stability analysis and synthesis of nonlinear time delay systems via linear takagi sugeno fuzzy models abstract this paper concerns with the stability analysis and synthesis of nonlinear retarded systems via linear takagi sugeno ts fuzzy model approach first the ts fuzzy models with time delay are present and the stability conditions are derived using lyapunov razumikhin functional approach then a stabilization approach for nonlinear retarded systems through fuzzy state feedback and fuzzy observer based controller is proposed it shows that the analysis results provide an efficient technique for the design of fuzzy controllers sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain of the time delay systems are derived through the numerical solution of a set of coupled linear matrix inequalities

the true self repelling motion we construct and study a continuous real valued random process which is of a new type it is self interacting self repelling but only in a local sense it only feels the self repellance due to its occu pation time measure density in the immediate neighbourhood of the point it is just visiting we focus on the most natural process with these properties that we call true self repelling motion this is the continuous counterpart to the integer valued true self avoiding walk which had been studied among others by the first author one of the striking properties of true self repelling motion is that although the coupleoxt occupation time measure of x at time tu is a continuous markov process x is not driven by a stochastic diaerential equation and is not a semi martingale it turns out for instance that it has a finite variation of order 3 2 which contrasts with the finite quadratic variation of semi martingales one of the key tools in the construction of x is a continuous system of coalescing brownian motions similar to those that have been constructed by arratia a1 a2 we derive various properties of x existence and properties of the occupation time densities ltoxu local variation etc and an identity that shows that the dynamics of x can be very loosely speaking described as follows dxt is equal to the gradient in space of ltoxu in a gener alized sense even though x7 ltoxu is not diaerentiable

long time tails in the parabolic anderson model with bounded potential we consider the parabolic anderson problem t u u u on 0 z d with random i i d potential z z zd and the initial condition u 0 1 our main assumption is that esssup 0 0 depending on the thickness of the distribution prob 0 close to its essential supremum we identify both the asymptotics of the moments of u t 0 and the almost sure asymptotics of u t 0 as t in terms of variational problems as a by product we establish lifshitz tails for the random schrodinger operator at the bottom of its spectrum in our class of distributions the lifshitz exponent ranges from d 2 to the power law is typically accompanied by lower order corrections

constrained mpc algorithm for uncertain time varying systems with state delay in this note we present a model predictive control mpc algorithm for uncertain time varying systems with input constraints and state delay uncertainty is assumed to be polytopic and delay is assumed to be unknown but with a known upper bound for a memoryless state feedback mpc law we define an optimization problem that minimizes a cost function and relaxes it to two other optimization problems by finding an upper bound of the cost function one is solvable and the other is not we prove equivalence and feasibilities of the two optimization problems under a certain assumption on the weighting matrix based on these properties and optimality we show that feasible mpc from the optimization problems stabilizes the closed loop system then we present an improved mpc algorithm that includes relaxation procedures of the assumption on the weighting matrix and stabilizes the closed loop system finally a numerical example illustrates the performance of the proposed algorithm

the critical attractive random polymer in dimension one a polymer chain with attractive and repulsive forces between the building blocks is modeled by attaching a weight e for every self intersection and e 2d for every self contact to the probability of an n step simple random walk on d where 0 are parameters it is known that for d 1 and the chain collapses down to finitely many sites while for d 1 and it spreads out ballistically here we study for d 1 the critical case corresponding to the collapse transition and show that the end to end distance runs on the scale n sqrt n log n 1 4 we describe the asymptotic shape of the accordingly scaled local times in terms of an explicit variational formula and prove that the scaled polymer chain occupies a region of size n times a constant moreover we derive the asymptotics of the partition function

localization transition for a polymer near an interface consider the directed process i s i where the second component is simple random walk on mathbb z s 0 0 define a transformed path measure by weighting each n step path with a factor exp lambda sum 1 leq i leq n omega i h sign s i here omega i i geq 1 is an i i d sequence of random variables taking values pm 1 with probability 1 2 acting as a random medium while lambda in 0 infty and h in 0 1 are parameters the weight factor has a tendency to pull the path towards the horizontal because it favors the combinations s i 0 omega i 1 and s i 0 omega i 1 the transformed path measure describes a heteropolymer consisting of hydrophylic and hydrophobic monomers near an oil water interface we study the free energy of this model as n to infty and show that there is a critical curve lambda to h c lambda where a phase transition occurs between localized and delocalized behavior in the vertical direction we derive several properties of this curve in particular its behavior for lambda downarrow 0 to obtain this behavior we prove that as lambda h downarrow 0 the free energy scales to its brownian motion analogue

