this paper we show how to compute an over approximation for the reachable set of uncertain nonlinear continuous dynamical systems by using guaranteed set integration we introduce two ways to do so the first one is a full interval method which handles whole domains for set computation and relies on state of the art validated numerical integration methods the second one relies on comparison theorems for differential inequalities in order to bracket the uncertain dynamics between two dynamical systems where there is no uncertainty since the derived bracketing systems are piecewise ck differentiable functions validated numerical integration methods cannot be used directly hence our contribution resides in the use of hybrid automata to model the bounding systems we give a rule for building these automata and we show how to run them and address mode switching in a guaranteed way in order to compute the over approximation for the reachable set the computational cost of our method is also analyzed and shown to be smaller that the one of classical interval techniques sufficient conditions are given which ensure the epsiv practical stability of the enclosures given by our hybrid bounding method two examples are also given which show that the performance of our method is very promising

sparse discriminative feature selection as sparse representation based classifier src is developed it has drawn more and more attentions in dimension reduction in this paper we introduce src based measurement criterion into feature selection and then propose a novel method called sparse discriminative feature selection our objective function aims to find a subset of features which minimize the within class reconstruction residual and simultaneously maximize the between class reconstruction residual in the subspace of selected features a greedy algorithm and a joint selection algorithm are devised to efficiently solve the proposed combinatorial optimization formulation in particular our joint selection algorithm adds l 2 1 norm minimization into the objective function which reduces the redundant and learns features weights simultaneously a new iterative algorithm is also developed to optimize the proposed objective function experiments on benchmark data sets demonstrate the performance of our feature selection method highlightsthe proposed method selects features that can preserve the sparse reconstructive relationship of the data a greedy algorithm and a joint selection algorithm are devised to efficiently solve the proposed formulation we incorporate discriminative analysis and l2 1 norm minimization into a joint feature selection

complementarity modeling of hybrid systems a complementarity framework is described for the modeling of certain classes of mixed continuous discrete dynamical systems the use of such a framework is well known for mechanical systems with inequality constraints but we give a more general formulation which also applies for instance to switching control systems the main theoretical results in the paper are concerned with uniqueness of smooth continuations the solution of this problem requires the construction of a map from the continuous state to the discrete state a crucial technical tool is the so called linear complementarity problem from mathematical programming and we introduce various generalizations of this problem

synthesis and infeasibility analysis for stochastic models of biochemical systems using statistical model checking and abstraction refinement the stochastic dynamics of biochemical reaction networks can be modeled using a number of succinct formalisms all of whose semantics are expressed as continuous time markov chains ctmc while some kinetic parameters for such models can be measured experimentally most are estimated by either fitting to experimental data or by performing ad hoc and often manual search procedures we consider an alternative strategy to the problem and introduce algorithms for automatically synthesizing the set of all kinetic parameters such that the model satisfies a given high level behavioral specification our algorithms which integrate statistical model checking and abstraction refinement can also report the infeasibility of the model if no such combination of parameters exists behavioral specifications can be given in any finitely monitorable logic for stochastic systems including the probabilistic and bounded fragments of linear and metric temporal logics the correctness of our algorithms is established using a novel combination of arguments based on survey sampling and uniform continuity we prove that the probability of a measurable set of paths is uniformly and jointly continuous with respect to the kinetic parameters under a suitable technical condition we also show that the unbiased statistical estimator for the probability of a measurable set of paths is monotonic in the parameter space we apply our algorithms to two benchmark models of biochemical signaling and demonstrate that they can efficiently find parameter regimes satisfying a given high level behavioral specification in particular we show that our algorithms can synthesize up to 6 parameters simultaneously which is more than that reported by any other synthesis algorithm for stochastic systems moreover when parameter estimation is desired as opposed to synthesis we show that our approach can scale to even higher dimensional spaces by identifying the single parameter combination that maximizes the probability of the behavior being true in an 11 dimensional system

critical curves for the total normal curvature in surfaces of 3 dimensional space forms abstract a variational problem closely related to the bending energy of curves contained in surfaces of real 3 dimensional space forms is considered we seek curves in a surface which are critical for the total normal curvature energy and its generalizations we start by deriving the first variation formula and the corresponding euler lagrange equations of these energies and apply them to study critical special curves geodesics asymptotic lines lines of curvature on surfaces then we show that a rotation surface in a real space form for which every parallel is a critical curve must be a special type of a linear weingarten surface finally we give some classification and existence results for this family of rotation surfaces

impulse differential inclusions a viability approach to hybrid systems impulse differential inclusions are introduced as a framework for modeling hybrid phenomena connections to standard problems in the area of hybrid systems are discussed conditions are derived that allow one to determine whether a set of states is viable or invariant under the action of an impulse differential inclusion for sets that violate these conditions methods are developed for approximating their viability and invariance kernels that is the largest subset that is viable or invariant under the action of the impulse differential inclusion the results are demonstrated on examples

