configuration flatness of lagrangian control systems with fewer controls than degrees of freedom abstract a lagrangian control system is said to be configuration flat if its states are determined by configuration flat outputs depending on configuration variables only this paper gives a necessary condition and two types of sufficient conditions for lagrangian control systems with n degrees of freedom and m controls with m n to be configuration flat and further makes a remark on the choice of output variables for configuration flatness two examples are given in which the sufficient conditions are utilized for finding configuration flat outputs

parameter estimation of delay dynamical system from a scalar time series under external noise we introduce an adaptive learning rules for estimating all unknown parameters of delay dynamical system using a scalar time series sufficient condition for synchronization is derived using krasovskii lyapunov theory this scheme is highly applicable in secure communication since multiple messages can be transmitted through multiple parameter modulations one of the advantage of this method is that parameter estimation is also possible even when only one time series of the transmitter is available we present numerical examples for mackey glass system with periodic delay time which are used to illustrate the validity of this scheme the corresponding numerical results and the effect of external noise are also studied

controllability of a planar body with unilateral thrusters investigates the minimal number of unilateral thrusters required for different versions of nonlinear controllability of a planar rigid body for one to three unilateral thrusters one gets a new property with each additional thruster one thruster suffices for small time accessibility on the body s state space tse 2 two thrusters suffice for global controllability on tse 2 and three thrusters suffice for small time local controllability at zero velocity states

colored noise induced chaotic array synchronization the effect of a time correlated gaussian noise on one dimensional arrays consisting of diffusively coupled chaotic cells is analyzed a resonance effect between the time scale of the chaotic attractor and the colored gaussian noise has been found as well depending on the number of cells coupling and noise strength an improvement of the synchronization or a poor synchronization between cells within the array can occur for some values of the time correlation these nonlinear cooperative effects are studied in terms of a linear stability analysis around the uniform synchronized behavior

simple mechanical control systems with constraints and symmetry we develop tools for studying the control of underactuated mechanical systems that evolve on a configuration space with a principal fiber bundle structure taking the viewpoint of affine connection control systems we derive reduced formulations of the levi civita and the nonholonomic affine connections along with the symmetric product in the presence of symmetries and nonholonomic constraints we note that there are naturally two kinds of connections to be considered here affine and principal connections leading to what we term a connection within a connection these results are then used to describe controllability tests that are specialized to simple underactuated mechanical systems on principal fiber bundles including the notion of fiber configuration controllability we present examples of the use of these tools in studying the planar rigid body with a variable direction vectored thruster and the snakeboard robot

ifra properties of some markov jump processes with general state space consider a stochastically monotone increasing regular markov jump process on a partially ordered measurable space x it is shown that the first passage time to any upper set u is ifra a conjecture of brown and chaganty brown m chaganty n r 1983 on the first passage time distribution for a class of markov chains ann probab 11 1000 1008 is verified and results of brown and chaganty brown m chaganty n r 1983 on the first passage time distribution for a class of markov chains ann probab 11 1000 1008 and of ross ross s m 1981 generalized poisson shock models ann probab 9 896 898 are extended

stochastic dynamics of the cubic map a study of noise induced transition phenomena the effects of finite amplitude additive noise on the dynamics generated by a one dimensional two parameter cubic map are considered the underlying deterministic system exhibits bistability and hysteresis and noise induced processes associated with these phenomena are studied if a bounded noise source is applied to this system trajectories may be confined to a finite region mechanisms are given for the merging transitions between different parts of this region and the eventual escape from it as the noise level is increased the noisy dynamics is also represented by an integral evolution operator with an equilibrium density function with finite support the operator s spectrum is determined as a function of map parameters and noise amplitude such noisy one dimensional maps can provide models for the study of noise induced phenomena described by stochastic differential equations

average trajectories and fluctuations from noisy nonlinear maps the average trajectories and fluctuations around them resulting from an ensemble of noisy nonlinear maps are analyzed the bifurcation diagram for the average value obtained from the computer simulation of noisy maps ensemble is discussed first then a deterministic average equation of motion describing in an approximate way the time evolution of the average value and of the variance is analyzed numerically this equation predicts the existence of the bifurcation gap and of the exceptional attractors for special initial points the scaling properties of the average value and of the variance are obtained with the help of this equation

multidimensional ifra processes abstract two types of multidimensional processes are defined the first of these generalizes a univariate ifra process due to ross and relates to a multivariate concept of ifra due to esary and marshall the second of these relates to a multivariate concept of ifra due to the present authors decompositions for multistate monotone structure functions are given and behavior of nonincreasing stochastic processes such as those given above is analyzed various coherence assumptions for multistate systems are also analyzed