a clt for the l2 modulus of continuity of brownian local time let l x t x t r 1 x r 1 denote the local time of brownian motion and l x t 2 dx let n 0 1 be independent of t for each fixed t l x h t l t x 2 dx 4ht h 3 2 l 64 3 1 2 t as h 0 equivalently l x 1 t l t x 2 dx 4t h 3 2 l 64 3 1 2 1 as t

the diffusive phase of a model of self interacting walks we consider simple random walk onzd perturbed by a factor exp t pjt wheret is the length of the walk and j t sum nolimits 0 leqslant i 0 ford 2 the diffusion constant is equal to 1 but ford 2 it is renormalized ford 1 andp 3 2 we prove diffusion for all real positive or negative ford 2 the scaling limit is brownian motion but ford 2 it is the edwards model with the wrong sign of the coupling when 0 which governs the limiting behaviour the latter arises since for p frac 4 d 2 t p j t is the discrete self intersection local time this establishes existence of a diffusive phase for this model existence of a collapsed phase for a very closely related model has been proven in work of bolthausen and schmock

green s function for a hierarchical self avoiding walk in four dimensions this is the second of two papers on the end to end distance of a weakly self repelling walk on a four dimensional hierarchical lattice it completes the proof that the expected value grows as a constant times sqrt t log frac 1 8 t left 1 o left frac log log t log t right right which is the same law as has been conjectured for self avoiding walks on the simple cubic lattice 4 apart from completing the program in the first paper the main result is that the green s function is almost equal to the green s function for the markov process with no self repulsion but at a different value of the killing rate which can be accurately calculated when the interaction is small furthermore the green s function is analytic in in a sector in the complex plane with opening angle greater than

on the character of convergence to brownian local time ii in this paper we consider the sequences of stochastic processes which converge weakly asn to brownian local time these processes are generated by a recurrent random walk with finite variance the main result is the following it is possible to redefine a random walk in such a way that for a wide class of processes the normalized differences between them and brownian local time converge in distribution to some stochastic process we also prove that such differences with probability one have the logarithmic upper bound it is so called strong invariance principles for local times

guaranteed cost control of uncertain discrete systems with delays in this paper we address the problems of robust performance analysis and control synthesis for a class of discrete time systems with parameter uncertainty and unknown state delay the parameter uncertainty is real time varying normbounded and the state delay is a constant within a prescribed interval for the robust performance analysis problem we adopt an appropriate notion of robust stability for discrete time uncertain time delay systems and show that this notion guarantees an upper bound on a linear quadratic cost function for the control synthesis problem we show that a robust state feedback controller can be constructed to render the closed loop system robustly stable while guaranteeing a prescribed level of performance the developed results are expressed in terms of algebraic matrix inequalities a numerical example is presented to illustrate the theory

self avoiding walk in 5 or more dimensions using an expansion based on the renormalization group philosophy we prove that for a t step weakly self avoiding random walk in five or more dimensions the variance of the endpoint is of order t and the scaling limit is gaussian as t

receding horizon controls for input delayed systems this paper presents a receding horizon control rhc for an unconstrained input delayed system to begin with we derive a finite horizon optimal control for a quadratic cost function including two final weighting terms the rhc is easily obtained by changing the initial and final times of the finite horizon optimal control a linear matrix inequality lmi condition on two final weighting matrices is proposed to meet the cost monotonicity under which the optimal cost on the horizon is monotonically nonincreasing with time and hence the asymptotical stability is guaranteed only if an observability condition is met it is shown through simulation that the proposed rhc stabilizes the input delayed system effectively and its performance can be tuned by adjusting weighting matrices with respect to the state and the input

constrained robust model predictive control for time delay systems with polytopic description this paper considers an infinite horizon min max model predictive control mpc problem for time delay discrete systems with a polytopic uncertainty description which has rarely been addressed in the literature several new solutions to this problem are proposed which are inter complementary if there is an input delay then the single state feedback solution requires all the system matrices to be stable this deficiency can be removed by adding free control moves before a modified state feedback law if there is no input delay then a computationally efficient off line state feedback solution can be applied in order to obtain desirable region of attraction while at the same time preserve reasonably low on line computational effort one can choose the standard solution simulation results are given to illustrate these new solutions

the range of stable random walks limit theorems are proved for the range of d dimensional random walks in the domain of attraction of a stable process of index p3 the range rn is the number of distinct sites of zd visited by the random walk before time n our results depend on the value of the ratio 3 d the most interesting results are obtained for 2 3 1 which can only occur if d 1 we prove the convergence in distribution of rn e rn toward some constant times the lebesgue measure of the range of the limiting stable process some of our results require regularity assumptions on the characteristic function of x

the drift of a one dimensional self avoiding random walk we prove that a self avoiding random walk on the integers with bounded increments grows linearly we characterize its drift in terms of the frobenius eigenvalue of a certain one parameter family of primitive matrices as an important tool we express the local times as a two block functional of a certain markov chain which is of independent interest