reachability and control synthesis for piecewise affine hybrid systems on simplices in this paper we consider the synthesis of control laws for piecewise affine hybrid systems on simplices the construction is based on the solution to the control to facet problem at the continuous level and on dynamic programming at the discrete level the construction is given as an explicit algorithm using only linear algebra and reach set computations for automata no numerical integration is required the method is conservative in that it may fail to find a control law where one exists but one cannot hope for a sharp algorithm for control synthesis since reachability for piecewise affine hybrid systems is undecidable

characterization of well posedness of piecewise linear systems one of the basic issues in the study of hybrid systems is the well posedness existence and uniqueness of solutions problem of discontinuous dynamical systems the paper addresses this problem for a class of piecewise linear discontinuous systems under the definition of solutions of caratheodory the concepts of jump solutions or of sliding modes are not considered here in this sense the problem to be discussed is one of the most basic problems in the study of well posedness for discontinuous dynamical systems first we derive necessary and sufficient conditions for bimodal systems to be well posed in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions next its extensions to the multimodal case are discussed as an application to switching control in the case that two state feedback gains are switched according to a criterion depending on the state we give a characterization of all admissible state feedback gains for which the closed loop system remains well posed

approximations of stochastic hybrid systems this paper develops a notion of approximation for a class of stochastic hybrid systems that includes as special cases both jump linear stochastic systems and linear stochastic hybrid automata our approximation framework is based on the recently developed notion of the so called stochastic simulation functions these lyapunov like functions can be used to rigorously quantify the distance or error between a system and its approximate abstraction for the class of jump linear stochastic systems and linear stochastic hybrid automata we show that the computation of stochastic simulation functions can be cast as a tractable linear matrix inequality problem this enables us to compute the modeling error incurred by abstracting some of the continuous dynamics or by neglecting the influence of stochastic noise or even the influence of stochastic discrete jumps

robustness of temporal logic specifications for continuous time signals in this paper we consider the robust interpretation of metric temporal logic mtl formulas over signals that take values in metric spaces for such signals which are generated by systems whose states are equipped with non trivial metrics for example continuous or hybrid robustness is not only natural but also a critical measure of system performance thus we propose multi valued semantics for mtl formulas which capture not only the usual boolean satisfiability of the formula but also topological information regarding the distance e from unsatisfiability we prove that any other signal that remains e close to the initial one also satisfies the same mtl specification under the usual boolean semantics finally our framework is applied to the problem of testing formulas of two fragments of mtl namely metric interval temporal logic mitl and closed metric temporal logic clmtl over continuous time signals using only discrete time analysis the motivating idea behind our approach is that if the continuous time signal fulfills certain conditions and the discrete time signal robustly satisfies the temporal logic specification then the corresponding continuous time signal should also satisfy the same temporal logic specification

a comprehensive method for reachability analysis of uncertain nonlinear hybrid systems reachability analysis of nonlinear uncertain hybrid systems i e continuous discrete dynamical systems whose continuous dynamics guard sets and reset functions are defined by nonlinear functions can be decomposed in three algorithmic steps computing the reachable set when the system is in a given operation mode computing the discrete transitions i e detecting and localizing when and where the continuous flowpipe intersects the guard sets and aggregating the multiple trajectories that result from an uncertain transition once the whole flow pipe has transitioned so that the algorithm can resume this paper proposes a comprehensive method that provides a nicely integrated solution to the hybrid reachability problem at the core of the method is the concept of mspb i e geometrical object obtained as the minkowski sum of a parallelotope and an axes aligned box mspb are a way to control the over approximation of the taylor s interval integration method as they happen to be a specific type of zonotope they articulate perfectly with the zonotope bounding method that we propose to enclose in an optimal way the set of flowpipe trajectories generated by the transition process the method is evaluated both theoretically by analyzing its complexity and empirically by applying it to well chosen hybrid nonlinear examples

parametric multisingular hybrid petri nets multisingular hybrid petri net mshpn is an extension of hybrid petri nets enriched with the capabilities of hybrid automata to achieve the practical expressive power of multisingular hybrid automata in this paper we define parametric multisingular hybrid petri nets p mshpns as a parametric extension of mshpns we present the parametric reachability analysis techniques and algorithms and prove that the parametric reachability analysis of p mshpns amounts to the analysis of standard mshpns once the parametric state space of a p mshpns model is computed it can either be used for parametric model checking analysis using the existing techniques or be instantiated to obtain non parametric state spaces p mshpns models can be analysed to obtain the set of feasible configurations for the system parameters we also give a method for deriving the set of constraints on the parameters that ensure the correctness of an invariant property and a method for finding the optimum parameter configuration