intrinsic observer based stabilization for simple mechanical systems on lie groups this paper presents a dynamic observer for a class of simple mechanical systems on lie groups this observer provides velocity estimates based on configuration measurements the observer is textit intrinsic so its performance does not depend on the choice of coordinates and it is textit coordinate free in the sense that the equations may be written explicitly without specifying coordinates for the configuration space our main result is obtained by specializing a previous result of aghannan and rouchon concerning velocity estimation of simple mechanical systems on riemannian manifolds to such systems on lie groups this specialization is nonobvious and extremely powerful further we extend the original result to include velocity dependent external forces this estimator combined with a coordinate free formulation of passivity based state feedback control allows the construction of a coordinate free intrinsic dynamic output feedback compensator this is to our knowledge the first time such a result has been reported explicit expressions are computed for the lie groups so 3 and se 3 allowing easy specialization to practical problems of rigid body motion the theory is illustrated via application to the axisymmetric top and to a six degrees of freedom microelectromechanical system

on mechanical control systems with nonholonomic constraints and symmetries abstract this paper presents a computationally efficient method for deriving coordinate representations for the equations of motion and the affine connection describing a class of lagrangian systems we consider mechanical systems endowed with symmetries and subject to nonholonomic constraints and external forces the method is demonstrated on two robotic locomotion mechanisms known as the snakeboard and the roller racer the resulting coordinate representations are compact and lead to straightforward proofs of various controllability results

multivariate new better than used distributions a general theory of multivariate new better than used nbu distributions is developed using the general theory some multivariate nbu conditions are introduced and studied some of the results apply as well to multivariate increasing hazard rate average ihra and exponential distributions proofs of some related well known implications are simplified

brief analysis of exclusively kinetic two link underactuated mechanical systems analysis of exclusively kinetic two link underactuated mechanical systems is undertaken in this paper it is first shown that such systems are not full state feedback linearizable around any equilibrium point also the equilibrium points for which the system is small time locally controllable stlc is at most a one dimensional submanifold a concept less restrictive than stlc termed the small time local output controllability stloc is introduced the satisfaction of which guarantees that a chosen configuration output can be controlled at its desired value it is shown that the class of systems considered is stloc if the inertial coupling between the input and output is nonzero also in such a case the system is nonminimum phase an example section illustrates all the results presented

the onsager machlup theory for markov processes with discrete time parameter a characterisation of the detailed balance the onsager machlup om function is introduced for a spatially uniform system evolving in accordance with a discrete time markovian law circulation of probability flow is expressed in terms of the om function equivalence is established between the two conditions circulation identical to 0 and the fulfilment of the detailed balance

correlation anti correlation transition by state dependent poisson noise noise may induce some degrees of order in many biological and complex systems we present an example of a noise dependent transition from correlation to anti correlation of the states of a bivariate system coupled by state dependent poisson noises by varying the degree of dependence of the rate of jumps on the other variable the system undergoes different degrees of correlation from independence to perfect correlation which in this case coincides with perfect synchronization in the limit of the deterministic periodic case

from nonlinear to hamiltonian via feedback mechanical control systems are an especially interesting and important class of nonlinear control systems they possess a rich mathematical structure and yet physical considerations are extremely important for the solution of a large class of control problems we broaden the applicability of design methodologies developed for mechanical control systems by rendering nonlinear control systems mechanical by a proper choice of feedback in particular we characterize which control systems can be transformed to hamiltonian control systems by a feedback transformation

the influence of noise on the logistic model the behavior of the logistic system which is generated by the functionf x ax 1 x changes in an interesting way if it is perturbed by external noise it turns out that the chaotic behavior which was predicted by li and yorke for orbits of period 3 becomes visible and that a sequence of mergence transitions occurs at the critical parameter the change of the invariant probability density and the lyapunov exponents are examined numerically the power spectrum for the period 3 orbit for different fluctuations is calculated and a recursion formula for the time evolution of the probability density is presented as a discrete time analog of a chapman kolmogorov equation

simple mechanical control systems with constraints we apply some recently developed control theoretic techniques to the analysis of a class of mechanical systems with constraints certain simple aspects of the theory of affine connections play an important part in our presentation the necessary background is presented in order to illustrate how the methods may be applied the bulk of this paper is devoted to a detailed analysis of some examples of nonholonomic mechanical control systems we look at the heisenberg system the upright rolling disk the roller racer and the snakeboard