interval type 2 fuzzy model predictive control of nonlinear networked control systems in this paper the problem of fuzzy predictive control of nonlinear networked control systems subject to parameter uncertainties and defective communication links is studied stochastic variables with bernoulli random binary distribution are used to represent the defective communication links with packets loss occurring intermittently between the controller and the physical plant an interval type 2 it2 takagi sugeno t s fuzzy model is employed to describe the nonlinear plant subject to parameter uncertainties which can be captured with the lower and upper membership functions the it2 fuzzy model and it2 fuzzy controller are not required to share the same lower and upper membership functions in order to design the state feedback fuzzy model predictive controller an optimization problem which minimizes the upper bound of a quadratic objective function subject to input constraints and packets dropout is formulated and solved at every sampling instant in the finite time horizon by introducing some slack matrices less conservative conditions are developed for system stability analysis two examples are given to demonstrate the effectiveness and merits of the proposed new design techniques

large deviations for local times and intersection local times of fractional brownian motions and riemann liouville processes in this paper we prove exact forms of large deviations for local times and intersection local times of fractional brownian motions and riemann liouville processes we also show that a fractional brownian motion and the related riemann liouville process behave like constant multiples of each other with regard to large deviations for their local and intersection local times as a consequence of our large deviation estimates we derive laws of iterated logarithm for the corresponding local times the key points of our methods 1 logarithmic superadditivity of a normalized sequence of moments of exponentially randomized local time of a fractional brownian motion 2 logarithmic subadditivity of a normalized sequence of moments of exponentially randomized intersection local time of riemann liouville processes 3 comparison of local and intersection local times based on embedding of a part of a fractional brownian motion into the reproducing kernel hilbert space of the riemann liouville process

nonlinear schrodinger equations and sharp interpolation estimates a sharp sufficient condition for global existence is obtained for the nonlinear schrodinger equation begin array 20 c nls 2i phi t delta phi left phi right 2 sigma phi 0 x in mathbb r n t in mathbb r end array in the case 2 n this condition is in terms of an exact stationary solution nonlinear ground state of nls it is derived by solving a variational problem to obtain the best constant for classical interpolation estimates of nirenberg and gagliardo

stabilization of polytopic delay difference inclusions via the razumikhin approach polytopic delay difference inclusions ddis have received increasing attention recently mostly due to their ability to model a wide variety of relevant processes including networked control systems one of the fundamental problems for ddis that poses a non trivial challenge is stabilization this paper embraces the razumikhin approach and provides several solutions to the stabilization problem as follows firstly a method to synthesize a control lyapunov razumikhin function clrf is presented for unconstrained ddis secondly for constrained ddis a receding horizon controller based on the clrf for the unconstrained system is proposed along with a closed loop stability analysis thirdly it is shown that a tractable implementation of the developed control algorithm can be attained even for large delays by means of an on line minkowski set addition an advantageous feature of the developed methodology is that all the synthesis algorithms can be formulated as a low complexity semi definite programming problem for quadratic clrf candidates a comparison with alternative synthesis methods demonstrates the advances provided by the developed theory

large deviations for the one dimensional edwards model in this article we prove a large deviation principle for the empirical drift of a one dimensional brownian motion with self repellence called the edwards model our results extend earlier work in which a law of large numbers and a central limit theorem were derived in the edwards model a path of length t receives a penalty e ht w hereht is the selfintersection local time of the path and 0 is a parameter called the strength of self repellence we identify the rate function in the large deviation principle for the endpoint of the path as 2 3 i 1 3 with i given in terms of the principal eigenvalues of a one parameter family of sturm liouville operators we show that there exist numbers 0 b b such that 1 i is linearly decreasing on 0 b 2 i is real analytic and strictly convex on b 3 i is continuously differentiable at b and 4 i has a unique zero at b the latter fact identifies b as the asymptotic drift of the endpoint the critical drift b is associated with a crossover in the optimal strategy of the path for b b the path assumes local drift b during the full time t while for 0 b b it assumes local drift b during time b b 2b t and local drift b during the remaining time b b 2b t thus in the second regime the path makes an overshoot of size b b 2 t so as to reduce its intersection local time

central limit theorem for the edwards model the edwards model in one dimension is a transformed path measure for standard brownian motion discouraging self intersections we prove a central limit theorem for the endpoint of the path extending a law of large numbers proved by westwater the scaled variance is characterized in terms of the largest eigenvalue of a one parameter family of differential operators introduced and analyzed by van der hofstad and den hollander interestingly the scaled variance turns out to be independent of the strength of self repellence and to be strictly smaller than one the value for free brownian motion

