rigorous remarks about scaling laws in turbulent fluids a definition of scaling law for suitable families of measures is given and investigated first a number of necessary conditions are proved they imply the absence of scaling laws for 2d stochastic navier stokes equations and for the stochastic stokes linear problem in any dimension while they imply a lower bound on the mean vortex stretching in 3d second for the 3d stochastic navier stokes equations necessary and sufficient conditions for scaling laws to hold are given translating the problem into bounds for energy and enstrophy of high and low modes respectively unlike in the 2d case the validity or invalidity of such conditions in 3d remains open

a computational algorithm for a class of non smooth optimal control problems arising in aquaculture operations this paper introduces a computational approach for solving non linear optimal control problems in which the objective function is a discontinuous function of the state we illustrate this approach using a dynamic model of shrimp farming in which shrimp are harvested at several intermediate times during the production cycle the problem is to choose the optimal harvesting times and corresponding optimal harvesting fractions the percentage of shrimp stock extracted to maximize total revenue the main difficulty with this problem is that the selling price of shrimp is modelled as a piecewise constant function of the average shrimp weight and thus the revenue function is discontinuous by performing a time scaling transformation and introducing a set of auxiliary binary variables we convert the shrimp harvesting problem into an equivalent optimization problem that has a smooth objective function we then use an exact penalty method to solve this equivalent problem we conclude the paper with a numerical example

on a comparison principle for delay coupled systems with nonlocal and nonlinear boundary conditions abstract this paper is concerned with delay coupled systems of parabolic equations with nonlocal and nonlinear boundary conditions for them a new and general comparison principle is established which is more general and useful than the existing results

uniform stability of switched linear systems extensions of lasalle s invariance principle this paper addresses the uniform stability of switched linear systems where uniformity refers to the convergence rate of the multiple solutions that one obtains as the switching signal ranges over a given set we provide a collection of results that can be viewed as extensions of lasalle s invariance principle to certain classes of switched linear systems using these results one can deduce asymptotic stability using multiple lyapunov functions whose lie derivatives are only negative semidefinite depending on the regularity assumptions placed on the switching signals one may be able to conclude just asymptotic stability or uniform exponential stability we show by counter example that the results obtained are tight

stability analysis of impulsive stochastic nonlinear systems this paper studies stochastic input to state stability and stochastic global stability for impulsive stochastic nonlinear systems using fixed dwell time condition and lyapunov based approach sufficient conditions are established for the stability properties two cases are studied 1 the case that the continuous dynamics is stable and 2 the case that the impulsive effects are stable furthermore the relations among different dwell time conditions are studied finally two examples are used to illustrate the developed theory

bounds on kolmogorov spectra for the navier stokes equations let u x t be a possibly weak solution of the navier stokes equations on all of r 3 or on the torus r 3 z 3 denoting the fourier transform by u fu the energy spectrum of u t is the spherical integral

critical strong feller regularity for markov solutions to the navier stokes equations abstract the main purpose of this paper is to show that markov solutions to the 3d navier stokes equations driven by gaussian noise have the strong feller property up to the critical topology given by the domain of the stokes operator to the power one fourth

on the multiplicity of the solution set of some nonlinear boundary value problems ii on considere le probleme non lineaire lu f u s 1 h dans u 0 sur soit h l 2 f est de classe c et que f 1 et n f n 1 n 1 alors il existe s 0 tel que pour tout s s 0 l equation a au moins 2 solutions si n est impair et 3 solutions si n est pair

existence of densities for the 3d navier stokes equations driven by gaussian noise we prove three results on the existence of densities for the laws of finite dimensional functionals of the solutions of the stochastic navier stokes equations in dimension 3 in particular under very mild assumptions on the noise we prove that finite dimensional projections of the solutions have densities with respect to the lebesgue measure which have some smoothness when measured in a besov space this is proved thanks to a new argument inspired by an idea introduced in fournier and printems 2010

on the h0 h stabilization of switched nonlinear systems via state dependent switching rule abstract this paper considers switching stabilization of some general nonlinear systems assuming certain properties of a convex linear combination of the nonlinear vector fields two ways of generating stabilizing switching signals are proposed i e the minimal rule and the generalized rule both based on a partition of the time state space the main theorems show that the resulting switched system is globally uniformly asymptotically stable and globally uniformly exponentially stable respectively it is shown that the stabilizing switching signals do not exhibit chattering i e two consecutive switching times are separated by a positive amount of time in addition under the generalized rule the switching signal does not exhibit zeno behavior accumulation of switching times in a finite time stability analysis is performed in terms of two measures so that the results can unify many different stability criteria such as lyapunov stability partial stability orbital stability and stability of an invariant set applications of the main results are shown by several examples and numerical simulations are performed to both illustrate and verify the stability analysis