tracking for fully actuated mechanical systems a geometric framework we present a general framework for the control of lagrangian systems with as many inputs as degrees of freedom relying on the geometry of mechanical systems on manifolds we propose a design algorithm for the tracking problem the notions of error function and transport map lead to a proper definition of configuration and velocity error these are the crucial ingredients in designing a proportional derivative feedback and feedforward controller the proposed approach includes as special cases a variety of results on control of manipulators pointing devices and autonomous vehicles our design provides particular insight into both aerospace and underwater applications where the configuration manifold is a lie group

stabilization of relative equilibria for underactuated systems on riemannian manifolds steady motions of mechanical systems with symmetry are stabilized via a potential shaping and damping control a general methodology based on riemannian geometry tools provides exponential stabilization over the full phase space

controllability of a class of underactuated mechanical systems with symmetry in this paper we develop results based on geometric mechanics to study the controllability of a class of controlled under actuated left invariant mechanical systems on lie groups we exploit the invariance of the controlled nonlinear dynamics to the group action symmetry to derive a set of reduced dynamics for the system we first present sufficient conditions for the controllability of the reduced dynamics we prove conditions boundedness of coadjoint orbits and existence of a radially unbounded lyapunov function under which the drift vector field of the reduced system is weakly positively poisson stable wpps the wpps nature of the drift vector field along with the lie algebra rank condition is used to show controllability of the reduced system we then extend these results to the unreduced dynamics considering separately the cases when the symmetry group is compact and noncompact in the noncompact case under further assumptions of equilibrium controllability sufficient conditions for controllability of the unreduced dynamics are derived jetpuck hovercraft and underwater vehicles are used as mechanical systems to motivate our work and illustrate our theoretical results

intermittency in the presence of noise we analyse iterations of maps on an interval with an added noise term in the neighbourhood of an intermittency threshold we rigorously derive a universal scaling function for the laminar time expressed as a function of the distance from the threshold and the variance of the noise

an intrinsic observer for a class of lagrangian systems we propose a new design method of asymptotic observers for a class of nonlinear mechanical systems lagrangian systems with configuration position measurements our main contribution is to introduce a state position and velocity observer that is invariant under any changes of the configuration coordinates the observer dynamics equations as the euler lagrange equations are intrinsic the design method uses the riemannian structure defined by the kinetic energy on the configuration manifold the local convergence is proved by showing that the jacobian of the observer dynamics is negative definite contraction for a particular metric defined on the state space a metric derived from the kinetic energy and the observer gains from a practical point of view such intrinsic observers can be approximated when the estimated configuration is close to the true one by an explicit set of differential equations involving the riemannian curvature tensor these equations can be automatically generated via symbolic differentiations of the metric and potential up to order two numerical simulations for the ball and beam system an example where the scalar curvature is always negative show the effectiveness of such approximation when the measured positions are noisy or include high frequency neglected dynamics

stability of a stochastic two dimensional non hamiltonian system we study the top lyapunov exponent of the response of a two dimensional non hamiltonian system driven by additive white noise the origin is not a fixed point for the system however there is an invariant measure for the one point motion of the system in this paper we consider the stability of the two point motion by khasminskii s method of linearization along trajectories the specific system we consider is the third order truncated normal form of the unfolding of a hopf bifurcation we show that in the small noise limit the top lyapunov exponent always approaches zero from below and is thus negative for noise sufficiently small we also show that there exist open sets of parameters for which the top lyapunov exponent is positive thus the two point motion can be either stable or unstable while the stationary density that describes the one point motion always exists

computing the topological entropy of maps we give an algorithm for determining the topological entropy of a unimodal map of the interval given its kneading sequence we also show that this algorithm converges exponentially in the number of letters of the kneading sequence

on the first failure time of dependent multicomponent reliability systems in this paper multicomponent reliability systems are considered where component failure and repair completion rates depend on the state ages and current repair durations of the other components this is a generalization of a model of ross ross s m 1984 a model in which component failure rates depend on working set naval res logist quart 31 297 300 sufficient conditions on the sets of rates which imply stochastic ordering between first failure times of two such systems are found sufficient conditions on the rates which imply that the first failure time of such a system is new better than used nbu are given some results of barlow and proschan barlow r e proschan f 1976 theory of maintained systems distribution of time to first system failure math oper res 1 32 42 chiang and niu chiang d t niu s c 1980 on the distribution of time to first system failure j appl probab 17 481 489 and ross ross s m 1976 on the time to first failure in multicomponent exponen