random walks with short range interaction and mean field behavior we introduce a model of self repelling random walks where the short range interaction between two elements of the chain decreases as a power of the difference in proper time the model interpolates between the lattice edwards model and the ordinary random walk we show by means of monte carlo simulations in two dimensions that the exponentvmf obtained through a mean field approximation correctly describes the numerical data and is probably exact as long as it is smaller than the corresponding exponent for self avoiding walks we also compute the exponent and present a numerical study of the scaling functions

large deviations estimates for self intersection local times for simple random walk in mathbb z 3 we obtain large deviations estimates for the self intersection local times for a simple random walk in dimension 3 also we show that the main contribution to making the self intersection large in a time period of length n comes from sites visited less than some power of log n this is opposite to the situation in dimensions larger or equal to 5 finally we present an application of our estimates to moderate deviations for random walk in random sceneries

large deviations for renormalized self intersection local times of stable processes we study large deviations for the renormalized self intersection local time of d dimensional stable processes of index 2d 3 d we find a difference between the upper and lower tail in addition we find that the behavior of the lower tail depends critically on whether d or d

ballistic behavior in a 1d weakly self avoiding walk with decaying energy penalty we consider a weakly self avoiding walk in one dimension in which the penalty for visiting a site twice decays as exp t s p wheret ands are the times at which the common site is visited andp is a parameter we prove that ifp 3 2 then the walk should have diffusive behavior the proof and the heuristic argument make use of a real space renormalization group transformation

measuring the range of an additive levy process the primary goal of this paper is to study the range of the random field x t nj 1xj tj where x1 xn vspace 1pt are independent levy processes in rd to cite a typical result of this paper let us suppose that i denotes the levy exponent of xi for each i 1 n then under certain mild conditions we show that a necessary and sufficient condition for x rn to have positive d dimensional lebesgue measure is the integrability of the function rd nj 1r 1 j 1 this extends a celebrated result of kesten and of bretagnolle in the one parameter setting furthermore we show that the existence of square integrable local times is yet another equivalent condition for the mentioned integrability criterion this extends a theorem of hawkes to the present random fields setting and completes the analysis of local times for additive levy processes initiated in a companion by paper khoshnevisan xiao and zhong

proprietes d intersection des marches aleatoires i convergence vers le temps local d intersection we study intersection properties of multi dimensional random walks letx andy be two independent random walks with values in d d 3 satisfying suitable moment assumptions and letin denote the number of common points to the paths ofx andy up to timen the sequence in suitably normalized is shown to converge in distribution towards the intersection local time of two independent brownian motions results are applied to the proof of a central limit theorem for the range of a two dimensional recurrent random walk thus answering a question raised by n c jain and w e pruitt

robust constrained model predictive control using linear matrix inequalities abstract the primary disadvantage of current design techniques for model predictive control mpc is their inability to deal explicitly with plant model uncertainty in this paper we present a new approach for robust mpc synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation the uncertainty is expressed in both the time and frequency domains the goal is to design at each time step a state feedback control law that minimizes a worst case infinite horizon objective function subject to constraints on the control input and plant output using standard techniques the problem of minimizing an upper bound on the worst case objective function subject to input and output constraints is reduced to a convex optimization involving linear matrix inequalities lmis it is shown that the feasible receding horizon state feedback control design robustly stabilizes the set of uncertain plants several extensions such as application to systems with time delays problems involving constant set point tracking trajectory tracking and disturbance rejection which follow naturally from our formulation are discussed the controller design is illustrated with two examples

the true self avoiding walk with bond repulsion on z limit theorems the true self avoiding walk with bond repulsion is a nearest neighbor random walk on z for which the probability of jumping along a bond of the lattice is proportional to exp g number of previous jumps along that bond first we prove a limit theorem for the distribution of the local time process of this walk using this result later we prove a local limit theorem as a for the distribution of a 2 3 x s a where s a is a random time distributed geometrically with mean e s a 1 e s a 1 a s 0 1 as a by product we also obtain an apparently new identity related to brownian excursions and bessel bridges

the constants in the central limit theorem for the one dimensional edwards model the edwards model in one dimension is a transformed path measure for one dimensional brownian motion discouraging self intersections we study the constants appearing in the central limit theorem clt for the endpoint of the path which represent the mean and the variance and the exponential rate of the normalizing constant the same constants appear in the weak interaction limit of the one dimensional domb joyce model the domb joyce model is the discrete analogue of the edwards model based on simple random walk where each self intersection of the random walk path recieves a penalty e 2 we prove that the variance is strictly smaller than 1 which shows that the weak interaction limits of the variances in both clts are singular the proofs are based on bounds for the eigenvalues of a certain one parameter family of sturm liouville differential operators obtained by using monotonicity of the zeros of the eigen functions in combination with computer plots