computational method for a class of switched system optimal control problems we consider an optimal control problem with dynamics that switch between several subsystems of nonlinear differential equations each subsystem is assumed to satisfy a linear growth condition furthermore each subsystem switch is accompanied by an instantaneous change in the state these instantaneous changes called ldquostate jumpsrdquo are influenced by a set of control parameters that together with the subsystem switching times are decision variables to be selected optimally we show that an approximate solution for this optimal control problem can be computed by solving a sequence of conventional dynamic optimization problems existing optimization techniques can be used to solve each problem in this sequence a convergence result is also given to justify this approach

ergodic control of switching diffusions we study the ergodic control problem of switching diffusions representing a typical hybrid system that arises in numerous applications such as fault tolerant control systems flexible manufacturing systems etc under fairly general conditions we establish the existence of a stable nonrandomized markov policy which almost surely minimizes the pathwise long run average cost we then study the corresponding hamilton jacobi bellman hjb equation and establish the existence of a unique solution in a certain class using this we characterize the optimal policy as a minimizing selector of the hamiltonian associated with the hjb equations as an example we apply the results to a failure prone manufacturing system and obtain closed form solutions for the optimal policy

lyapunov like techniques for stochastic stability the purpose of this paper is to study the stabilizability problem for control stochastic nonlinear systems driven by a wiener process sufficient conditions for the existence of stabilizing feedback laws that are smooth except possibly at the equilibrium point of the system are provided by means of stochastic lyapunov like techniques the notion of dynamic asymptotic stability in probability of control stochastic differential systems is introduced and the stabilization by means of dynamic controllers is studied

uniqueness and blow up for a stochastic viscous dyadic model we consider the dyadic model with viscosity and additive gaussian noise as a simplified version of the stochastic navier stokes equations with the purpose of studying uniqueness and emergence of singularities we prove pathwise uniqueness and absence of blow up in the intermediate intensity of the non linearity morally corresponding to the 3d case and blow up for stronger intensity moreover blow up happens with probability one for regular initial data

optimal control of switched systems based on parameterization of the switching instants this paper presents a new approach for solving optimal control problems for switched systems we focus on problems in which a prespecified sequence of active subsystems is given for such problems we need to seek both the optimal switching instants and the optimal continuous inputs in order to search for the optimal switching instants the derivatives of the optimal cost with respect to the switching instants need to be known the most important contribution of the paper is a method which first transcribes an optimal control problem into an equivalent problem parameterized by the switching instants and then obtains the values of the derivatives based on the solution of a two point boundary value differential algebraic equation formed by the state costate stationarity equations the boundary and continuity conditions along with their differentiations this method is applied to general switched linear quadratic problems and an efficient method based on the solution of an initial value ordinary differential equation is developed an extension of the method is also applied to problems with internally forced switching examples are shown to illustrate the results in the paper

analysis of equilibrium states of markov solutions to the 3d navier stokes equations driven by additive noise we prove that every markov solution to the three dimensional navier stokes equations with periodic boundary conditions driven by additive gaussian noise is uniquely ergodic the convergence to the unique invariant measure is exponentially fast

optimal control of switched systems and its parallel optimization algorithm in this paper a class of optimal switching control problems is considered in which the mode sequence of active subsystems and the number of mode switchings are not pre specified and both the switching sequence and the control inputs are to be chosen such that the cost functional is minimized for solving this problem we discuss the necessary conditions for optimality and the construction method for suboptimal solutions and develop a few sufficient conditions of judgment on the optimal or suboptimal solutions of the switched system according to the sufficient conditions a parallel computational algorithm is constructed to find optimal or suboptimal solutions for illustration two examples are solved using the proposed algorithm

on nonlinear oscillations in a suspension bridge system in this paper we study nonlinear oscillations in a suspension bridge system governed by two coupled nonlinear partial differential equations by applying the leray schauder degree theory it is proved that the suspension bridge system has at least two solutions one is a near equilibrium oscillation and the other is a large amplitude oscillation