stabilization of linear systems by noise it is proved that the biggest lyapunov number lambda max of the system dot x a f t x where a is a fixed d times d matrix and f t is a zero mean strictly stationary matrix valued stochastic process satisfies 1 d trace a leqq lambda max on the other hand for each varepsilon 0 there is a process f t for which lambda max leqq 1 d trace a varepsilon in particular the system dot x ax can be stabilized by zero mean stationary parameter noise if and only if trace a 0 the stabilization can be accomplished by a one dimensional noise source the results carry over to the case where a is a stationary process they are also true for f t white noise

configuration controllability of simple mechanical control systems in this paper we present a definition of configuration controllability for mechanical systems whose lagrangian is kinetic energy with respect to a riemannian metric minus potential energy a computable test for this new version of controllability is derived this condition involves an object that we call the symmetric product of particular interest is a definition of equilibrium controllability for which we are able to derive computable sufficient conditions examples illustrate the theory

controllability and motion algorithms for underactuated lagrangian systems on lie groups we provide controllability tests and motion control algorithms for underactuated mechanical control systems on lie groups with lagrangian equal to kinetic energy examples include satellite and underwater vehicle control systems with the number of control inputs less than the dimension of the configuration space local controllability properties of these systems are characterized and two algebraic tests are derived in terms of the symmetric product and the lie bracket of the input vector fields perturbation theory is applied to compute approximate solutions for the system under small amplitude forcing in phase signals play a crucial role in achieving motion along symmetric product directions motion control algorithms are then designed to solve problems of point to point reconfiguration static interpolation and exponential stabilization we illustrate the theoretical results and the algorithms with applications to models of planar rigid bodies satellites and underwater vehicles

almost global tracking of simple mechanical systems on a general class of lie groups we present a general intrinsic tracking controller design for fully actuated simple mechanical systems when the configuration space is one of a general class of lie groups we first express a state feedback controller in terms of a function the error function satisfying certain regularity conditions if an error function can be found then a general smooth and bounded reference trajectory may be tracked asymptotically from almost every initial condition with locally exponential convergence asymptotic convergence from almost every initial condition is referred to as almost global asymptotic stability error functions may be shown to exist on any compact lie group or any lie group diffeomorphic to the product of a compact lie group and r sup n this covers many cases of practical interest such as so n se n their subgroups and direct products we show here that for compact lie groups the dynamic configuration feedback controller obtained by composing the full state feedback law with an exponentially convergent velocity observer is also almost globally asymptotically stable with respect to the tracking error we emphasize that no invariance is needed for these results however for the special case where the kinetic energy is left invariant we show that the explicit expression of these controllers does not require coordinates on the lie group the controller constructions are demonstrated on so 3 and simulated for the axi symmetric top results show excellent performance

stability measures in metastable states with gaussian colored noise we present a study of the escape time from a metastable state of an overdamped brownian particle in the presence of colored noise generated by ornstein uhlenbeck process we analyze the role of the correlation time on the enhancement of the mean first passage time through a potential barrier and on the behavior of the mean growth rate coefficient as a function of the noise intensity we observe the noise enhanced stability effect for all the initial unstable states used and for all values of the correlation time tau c investigated we can distinguish two dynamical regimes characterized by weak and strong correlated noises depending on the value of tau c with respect to the relaxation time of the system

internal fluctuations period doubling and chemical chaos the effects of internal molecular fluctuations on period doubling bifurcations and chaotic band merging are studied in a well stirred reactive chemical system where spatial degrees of freedom play no role the calculations are carried out using a stochastic model based on reactive lattice gas cellular automata molecular fluctuations arising from reactive collisions are incorporated in the model and the mass action rate equations are recovered in the mean field limit large system sizes can be studied and permit the investigation of the internal noise scaling structure in the periodic and chaotic regimes for the willamowski r ossler system the noise scaling exponent is consistent with that found for one dimensional quadratic maps subject to external noise the model provides a means to study small non equilibrium reacting systems where fluctuations may not be neglected

brief steering of a class of nonholonomic systems with drift terms in the present paper nonholonomic systems with drift terms are studied the discussion is focused on a class of lagrangian systems with a cyclic coordinate we present an approach to open loop path planning in which the system evolution is studied on manifolds of dimension equal to the number of control inputs a control procedure is derived and it is applied to the planar diver