random walks and intersection local time with each random walk on z 2 we associate a functional related to the number of steps which the walk spends in sites occupied at least k times we show that if our random walk is in the domain of attraction of a stable process of order greater than 2 2k 2 2k 1 then our functional converges to the intersection local time of the limiting process

large deviations and laws of the iterated logarithm for the local times of additive stable processes we study the upper tail behaviors of the local times of the additive stable processes let x 1 t x p t be independent d dimensional symmetric stable processes with stable index 0 2 and consider the additive stable process x t 1 t p x 1 t 1 x p t p under the condition d ap we obtain a precise form of the large deviation principle for the local time x 0 t p t 0 t 0 x x 1 s 1 x p sp ds 1 ds p of the multiparameter process x t 1 t p and for its supremum norm sup x r d x 0 t p our results apply to the law of the iterated logarithm and our approach is based on fourier analysis moment computation and time exponentiation

weak interaction limits for one dimensional random polymers in this paper we present a new and flexible method to show that in one dimension various self repellent random walks converge to self repellent brownian motion in the limit of weak interaction after appropriate space time scaling our method is based on cutting the path into pieces of an appropriately scaled length controlling the interaction between the different pieces and applying an invariance principle to the single pieces in this way we show that the self repellent random walk large deviation rate function for the empirical drift of the path converges to the self repellent brownian motion large deviation rate function after appropriate scaling with the interaction parameters the method is considerably simpler than the approach followed in our earlier work which was based on functional analytic arguments applied to variational representations and only worked in a very limited number of situations

self intersections of 1 dimensional random walks consider a random walk snon the integers where the steps i have mean 0 and variance 2 let t be the time of first self intersection of the random walk it is shown that as t grows at rate 2 3 more precisely t 2 3 has a non degenerate limit distribution which can be described in terms of brownian motion local time

the lace expansion approach to ballistic behaviour for one dimensional weakly self avoiding walks we prove ballistic behaviour in dimension one fora model of weakly self avoiding walks where loops of length m are penalized by a factor e mp with p 0 1 and sufficiently large furthermore we prove that the fluctuations around the linear drift satisfy a centrallimit theorem the proof uses a variant of the lace expansion together with an inductive analysis of the arising recursion relation

scaling for a random polymer letq n be the law of then step random walk on d obtained by weighting simple random walk with a factore for every self intersection domb joyce model of soft polymers it was proved by greven and den hollander 1993 that ind 1 and for every 0 there exist 0 1 and such that under the lawq n asn begin array l i theta beta is the lim it empirical speed of the random walk ii mu beta is the limit empirical distribution of the local times end array a representation was given for and in terms of a largest eigenvalue problem for a certain family of x matrices in the present paper we use this representation to prove the following scaling result as 0 begin array l i beta textstyle 1 over 3 theta beta to b ii beta textstyle 1 over 3 mu beta left left lceil cdot beta textstyle 1 over 3 right rceil right to l 1 eta cdot end array the limitsb 0 and are identified in terms of a sturm liouville problem which turns out to have several interesting properties the techniques that are used in the proof are functional analytic and revolve around the notion of epi convergence of functionals onl 2 our scaling result shows that the speed of soft polymers ind 1 is not right differentiable at 0 which precludes expansion techniques that have been used successfully ind 5 hara and slade 1992a b in simulations the scaling limit is seen for 10 2

brownian intersection local times upper tail asymptotics and thick points we equip the intersection of p independent brownian paths in r d d 2 with the natural measure l defined by projecting the intersection local time measure via one of the brownian motions onto the set of intersection points given a bounded domain u c r d we show that as a the probability of the event l u a decays with an exponential rate of a 1 p where is described in terms of a variational problem in the important special case when u is the unit ball in r 3 and p 2 we characterize in terms of an ordinary differential equation we apply our results to the problem of finding the hausdorff dimension spectrum for the thick points of the intersection of two independent brownian paths in r 3

polymers as self avoiding walks a brief overview is presented of the relation of the properties of real polymers to the problem of self avoiding random walks the self consistent field method is discussed wherein the non markovian continuous self avoiding polymer is replaced by a self consistent markovian approximation an outline is presented of the method of solution of the resultant nonlinear integrodifferential equations a description is also presented of the scaling theories which provide a means for deducing some exponents in the asymptotic dependence of walk properties on the length of the walk in the limit of infinite length walks