stability and input to state stability for stochastic systems and applications this paper is concerned with establishing some stability and input to state stability iss properties in terms of two different measures h0 and h for nonlinear systems of stochastic differential equations of ito type to analyze these properties classical lyapunov s method and a comparison principle are used to justify the proposed theoretical results applications to state estimating systems of luenberger type and feedforward or cascade systems enhanced with numerical examples and simulations are presented

stability of abstract linear switched impulsive differential equations linear impulsive switched differential equations in hilbert space are studied we propose a new method of stability investigation which is based in constructing an equivalent impulsive system without switching using operator valued and scalar lyapunov functions sufficient conditions for lyapunov stability of linear switched impulsive equations in a banach space are established the examples of studies of this class of equations with periodic switching are given

adaptive search algorithms for discrete stochastic optimization a smooth best response approach this paper considers simulation based optimization of the performance of a regime switching stochastic system over a finite set of feasible configurations inspired by the stochastic fictitious play learning rules in game theory we propose an adaptive random search algorithm that uses a smooth best response sampling strategy and tracks the set of global optima yet distributes the search so that most of the effort is spent on simulating the system performance at the global optima the algorithm responds properly to the random unpredictable jumps of the global optimum even when the observations data are temporally correlated as long as a weak law of large numbers holds numerical examples show that the proposed scheme yields faster convergence and superior efficiency for finite sample lengths compared with several existing random search and pure exploration methods in the literature

stochastic tamed 3d navier stokes equations existence uniqueness and ergodicity in this paper we prove the existence of a unique strong solution to a stochastic tamed 3d navier stokes equation in the whole space as well as in the periodic boundary case then we also study the feller property of solutions and prove the existence of invariant measures for the corresponding feller semigroup in the case of periodic conditions moreover in the case of periodic boundary and degenerated additive noise using the notion of asymptotic strong feller property proposed by hairer and mattingly ann math 164 993 1032 2006 we prove the uniqueness of invariant measures for the corresponding transition semigroup

mathematical analysis of dynamic models of suspension bridges in this paper we present some mathematical analysis of dynamic pde models of suspension bridges as proposed by lazer and mckenna our results are illustrated by numerical simulation with physical interpretation

global stabilisation for a class of switched high order stochastic nonlinear systems abstractthis paper is devoted to the problem of global stabili sation for a class of switched high order stochastic nonlinear systems under arbitrary switchings by extending the adding a power integrator technique and choosing an appropriate common lyapunov function a common state feedback controller is explicitly constructed to render the closed loop system globally asymptotically stable in probability the effectiveness of the proposed approach is demonstrated by a simulation example

on the stability and convergence of self tuning control virtual equivalent system approach this article presents a unified understanding and judgement of the stability and convergence of a general self tuning control stc system which consists of arbitrary control strategy arbitrary parameter estimation algorithm and a deterministic stochastic linear time invariant lti plant the necessary conditions required for the global stability and convergence of a general stc system are relaxed i e the convergence of parameter estimates is removed for both deterministic and stochastic stc schemes to reach this goal virtual equivalent system ves concept and methodology is adopted with the help of ves the original nonlinear dominant nonlinear in structure problem is converted to a linear dominant linear in structure problem the results developed in this article show that stc systems are stable and convergent for the abundance of control strategies and parameter estimation algorithms which will provide great flexibility in the applications of stc

dwell time controllers for stochastic systems with switching markov chain we study the problem of feedback stabilization of a family of nonlinear stochastic systems with switching mechanism modeled by a markov chain we introduce a novel notion of stability under switching which guarantees a given probability that the trajectories of the system hit some target set in finite time and remain thereinafter our main contribution is to prove that if the expectation of the time between two consecutive switching dwell time is sufficiently large then the system is stable under switching with guaranteed probability we illustrate this methodology by constructing measurement feedback controllers for a wide class of stochastic nonlinear systems

markov inequality rule for switching among time optimal controllers in a multiple vehicle intercept problem abstract in this paper a markov inequality based switching rule is proposed to switch among numerically computed time optimal controllers in a multiple vehicle intercept problem each controller is optimal for the intercept of a single vehicle i e for the segment of the complete time varying multiple vehicle target set the switching rule guarantees that after every switch the time to the target set is shorter with a certain predefined probability furthermore the rule guarantees that the target set is reached after a finite number of switches and the rule scales well with the number of vehicles i e the segments covering the target set the problem and results are illustrated by a numerical example