modified kramers formulas for the decay rate in agreement with dynamical modeling abstract accuracy of the kramers approximate formulas for the thermal decay rate of the metastable state is studied for the anharmonic shapes of the potential pocket and the barrier this is done by the comparison with the quasistationary rate resulting from the dynamical modeling disagreement between the kramers rate and the dynamical one is shown to reach 15 in the cases when much better agreement is expected corrections to the kramers formulas accounting for the higher derivatives of the potential are obtained the small parameters are the ratios of the thermal energy to the stiffnesses at the extremes of the potential the distance between the potential barrier and the absorptive border is accounted for as well this corrected kramers rate is demonstrated to agree with the dynamical rate typically within 2 probably the most interesting result is that despite the corrections are derived in the case of the overdamped brownian motion the above 2 agreement holds even in the case of medium friction

small random perturbations of dynamical systems and the definition of attractors the strange attractors plotted by computers and seen in physical experiments do not necessarily have an open basin of attraction in view of this we study a new definition of attractors based on ideas of conley we argue that the attractors observed in the presence of small random perturbations correspond to this new definition

synchronization of random linear maps abstract we study synchronization of random one dimensional linear maps for which the lyapunov exponent can be calculated exactly certain aspects of the dynamics of these maps are explained using their relation with a random walk we confirm that the lyapunov exponent changes sign at the complete synchronization transition we also consider partial synchronization of nonidentical systems it turns out that the way partial synchronization manifests depends on the type of differences in lyapunov exponent or in contraction points between the systems the crossover from partial to complete synchronization is also examined

noisy one dimensional maps near a crisis ii general uncorrelated weak noise the escape rate for one dimensional noisy maps near a crisis is investigated a previously introduced perturbation theory is extended to very general kinds of weak uncorrelated noise including multiplicative white noise as a special case for single humped maps near the boundary crisis at fully developed chaos an asymptotically exact scaling law for the rate is derived it predicts that transient chaos is stabilized by basically any noise of appropriate strength provided the maximum of the map is of sufficiently large order a simple heuristic explanation of this effect is given the escape rate is discussed in detail for noise distributions of levy dichotomous and exponential type in the latter case the rate is dominated by an exponentially leading arrhenius factor in the deep precritical regime however the preexponential factor may still depend more strongly than any power law on the noise strength

a simple intrinsic reduced observer for geodesic flow aghannan and rouchon proposed a new design method of asymptotic observers for a class of nonlinear mechanical systems lagrangian systems with configuration position measurements the position and velocity observer is based on the riemannian structure of the configuration manifold endowed with the kinetic energy metric and is intrinsic they proved local convergence when the system is conservative we propose an intrinsic reduced order velocity observer based on the jacobi metric which can be initialized such that it converges exponentially for any initial true velocity for non conservative systems the observer can be used as a complement to the one of aghannan and rouchon more generally the reduced observer provides velocity estimation for geodesic flow with position measurements thus it can be formally used as a fluid flow soft sensor in the case of a perfect incompressible fluid when the curvature is negative in all planes the geodesic flow is sensitive to initial conditions surprisingly in this case we have global exponential convergence and the more unstable the flow is faster is the convergence

characterization of gradient control systems given a general nonlinear affine control system with outputs and a torsion free affine connection defined on its state space we investigate the gradient realization problem we give necessary and sufficient conditions under which the control system can be written as a gradient control system corresponding to some pseudo riemannian metric whose levi civita connection is equal to the given affine connection the results rely on a suitable notion of compatibility of the system with respect to the given affine connection and on the output behavior of the prolonged system and the gradient extension the symmetric product associated with an affine connection plays a key role throughout the discussion

stochastic bifurcations and coherencelike resonance in a self sustained bistable noisy oscillator we investigate the influence of additive gaussian white noise on two different bistable self sustained oscillators duffing van der pol oscillator with hard excitation and a model of a synthetic genetic oscillator in the deterministic case both oscillators are characterized with a coexistence of a stable limit cycle and a stable equilibrium state we find that under the influence of noise their dynamics can be well characterized through the concept of stochastic bifurcation consisting in a qualitative change of the stationary amplitude distribution for the duffing van der pol oscillator analytical results obtained for a quasiharmonic approach are compared with the result of direct computer simulations in particular we show that the dynamics is different for isochronous and anisochronous systems moreover we find that the increase of noise intensity in the isochronous regime leads to a narrowing of the spectral line this effect is similar to coherence resonance however in the case of anisochronous systems this effect breaks down and a new phenomenon anisochronous based stochastic bifurcation occurs

the asymptotic stability of a noisy non linear oscillator abstract the purpose of this work is to obtain an approximation for the top lyapunov exponent the exponential growth rate of the response of a single well kramers oscillator driven by either a multiplicative or an additive white noise process to this end we consider the equations of motion as dissipative and noisy perturbations of a two dimensional hamiltonian system a perturbation approach is used to obtain explicit expressions for the exponent in the presence of small intensity noise and small dissipation we show analytically that the top lyapunov exponent is positive and for small values of noise intensity e and dissipation e the exponent grows in proportion with e1 3