robust memory state feedback model predictive control for discrete time uncertain state delayed systems in this paper we propose a memory state feedback model predictive control mpc law for a discrete time uncertain state delayed system with input constraints the model uncertainty is assumed to be polytopic and the delay is assumed to be unknown but with a known upper bound we derive a sufficient condition for cost monotonicity in terms of lmi which can be easily solved by an efficient convex optimization algorithm a delayed state dependent quadratic function with an estimated delay index is considered for incorporating mpc problem formulation the mpc problem is formulated to minimize the upper bound of infinite horizon cost that satisfies the sufficient conditions therefore a less conservative sufficient conditions in terms of linear matrix inequality lmi can be derived to design a more robust mpc algorithm a numerical example is included to illustrate the effectiveness of the proposed method

implementation of stabilizing receding horizon controls for time varying systems in this paper a new stabilizing receding horizon control rhc scheme is proposed for linear discrete time varying systems which can be easily implemented by using linear matrix inequality lmi optimization the control scheme is based on the minimization of the finite horizon cost with a finite terminal weighting matrix the resulting stabilizing rhc scheme leads to time varying finite terminal weighting matrices even for time invariant systems which is more general than in the case of using constant matrices based on the proposed scheme another implementation method is also discussed for easy computation and numerical feasibility consideration of lmi optimization although the second method does not guarantee the closed loop stability theoretically through a simulation example the effectiveness of the proposed schemes is illustrated

exponential asymptotics and law of the iterated logarithm for intersection local times of random walks let a 0 1 p denote the intersection local time of p independent d dimensional brownian motions running up to the time 1 under the conditions p d 2 2 we prove lim t 1 log p 0 1 p t d p 1 2 d p with the right hand side being identified in terms of the the best constant of the gagliardo nirenberg inequality within the scale of moderate deviations we also establish the precise tail asymptotics for the intersection local time in k 1 k p 1 n p s 1 k 1 s p k p run by the independent symmetric z d valued random walks s 1 n s p n our results apply to the law of the iterated logarithm our approach is based on feynman kac type large deviation time exponentiation moment computation and some technologies along the lines of probability in banach space as an interesting coproduct we obtain the inequality formula math in the case of random walks

on edwards model for polymer chains ii the self consistent potential we obtain an existence and uniqueness theorem for the self consistent potential in edwards model for polymer chains and confirm the asymptotic analysis proposed by him on the basis of wkb arguments

output regulation for linear systems subject to input saturation the purpose of this paper is to examine the problem of controlling a linear time invariant system subject to input saturation in order to have its output track or reject a family of reference or disturbance signals produced by some external generator it is shown that a semiglobal framework for this problem is a natural one within this framework a set of solvability conditions are given and feedback laws that solve the problem are constructed the theory developed in this paper incorporates earlier results established for linear systems without input saturation

the drift of a one dimensional self repellent random walk with bounded increments consider a one dimensional walk s k k having steps of bounded size and weight the probability of the path with some factor 1 0 1 for every single self intersection up to timen we prove thats n ss converges towards some deterministic number called the effective drift of the self repellent walk furthermore this drift is shown to tend to the basic drift as tends to 0 and as tends to 1 to the self avoiding walk s drift which is introduced in 10 the main tool of the present paper is a representation of the sequence of the local times as a functional of a certain markov process

self intersection local times of random walks exponential moments in subcritical dimensions fix p 1 not necessarily integer with p d 2 0 that are bounded from above possibly tending to zero the speed is identified in terms of mixed powers of t and t and the precise rate is characterized in terms of a variational formula which is in close connection to the gagliardo nirenberg inequality as a corollary we obtain a large deviation principle for lt p trt for deviation functions rt satisfying t r t gg mathbb e ell t p informally it turns out that the random walk homogeneously squeezes in a t dependent box with diameter of order t1 d to produce the required amount of self intersections our main tool is an upper bound for the joint density of the local times of the walk

the scaling limit of lattice trees in high dimensions we prove that above eight dimensions the scaling limit of sufficiently spread out lattice trees is the variant of super brownian motion known as integrated super brownian excursion ise as conjectured by aldous the same is true for nearest neighbour lattice trees in sufficiently high dimensions the proof uses the lace expansion

constrained rhc for lpv systems with bounded rates of parameter variations this paper studies a stabilization problem of polytopically uncertain linear parameter varying systems with input constraints and bounded rates of parameter variations in the framework of finite receding horizon control rhc a system containing parameter uncertainties is modified into a system with parameter incremental uncertainties within each horizon for the system modified in this manner a robust rhc is designed by solving an optimization problem at each time instant based on the feasibility of the problem and the optimality of its solution the closed loop system stability is guaranteed a numerical example is included to illustrate the validity of the results