uniform input to state stability for switched and time varying impulsive systems we provide a lyapunov function based method for establishing different types of uniform input to state stability iss for time varying impulsive systems the method generalizes to impulsive systems with inputs the well established philosophy of assessing the stability of a system by reducing the problem to that of the stability of a scalar system given by the evolution of the lyapunov function on the system trajectories this reduction is performed in such a way that the resulting scalar system has no inputs novel sufficient conditions for iss are provided which generalize existing results for time invariant and time varying switched and nonswitched impulsive and nonimpulsive systems in several directions

brief paper on optimal control of non autonomous switched systems with a fixed mode sequence we consider differentiability with respect to the switch times of the value function of an optimal control problem for a non autonomous switched system the control variables are the switch times between the modes and the input in each mode we provide a method to compute the derivative of the cost function given a nominal input then we view the optimal control problem as a parametrized optimization problem in which the switch times are the parameters and the optimization is over the set of feasible inputs of each mode from this point of view we provide conditions under which the continuity and differentiability of the optimal value function that is the cost function optimized over the inputs can be guaranteed

optimal practical stabilization and controllability of systems with markovian jumps abstract classical lyapunov theory provides only qualitative type of information from the concept of stability if one is interested not only in the qualitative behavior but also in the quantitative data such as specific trajectory bounds and specific transient behavior then practical stability is very useful in this paper the practical stabilization is investigated for continuous time nonlinear systems with markovian jumps using vector lyapunov methods the stabilization is posed in terms of the vector lyapunov like function techniques which together with comparison principle allows us to compute the stabilizing controller sufficient conditions are established for practical stability criteria in the p th mean under less restrictive conditions compared to the lyapunov stability for nonlinear systems with markovian jump perturbations finally controllability and optimal practical stabilization based on the hjb equation are established two numerical examples are given to show the fruitfulness of our results

symbolic models for stochastic switched systems stochastic switched systems are a relevant class of stochastic hybrid systems with probabilistic evolution over a continuous domain and control dependent discrete dynamics over a finite set of modes in the past few years several different techniques have been developed to assist in the stability analysis of stochastic switched systems however more complex and challenging objectives related to the verification of and the controller synthesis for logic specifications have not been formally investigated for this class of systems as of yet with logic specifications we mean properties expressed as formulae in linear temporal logic or as automata on infinite strings this paper addresses these complex objectives by constructively deriving approximately equivalent bisimilar symbolic models of stochastic switched systems more precisely this paper provides two different symbolic abstraction techniques one requires state space discretization but the other one does not require any space discretization which can be potentially more efficient than the first one when dealing with higher dimensional stochastic switched systems both techniques provide finite symbolic models that are approximately bisimilar to stochastic switched systems under some stability assumptions on the concrete model this allows formally synthesizing controllers switching signals that are valid for the concrete system over the finite symbolic model by means of mature automata theoretic techniques in the literature the effectiveness of the results are illustrated by synthesizing switching signals enforcing logic specifications for two case studies including temperature control of a six room building

common lyapunov functions for families of commuting nonlinear systems abstract we present constructions of a local and global common lyapunov function for a finite family of pairwise commuting globally asymptotically stable nonlinear systems the constructions are based on an iterative procedure which at each step invokes a converse lyapunov theorem for one of the individual systems our results extend a previously available one which relies on exponential stability of the vector fields

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

class kl estimates and input to state stability analysis of impulsive switched systems abstract in this paper we investigate input to state stability of impulsive switched systems the goal is to bridge two apparently different but both useful stability notions input to state stability and stability in terms of two measures in the hybrid systems setting based on two class kl function estimates and a comparison theorem for impulsive differential equations two sets of sufficient lyapunov type conditions for input to state stability in terms of two measures are obtained for impulsive switched systems these conditions exploit some nonlinear integral constraints in terms of generalized dwell time conditions to balance the continuous dynamics and impulsive dynamics so that input to state stability is achieved despite possible instability of individual continuous subsystems or destabilizing impulsive effects an illustrative example is presented together with numerical simulations to demonstrate the main results

exponential ergodicity for stochastic burgers and 2d navier stokes equations abstract it is shown that transition measures of the stochastic navier stokes equation in 2 d converge exponentially fast to the corresponding invariant measures in the distance of total variation as a corollary we obtain the existence of spectral gap for a related semigroup obtained by a sort of ground state transformation analogous results are proved for the stochastic burgers equation