constructive effects of noise in homoclinic chaotic systems many chaotic oscillators have coherent phase dynamics but strong fluctuations in the amplitudes at variance with such a behavior homoclinic chaos is characterized by quite regular spikes but strong fluctuation in their time intervals due to the chaotic recurrence to a saddle point we study influences of noise on homoclinic chaos we demonstrate both numerically and experimentally on a co2 laser various constructive effects of noise including coherence resonance noise induced synchronization in uncoupled systems and noiseenhanced phase synchronization deterministic resonance with respect to signal frequency and stochastic resonance versus noise intensity in response to weak signals the peculiar sensitivity of the system along the weak unstable manifold of the saddle point underlines the unified mechanism of these nontrivial and constructive noise induced phenomena

on nonlinear controllability and series expansions for lagrangian systems with dissipative forces this paper presents series expansions and nonlinear controllability results for lagrangian systems subject to dissipative forces the treatment relies on the assumption of dissipative forces of linear isotropic nature the approach is based on the affine connection formalism for lagrangian control systems and on the homogeneity property of all relevant vector fields

controlled lagrangians and the stabilization of mechanical systems i the first matching theorem we develop a method for the stabilization of mechanical systems with symmetry based on the technique of controlled lagrangians the procedure involves making structured modifications to the lagrangian for the uncontrolled system thereby constructing the controlled lagrangian the euler lagrange equations derived from the controlled lagrangian describe the closed loop system where new terms in these equations are identified with control forces since the controlled system is lagrangian by construction energy methods can be used to find control gains that yield closed loop stability we use kinetic shaping to preserve symmetry and only stabilize systems module the symmetry group the procedure is demonstrated for several underactuated balance problems including the stabilization of an inverted planar pendulum on a cart moving on a line and an inverted spherical pendulum on a cart moving in the plane

chaos noise and synchronization reconsidered in a recent paper maritan and banavar phys rev lett 72 1451 1994 reported the synchronization of identical chaotic systems by additive noise we relate such a synchronization to the maximum lyapunov exponent of a single system and discuss the underlying mechanisms of the effect in the case of the lorenz equations the nonvanishing mean of the noise mimics a parameter change leading to synchronization for the logistic map a state dependence of the fluctuations is induced by the boundary conditions

proximity to periodic windows in bifurcation diagrams as a gateway to coherence resonance in chaotic systems we show that chaotic states situated in the proximity of periodic windows in bifurcation diagrams are eligible for the observation of coherence resonance in particular additive gaussian noise of appropriate intensity can enhance the temporal order in such chaotic states in a resonant manner results obtained for the logistic map and the lorenz equations suggest that the presented mechanism of coherence resonance is valid beyond particularities of individual systems we attribute the findings to the increasing attraction of imminent periodic orbits and the ability of noise to anticipate their existence and use a modified wavelet analysis to support our arguments

nbu processes with general state space waiting times for many kinds of events can be represented as first passage times for appropriate stochastic processes in some applications the most natural stochastic process is multidimensional in other applications it may be more natural to consider a stochastic process which takes on values in a more general space in this paper we consider new better than used nbu stochastic processes on partially ordered separable banach spaces that is processes which have nbu first passage times to closed upper sets various equivalent conditions for a process to be nbu are derived some of the results can be used also to characterize increasing hazard rate average ihra processes examples of such processes include processes with shocks and recovery and processes with random repair times some applications in reliability theory and in other areas of probability are given

relationship between directed percolation and the synchronization transition in spatially extended systems we study the nature of the synchronization transition in spatially extended systems by discussing a simple stochastic model an analytic argument is put forward showing that in the limit of discontinuous processes the transition belongs to the directed percolation dp universality class the analysis is complemented by a detailed investigation of the dependence of the first passage time for the amplitude of the difference field on the adopted threshold we find the existence of a critical threshold separating the regime controlled by linear mechanisms from that controlled by collective phenomena as a result of this analysis we conclude that the synchronization transition belongs to the dp class also in continuous models the conclusions are supported by numerical checks on coupled map lattices too

decompositions for control systems on manifolds with an affine connection in this letter we present a decomposition for control systems whose drift vector field is the geodesic spray associated with an affine connection with the geometric insight gained with this decomposition we are able to easily prove some special results for this class of control systems examples illustrate the theory