quasi min max mpc algorithms for lpv systems in this paper a new model predictive controller mpc is developed for polytopic linear parameter varying lpv systems we adopt the paradigm used in gain scheduling and assume that the time varying parameters are measured on line but their future behavior is uncertain and contained in a given polytope at each sampling time optimal control action is computed by minimizing the upper bound on the quasi worst case value of an infinite horizon quadratic objective function subject to constraints on inputs and outputs the mpc algorithm is called quasi because the first stage cost can be computed without any uncertainty this allows the inclusion of the first move u k k separately from the rest of the control moves governed by a feedback law and is shown to reduce conservatism and improve feasibility characteristics with respect to input and output constraints proposed optimization problems are solved by semi definite programming involving linear matrix inequalities it is shown that closed loop stability is guaranteed by the feasibility of the linear matrix inequalities a numerical example demonstrates the unique features of the mpc design

technical communique an lmi approach to guaranteed cost control of linear uncertain time delay systems the guaranteed cost control problem via memoryless state feedback controllers is studied in this paper for a class of linear time delay systems with norm bounded time varying parametric uncertainty and a given quadratic cost function sufficient conditions for the existence of guaranteed cost controllers are given in terms of linear matrix inequalities lmis furthermore a convex optimization problem with lmi constraints is formulated to design the optimal guaranteed cost controller which minimizes the guaranteed cost of the closed loop uncertain system

large and moderate deviations for intersection local times we study the large and moderate deviations for intersection local times generated by respectively independent brownian local times and independent local times of symmetric random walks our result in the brownian case generalizes the large deviation principle achieved in mansmann 1991 for the l 2 norm of brownian local times and coincides with the large deviation obtained by csorgo shi and yor 1991 for self intersection local times of brownian bridges our approach relies on a feynman kac type large deviation for brownian occupation time certain localization techniques from donsker varadhan 1975 and mansmann 1991 and some general methods developed along the line of probability in banach space our treatment in the case of random walks also involves rescaling spectral representation and invariance principle the law of the iterated logarithm for intersection local times is given as an application of our deviation results

on stability of constrained receding horizon control with finite terminal weighting matrix in this paper a new stabilizing receding horizon control based on a finite input and state horizon cost with a finite terminal weighting matrix is proposed for time varying discrete linear systems with constraints we propose matrix inequality conditions on the terminal weighting matrix under which closed loop stability is guaranteed for both cases of unconstrained and constrained systems with input and state constraints we show that such a terminal weighting matrix can be obtained by solving a linear matrix inequality lmi in the case of constrained time invariant systems an artificial invariant ellipsoid constraint is introduced in order to relax the conventional terminal equality constraint and to handle constraints using the invariant ellipsoid constraints a feasibility condition of the optimization problem is presented and a region of attraction is characterized for constrained systems with the proposed receding horizon control

law of the iterated logarithm for the range of random walks in two and three dimensions let s n be a random walk in z d and let r n be the range of s n we prove an almost sure invariance principle for r n when d 3 and a law of the iterated logarithm for r n when d 2

an lmi based scheduling algorithm for constrained stabilization problems we propose a gain scheduling control algorithm for locally stabilizing a discrete time linear system with input saturation the proposed control law has a structure that a high gain control law and a low gain control law are interpolated by using a single scheduling parameter the scheduling parameter is computed on line by solving a convex optimization problem with lmi constraints

predictor based control of linear systems with state input and output delays in this paper we develop a predictor based controller for linear systems with state input and output delays first a state predictor is developed for state feedback control this predictor is formulated recursively over the prediction time by partitioning the input delay into sections smaller than the state delays the partitioning of the input delay ensures that the resulting predictor equation only depends on the past values of the state and input it is shown that the proposed predictor gives an exact prediction of the future states this recursive predictor is then reformulated into a cascade form in order to reduce the number of redundant calculations and to simplify the predictor equation for practical implementation we construct a predictor based state feedback control law and show that the spectrum of the closed loop time delay system under the constructed control law is the same as that of an equivalent time delay system without input delay and under the nominal state feedback control therefore the proposed predictor based solution can stabilize the delay system if a stabilizing state feedback control law exists for the input delay free system these state feedback results are then extended to the case of delayed output feedback the theoretical derivation is verified through numerical examples

a central limit theorem for a one dimensional polymer measure let s n n n 0 be a random walk on the integers having bounded steps the self repellent resp self avoiding walk is a sequence of transformed path measures which discourage resp forbid self intersections this is used as a model for polymers previously we proved a law of large numbers that is we showed the convergence of s n n toward a positive number under the polymer measure the present paper proves a classical central limit theorem for the self repellent and self avoiding walks that is we prove the asymptotic normality of s n n n for large n the proof refines and continues results and techniques developed previously

