on nonperiodic euler flows with holder regularity in isett regularity in time along the coarse scale flow for the euler equations 2013 the first author proposed a strengthening of onsager s conjecture on the failure of energy conservation for incompressible euler flows with holder regularity not exceeding 1 3 this stronger form of the conjecture implies that anomalous dissipation will fail for a generic euler flow with regularity below the onsager critical space l t infty b 3 infty 1 3 due to low regularity of the energy profile this paper is the first and main paper in a series of two the results of which may be viewed as first steps towards establishing the conjectured failure of energy regularity for generic solutions with holder exponent less than 1 5 the main result of the present paper shows that any given smooth euler flow can be perturbed in c 1 5 epsilon t x on any pre compact subset of mathbb r times mathbb r 3 to violate energy conservation furthermore the perturbed solution is no smoother than c 1 5 epsilon t x as a corollary of this theorem we show the existence of nonzero c 1 5 epsilon t x solutions to euler with compact space time support generalizing previous work of the first author isett holder continuous euler flows in three dimensions with compact support in time 2012 to the nonperiodic setting

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

lagrangian eulerian methods for uniqueness in hydrodynamic systems abstract we present a lagrangian eulerian strategy for proving uniqueness and local existence of solutions of limited smoothness for a class of incompressible hydrodynamic models including oldroyd b type complex fluid models and zero magnetic resistivity magneto hydrodynamics equations

onsager s conjecture on the energy conservation for solutions of euler s equation we give a simple proof of a result conjectured by onsager 1 on energy conservation for weak solutions of euler s equation

on admissibility criteria for weak solutions of the euler equations we consider solutions to the cauchy problem for the incompressible euler equations satisfying several additional requirements like the global and local energy inequalities using some techniques introduced in an earlier paper we show that for some bounded compactly supported initial data none of these admissibility criteria singles out a unique weak solution as a byproduct in more than one space dimension we show bounded initial data for which admissible solutions to the p system of isentropic gas dynamics in eulerian coordinates are not unique

dissipative euler flows with onsager critical spatial regularity for any 0 we show the existence of continuous periodic weak solutions v of the euler equations that do not conserve the kinetic energy and belong to the space lt1 cx1 3 e namely x v x t is e holder continuous in space at a e time t and the integral t 1 3 edt is finite a well known open conjecture of l onsager claims that such solutions exist even in the class lt cx1 3 e 2016 wiley periodicals inc

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

convex integration for a class of active scalar equations we show that a general class of active scalar equa tions including porous media and certain magnetostrophic tur bulence models admit non unique weak solutions in the class of bounded functions the proof is based upon the method of convex integration recently implemented for equations of fluid dynamics in 2 3

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

control of vector discrete event systems i the base model a vector discrete event system vdes is a discrete event system model in which the system state is represented by a vector with integer components and state transitions by integer vector addition the authors investigate such structures from the viewpoint of control theory the objective is to specialize to vdes the general automation based control theory of p j ramadge and w m wonham 1987 and w m wonham and p j ramadge 1988 it is shown that within the vdes framework a useful class of control systems can be compactly modeled and some of the associated control problems of ramadge and wonham can be more efficiently solved

on the nonuniqueness of weak solution of the euler equation weak solution of the euler equations is defined as an l2 vector field satisfying the integral relations expressing the mass and momentum balance their general nature has been quite unclear in this work an example of a weak solution on a 2 dimensional torus is constructed that is identically zero outside a finite time interval this example is simpler and more transparent than the previous example of v scheffer j geom anal 3 4 1993 pp 343 401 1997 john wiley sons inc

weak strong uniqueness for measure valued solutions we prove the weak strong uniqueness for measure valued solutions of the incompressible euler equations these were introduced by diperna and majda in their landmark paper commun math phys 108 4 667 689 1987 where in particular global existence to any l2 initial data was proven whether measure valued solutions agree with classical solutions if the latter exist has apparently remained open

stability analysis of a controlled mechanical system with parametric uncertainties in lugre friction model abstractparameters of friction model identified for a specific control system development are not constants they vary over time and have a significant effect on the control system stability altho

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

stability analysis via the concept of lyapunov exponents a case study in optimal controlled biped standing balancing control is important for biped standing in spite of large efforts it is very difficult to design balancing control strategies satisfying three requirements simultaneously maintaining postural stability improving energy efficiency and satisfying the constraints between the biped feet and the ground in this article a proportional derivative pd controller is proposed for a standing biped which is simplified as a two link inverted pendulum with one additional rigid foot link the genetic algorithm ga is used to search for the control gain meeting all three requirements the stability analysis of such a deterministic biped control system is carried out using the concept of lyapunov exponents les based on which the system stability where the disturbance comes from the initial states and the structural stability where the disturbance comes from the pd gains are examined quantitively in terms of stability region this article contributes to the biped balancing control more significan

synthesis of supervisors enforcing general linear constraints in petri nets efficient techniques exist for the design of supervisors enforcing constraints consisting of linear marking inequalities this note shows that without losing the benefits of the prior techniques the class of constraints can be generalized to linear constraints containing marking terms firing vector terms and parikh vector terms we show that this extended class of constraints is more expressive furthermore we show that the extended constraints can describe any supervisor consisting of control places arbitrarily connected to the transitions of a plant petri net pn the supervisor design procedure we propose is as follows for pns without uncontrollable and unobservable transitions a direct method for the design of a pn supervisor that is least restrictive is given for pns with uncontrollable and or unobservable transitions we reduce the problem to the design of supervisors enforcing linear marking inequalities

lack of uniqueness for weak solutions of the incompressible porous media equation in this work we consider weak solutions of the incompressible two dimensional porous media ipm equation by using the approach of de lellis szekelyhidi we prove non uniqueness for solutions in l in space and time

anomalous dissipation for 1 5 holder euler flows recently the second and fourth authors developed an iterative scheme for obtaining rough solutions of the 3d incompressible euler equations in holder spaces the motivation comes from onsager s conjecture the construction involves a superposition of weakly interacting perturbed beltrami flows on infinitely many scales an obstruction to better regularity arises from the errors in the linear transport of a fast periodic flow by a slow velocity field in a recent paper the third author has improved upon the methods introducing some novel ideas on how to deal with this obstruction thereby reaching a better holder exponent albeit weaker than the one conjectured by onsager in this paper we give a shorter proof of this final result adhering more to the original scheme of the second and fourth authors and introducing some new devices more precisely we show that for any positive e there exist periodic solutions of the 3d incompressible euler equations that dissipate the total kinetic energy and belong to the holder class c 1 5 epsilon

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

the euler equations as a differential inclusion we propose a new point of view on weak solutions of the euler equations describing the motion of an ideal incompressible fluid in r n with n 2 we give a reformulation of the euler equations as a differential inclusion and in this way we obtain transparent proofs of several celebrated results of v scheffer and a shnirelman concerning the non uniqueness of weak solutions and the existence of energy decreasing solutions our results are stronger because they work in any dimension and yield bounded velocity and pressure