instability of stochastic switched systems abstract the instability problem of stochastic switched systems is investigated in this paper definitions of instability are given in the forms of instability in probability m th instability moment exponential instability and almost sure exponential instability by the aid of dynkin s formula ito s formula and strong law of large numbers the criteria on instability of stochastic switched systems under arbitrary switching are established based on lyapunov like techniques simulation examples are presented to illustrate the validity of the results

distributed tracking of correlated equilibria in regime switching noncooperative games we consider a class of regime switching noncooperative repeated games where agents exchange information over a graph the parameters of the game number of agents payoffs information exchange graph evolve randomly over time according to a markov chain we present a regret based stochastic approximation algorithm with constant step size that prescribes how individual agents update their randomized strategies over time we show that if the markov chain jump changes on the same timescale as the adaptation rate of the stochastic approximation algorithm and agents independently follow this algorithm their collective behavior is agile in tracking the time varying convex polytope of correlated equilibria the analysis is carried out using weak convergence methods and lyapunov stability of switched markovian differential inclusions

multiple periodic solutions for suspension bridge systems abstract this paper studies the existence of multiple periodic oscillations of the suspension bridge system governed by the coupled nonlinear beam and wave equations by using the degree theory it is proved that the system has at least three periodic solutions

brief paper optimal switching instants for a switched capacitor dc dc power converter we consider a switched capacitor dc dc power converter with variable switching instants the determination of optimal switching instants giving low output ripple and strong load regulation is posed as a non smooth dynamic optimization problem by introducing a set of auxiliary differential equations and applying a time scaling transformation we formulate an equivalent optimization problem with semi infinite constraints existing algorithms can be applied to solve this smooth semi infinite optimization problem the existence of an optimal solution is also established for illustration the optimal switching instants for a practical switched capacitor dc dc power converter are determined using this approach

exponential mixing for the 3d stochastic navier stokes equations we study the navier stokes equations in dimension 3 ns3d driven by a noise which is white in time we establish that if the noise is at the same time sufficiently smooth and non degenerate in space then the weak solutions converge exponentially fast to equilibrium

martingale and stationary solutions for stochastic navier stokes equations we prove the existence of martingale solutions and of stationary solutions of stochastic navier stokes equations under very general hypotheses on the diffusion term the stationary martingale solutions yield the existence of invariant measures when the transition semigroup is well defined the results are obtained by a new method of compactness

markov selections for the 3d stochastic navier stokes equations we investigate the markov property and the continuity with respect to the initial conditions strong feller property for the solutions to the navier stokes equations forced by an additive noise first we prove by means of an abstract selection principle that there are markov solutions to the navier stokes equations due to the lack of continuity of solutions in the space of finite energy the markov property holds almost everywhere in time then depending on the regularity of the noise we prove that any markov solution has the strong feller property for regular initial conditions we give also a few consequences of these facts together with a new sufficient condition for well posedness

stability analysis of deterministic and stochastic switched systems via a comparison principle and multiple lyapunov functions this paper presents a general framework for analyzing stability of nonlinear switched systems by combining the method of multiple lyapunov functions with a suitably adapted comparison principle in the context of stability in terms of two measures for deterministic switched systems this leads to a unification of representative existing results and an improvement upon the current scope of the method of multiple lyapunov functions for switched systems perturbed by white noise we develop new results which may be viewed as natural stochastic counterparts of the deterministic ones in particular we study stability of deterministic and stochastic switched systems under average dwell time switching

a model for stochastic hybrid systems with application to communication networks abstract we propose a model for stochastic hybrid systems shss where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuous time markov chains however the rate at which transitions occur is allowed to depend both on the continuous and the discrete states of the shs based on results available for piecewise deterministic markov process pdps we provide a formula for the extended generator of the shs which can be used to compute expectations and the overall distribution of the state as an application we construct a stochastic model for on off tcp flows that considers both the congestion avoidance and slow start modes and takes directly into account the distribution of the number of bytes transmitted using the tools derived for shss we model the dynamics of the moments of the sending rate by an infinite system of odes which can be truncated to obtain an approximate finite dimensional model this model shows that for transfer size distributions reported in the literature the standard deviation of the sending rate is much larger than its average moreover the later seems to vary little with the probability of packet drop this has significant implications for the design of congestion control mechanisms