self avoiding walk in five or more dimensions i the critical behaviour we use the lace expansion to study the standard self avoiding walk in thed dimensional hypercubic lattice ford 5 we prove that the numbercn ofn step self avoiding walks satisfiescn a n where is the connective constant i e 1 and that the mean square displacement is asymptotically linear in the number of steps i e v 1 2 a bound is obtained forcn x the number ofn step self avoiding walks ending atx the correlation length is shown to diverge asymptotically like z 1 2 the critical two point function is shown to decay at least as fast as x 2 and its fourier transform is shown to be asymptotic to a multiple ofk 2 ask 0 i e 0 we also prove that the scaling limit is gaussian in the sense of convergence in distribution to brownian motion the infinite self avoiding walk is constructed in this paper we prove these results assuming convergence of the lace expansion the convergence of the lace expansion is proved in a companion paper

self avoiding fractional brownian motion the edwards model in this work we extend varadhan s construction of the edwards polymer model to the case of fractional brownian motions in d for any dimension d 2 with arbitrary hurst parameters h 1 d

on self repellent one dimensional random walks we consider an ordinary one dimensional recurrent random walk on a self repellent random walk is defined by changing the ordinary law of the random walk in the following way a path gets a new relative weight by multiplying the old one with a factor 1 for every self intersection of the path 0 1 is a parameter

a survey of one dimensional random polymers in the last decade there has been an enormous progress in the mathematical understanding of one dimensional polymer measures which are path measures that suppress self intersections we are currently in the situation that many interesting questions have either been answered or that essential new ideas are needed in this survey paper we discuss the most relevant results open questions and heuristics

a new inductive approach to the lace expansion for self avoiding walks we introduce a new inductive approach to the lace expansion and apply it to prove gaussian behaviour for the weakly self avoiding walk on d where loops of length m are penalised by a factor e m p 0 4 p 0 2 d 4 in particular we derive results first obtained by brydges and spencer and revisited by other authors for the case d 4 p 0 in addition we prove a local central limit theorem with the exception of the case d 4 p 0

robust model predictive control for multiple time delay systems with polytopic uncertainty description this article addresses the robust model predictive control mpc for systems with polytopic uncertainty description in the case of multiple state delays some results are given in the previous works however previous works are not well established for input delay systems this article proposes new approaches that can effectively handle not only the input delay but also the multiple delayed input for the time delay system a general mpc solution is based on the use of augmented delay free state space description which can be computationally expensive hence in general there are simplified formulations based on the time delay description which can be applied in different situations this article proposes three simplified formulations with the first incorporating a previous result as a special case the second being a solution for a unique class of systems and the third being a more general solution without special assumptions on the plant numerical examples illustrate the effectiveness of the propo

on improving transient performance in global control of multiple integrators system by bounded feedback abstract the global stabilization problem for multiple integrators systems by bounded control is considered two classes of nonlinear feedback laws are proposed the first one consisting of nested saturation functions is a modification and generalization of that in a r teel global stabilization and restricted tracking for multiple integrators with bounded controls systems control letters 18 3 1992 165 171 and the other one consists of parallel connections of saturation functions both these two types of nonlinear feedback laws need only n n n 2 if n is even and n n 1 2 if n is odd where n is the length of the multiple integrators saturation elements furthermore the poles of the closed loop system can be placed on any location of the left real axis when none of the saturation elements in the control laws is saturated both of them exhibit simpler structure can significantly improve the transient performance of the closed loop system and are very superior to the other existing methods simulation of a fourth order system is used to illustrate the effectiveness of the proposed methods

self intersection local time critical exponent large deviations and laws of the iterated logarithm if t is renormalized self intersection local time for planar brownian motion we characterize when ee 1 is finite or infinite in terms of the best constant of a gagliardo nirenberg inequality we prove large deviation estimates for 1 and 1 we establish lim sup and lim inf laws of the iterated logarithm for t as t

a model of continuous polymers with random charges we study a model of polymers with random charges the possible shapes of the polymer are represented by the sample paths of a brownian motion and the cumulative charge distribution along a polymer is modeled by a realization of a brownian bridge charges interact through a general positive definite two body potential we study the infinite volume free energy density for a fixed realization of the brownian motion this is not self averaging but shows on the contrary a sample dependence through the local time of the brownian motion we obtain an explicit series representation for the free energy density this has a finite radius of convergence but the free energy is nevertheless analytic in the inverse temperature in the physical domain

random walk in random scenery and self intersection local times in dimensions d 5 let s k k 0 be a symmetric random walk on mathbb z d and eta x x in mathbb z d an independent random field of centered i i d random variables with tail decay p eta x t approx exp t alpha we consider a random walk in random scenery that is x n eta s 0 dots eta s n we present asymptotics for the probability over both randomness that x n n for 1 2 and 1 to obtain such asymptotics we establish large deviations estimates for the self intersection local times process sum x l n 2 x where l n x is the number of visits of site x up to time n