noise induced unstable dimension variability and transition to chaos in random dynamical systems results are reported concerning the transition to chaos in random dynamical systems in particular situations are considered where a periodic attractor coexists with a nonattracting chaotic saddle which can be expected in any periodic window of a nonlinear dynamical system under noise the asymptotic attractor of the system can become chaotic as characterized by the appearance of a positive lyapunov exponent generic features of the transition include the following 1 the noisy chaotic attractor is necessarily nonhyperbolic as there are periodic orbits embedded in it with distinct numbers of unstable directions unstable dimension variability and this nonhyperbolicity develops as soon as the attractor becomes chaotic 2 for systems described by differential equations the unstable dimension variability destroys the neutral direction of the flow in the sense that there is no longer a zero lyapunov exponent after the noisy attractor becomes chaotic and 3 the largest lyapunov exponent becomes positive from zero in a continuous manner and its scaling with the variation of the noise amplitude is algebraic formulas for the scaling exponent are derived in all dimensions numerical support using both low and high dimensional systems is provided

positive lyapunov exponents in the kramers oscillator the maximum lyapunov exponent is computed numerically for the double well oscillator in a heat bath positive exponents are found in a wide range of friction coefficients in the low damping regime

control of underactuated mechanical systems via passive velocity field control application to snakeboard and 3d rigid body abstract in this paper we consider the application of a new formulation of passive velocity field control pvfc to the control problem of a class of underactuated mechanical systems uams in our previous report synthesizing the desired velocity vector fields for pvfc by the decoupling vector fields we were able to prove that control torques may be successfully obtained and the solvability of the synthesizing problem of pvfc for the uams may be guaranteed we newly develop this control design methodology and propose an explicit feedback solution to the control problems of the uams such as snakeboard underactuated 3d rigid bodies several simulations show the validity of the proposed control methodology

series expansions for the evolution of mechanical control systems this paper presents a series expansion that describes the evolution of a mechanical system starting at rest and subject to a time varying external force mechanical systems are presented as second order systems on a configuration manifold via the notion of affine connections the series expansion is derived by exploiting the homogeneity property of mechanical systems and the variations of constant formula a convergence analysis is obtained using some analytic functions and combinatorial analysis results this expansion provides a rigorous means of analyzing locomotion gaits in robotics and lays the foundation for the design of motion control algorithms for a large class of underactuated mechanical systems

dynamics and control of a class of underactuated mechanical systems this paper presents a theoretical framework for the dynamics and control of underactuated mechanical systems defined as systems with fewer inputs than degrees of freedom control system formulation of underactuated mechanical systems is addressed and a class of underactuated systems characterized by nonintegrable dynamics relations is identified controllability and stabilizability results are derived for this class of underactuated systems examples are included to illustrate the results these examples are of underactuated mechanical systems that are not linearly controllable or smoothly stabilizable

phase diagram of the random frequency oscillator the case of ornstein uhlenbeck noise abstract we study the stability of a stochastic oscillator whose frequency is a random process with finite time memory represented by an ornstein uhlenbeck noise this system undergoes a noise induced bifurcation when the amplitude of the noise grows the critical curve that separates the absorbing phase from an extended non equilibrium steady state corresponds to the vanishing of the lyapunov exponent that measures the asymptotic logarithmic growth rate of the energy we derive various expressions for this lyapunov exponent by using different approximation schemes this allows us to study quantitatively the phase diagram of the random parametric oscillator

noise induced jumps in two coupled duffing oscillators abstract we consider two coupled duffing oscillators with the coexistence of four attractors switching between the coexisting attractors by noises is investigated three types of noises such as gaussian amplitude dependent and dichotomous are used we observed noise induced extrinsic intermittency intermittent dynamics is characterized using power spectrum average and relative residence times on each precoupled attractors and probability distribution of time interval between successive switchings variation of probability distribution of state variables in poincare map is studied as a function of noise strength the effect of various noises is compared the occurrence of crisis induced and type i intermittencies are also presented

low order controllability and kinematic reductions for affine connection control systems controllability and kinematic modeling notions are investigated for a class of mechanical control systems first low order controllability results are given for the class of mechanical control systems second a precise connection is made between those mechanical systems which are dynamic i e have forces as inputs and those which are kinematic i e have velocities as inputs interestingly and surprisingly these two subjects are characterized and linked by a certain intrinsic vector valued quadratic form that can be associated to an affine connection control system

a class of multivariate new better than used distributions a class of multivariate distributions with new better than used nbu marginals is introduced a number of necessary and sufficient conditions for a distribution to be a member in the class are given closure results which are useful for the identification or construction of members in the class are derived in particular simple proofs of some well known preservation properties of the class of the univariate nbu distributions are obtained two examples of replacement models that give rise to multivariate nbu distributions in the class are discussed

symbolic dynamics of noisy chaos abstract one model of randomness observed in physical systems is that low dimensional deterministic chaotic attractors underly the observations a phenomenological theory of chaotic dynamics requires an accounting of the information flow from the observed system to the observer the amount of information available in observations and just how this information affects predictions of the system s future behavior in an effort to develop such a description we discuss the information theory of highly discretized observations of random behavior metric entropy and topological entropy are well defined invariant measures of such an attractor s level of chaos and are computable using symbolic dynamics real physical systems that display low dimensional dynamics are however inevitably coupled to high dimensional randomless e g thermal noise we investigate the effects of such fluctuations coupled to deterministic chaotic systems in particular the metric entropy s response to the fluctuations we find that the entropy increases with a power law in the noise level and that the convergence of the entropy and the effect of fluctuations can be cast as a scaling theory we also argue that in addition to the metric entropy there is a second scaling invariant quantity that characterizes a deterministic system with added fluctuations i0 the maximum average information obtainable about the initial condition that produces a particular sequence of measurements or symbols

stationary energy probability density of oscillators driven by a random external force we derive rigorous analytical results for the stationary energy probability density function of linear and nonlinear oscillators driven by additive gaussian noise our study focuses on two cases i a harmonic oscillator subjected to gaussian colored noise with an arbitrary correlation function and ii nonlinear oscillators with a general potential driven by gaussian white noise we also derive analytical expressions for the stationary moments of the energy and investigate the partition of the mean energy between kinetic and potential energy to illustrate our general results we consider specifically the case of exponentially correlated noise for i and power law and bistable potentials for ii our theoretical results are substantiated by langevin simulations between the kinetic energy and the potential energy of the oscillator our studies focus on two cases first we consider a harmonically bound particle driven by general additive gaussian colored noise second we consider a particle in a general potential driven by gaussian white noise in both cases we develop a general theory and study specific illustrative examples the paper is organized as follows in sec ii we formulate the langevin equations for a particle with inertia in a general potential driven by an additive random force we also derive the general relation between the stationary energy pdf and the stationary pdf for the particle s position and velocity section iii is devoted to the motion of a particle in a harmonic potential driven by colored gaussian noise with an arbitrary correlation function the stationary energy pdf as well as the first and second moments of the energy is derived analytically we apply these results to the case of exponentially correlated gaussian noise and to gaussian white noise for these specific cases we also determine the partition of the energy between kinetic and potential energy we analyze the effect of the potential shape on the stationary energy pdf for oscillators driven by an additive gaussian white noise in sec iv w e apply our analytical results to two specific cases a general power law potential and a bistable potential the first type of oscillator without friction and with additive noise 36 and multiplicative noise 37 has recently been studied in the context of anomalous diffusion the second type the duffing oscillator has been investigated as an alternative to the linear oscillator for harvesting energy from external random sources 28 29 35 38 39

analysis and design of oscillatory control systems this paper presents analysis and design results for control systems subject to oscillatory inputs i e inputs of large amplitude and high frequency the key analysis results are a series expansion characterizing the averaged system and various lie algebraic conditions that guarantee the series can be summed various example systems provide insight into the results with regards to design we recover and extend a variety of point stabilization and trajectory tracking results using oscillatory controls we present novel developments on stabilization of systems with positive trace and on tracking for second order underactuated systems

configuration controllability of simple mechanical control systems in this paper we present a definition of configuration controllability for mechanical systems whose lagrangian is kinetic energy with respect to a riemannian metric minus potential energy a computable test for this new version of controllability is derived this condition involves an object which we call the symmetric product of particular interest is a definition of equilibrium controllability for which we are able to derive computable sufficient conditions examples illustrate the theory

local equilibrium controllability of multibody systems controlled via shape change we study local equilibrium controllability of shape controlled multibody systems the multibody systems are defined on a trivial principal fiber bundle by a lagrangian that characterizes the base body motion and shape dynamics a potential dependent on an advected parameter e g uniform gravitational potential is considered this potential breaks base body symmetries but a symmetry subgroup is assumed to exist symmetric product formulas are derived and important properties are obtained for symmetric products of horizontal shape control vector fields and a potential vector field that is dependent on an advected parameter based on these properties sufficient conditions for local equilibrium controllability and local fiber equilibrium controllability are developed these results are applied to two classes of shape controlled multibody systems in a uniform gravitational field multibody attitude systems and neutrally buoyant multibody underwater vehicles