nonlinear decoupling via feedback a differential geometric approach the paper deals with the nonlinear decoupling and noninteracting control problems a complete solution to those problems is made possible via a suitable nonlinear generalization of several powerful geometric concepts already introduced in studying linear multivariable control systems the paper also includes algorithms concerned with the actual construction of the appropriate control laws

freezing transition in the mean field approximation model of pedestrian counter flow abstract we study the freezing transition in the counter flow of pedestrians within the channel numerically and analytically we present the mean field approximation mfa model for the pedestrian counter flow the model is described in terms of a couple of nonlinear difference equations the excluded volume effect and bi directionality are taken into account the fundamental diagrams current density diagrams are derived when pedestrian density is higher than a critical value the dynamical phase transition occurs from the free flow to the freezing stopping state the critical density is derived by using the linear stability analysis also the velocity and current flow at the steady state are derived analytically the analytical result is consistent with that obtained by the numerical simulation

experiment and simulation for counterflow of people going on all fours abstract counterflow of students going on all fours is investigated by experiment and simulation the experiment is performed for the channel with open boundaries two types of students going to the right and to the left are taken into account the video recordings and measurements of individual arrival times are evaluated the characteristics of counterflow are clarified experimentally the counterflow of students on all fours is compared with the pedestrian counterflow the experiment is mimicked by the lattice gas simulation where each student going on all fours is simulated by a biased random walker occupying two sites the simulation result is compared with the experimental result it is shown that the experimental result is consistent with the simulation result

zeros at infinity for affine nonlinear control systems a definition of zeros at infinity for affine nonlinear control systems is proposed the definition is local which means that we exclude certain singularities we argue the reasonableness of our definition by showing its relevance to the problem of nonlinear decoupling in particular we give a necessary and sufficient condition for the solvability of the general regular decoupling problem for affine systems in terms of the zeros at infinity

almost disturbance decoupling for single input single output nonlinear systems the almost disturbance decoupling problem for nonlinear single input single output systems is addressed by using singular perturbation methods and high gain feedback sufficient conditions and the explicit high gain nonlinear state feedback in solvable cases are given they generalize both previous almost results for linear systems and exact ones for nonlinear systems the necessity of the conditions is discussed in particular an example is given where the main structural condition is not satisfied and the high gain control designed on the basis of linear approximations fails to achieve almost disturbance decoupling for the original system

kink soliton characterizing traffic congestion we study traffic congestion by analyzing a one dimensional traffic flow model developing an asymptotic method to investigate the long time behavior near a critical point we derive the modified korteweg de vries mkdv equation as the lowest order model there is an infinite number of kink solitons to the mkdv equation while it has been found by numerical simulations that the kink pattern arising in traffic congestion is uniquely determined irrespective of initial conditions in order to resolve this selection problem we consider higher order corrections to the mkdv equation and find that there is a kink soliton that can deform continuously with the perturbation represented by the addition of these corrections with numerical confirmation we show that this continuously deformable kink soliton characterizes traffic congestion we also discuss the relationship between traffic congestion and the slugging phenomenon in granular flow

global state and feedback equivalence of nonlinear systems the problem of finding global state space transformations and global feedback of the form u t x t to transform a given nonlinear system xdot f x g x u to a controllable linear system on rn or on an open subset of rn is considered here we give a complete set of differential geometric conditions which are equivalent to the existence of a solution to the above problem

influence of the exits configuration on evacuation process in a room without obstacle abstract the floor field model is the most popular cellular automata ca model which is used to simulate the pedestrian s behaviors in the floor field model the interaction between pedestrians is expressed by the dynamical field in this paper we proposed an improved and simple method to calculate the floor field in our method the pedestrians are treated as the movable obstacles which will increase the value of the floor field the additional value is interpreted as the blocking effect of preceding pedestrians and then the influence of the exits configuration on evacuation process in a room without obstacle is simulated the evacuation time for different widths and positions of the exits is investigated in the case of single exit there is a power law relationship between the evacuation time t and the exit width d w with a negative exponent when d w 6 mean flow rates and the using efficiency of each exit cell obtained by our model are higher than other models the simulation results indicate that pedestrians do not choose the shortest path but a faster path in our model for the case of two exits the relationships between the location of the exits and evacuation time are discussed when the total width of two exits is small i e d w 2 the main factor affecting the total evacuation time t is the exits capacity if the total width of two exits is large i e d w 12 the moving distance of pedestrians to exits is the main factor affecting the evacuation time and the corresponding phase diagrams are given

metastable states in a microscopic model of traffic flow it is a well known fact that metastable states of very high throughput and hysteresis effects exist in traffic flow which the simple cellular automaton model of traffic flow and its continuous generalization fail to reproduce it is shown that the model can be generalized to give a one parametric family of models a part of which reproduces the metastable states and the hysteresis the models that have that property and those that do not that are separated by a transition that can be clearly identified

scaling behaviour in discrete traffic models we investigate the noisy discrete single lane highway traffic model proposed by nagel and schreckenberg 1992 and demonstrate by computer simulations that as a function of the car density there is a dynamical transition from laminar flow to jammed traffic in the system related to the divergence of the relaxation time of average car velocity the critical density is close to the position of the maximum in the fundamental diagram we give estimates of the critical exponents related to this jamming transition the critical density of the geometrical 1 1 dimensional percolation transition of jammed regions can be rather far from the jamming point depending on the strength of the noise which indicates that cooperativity leading to the jamming transition can be long range in character

recovering of curves with involution by extended prym data the classical torelli theorem states that every smooth projective algebraic curve x is determined uniquely up to isomorphism by its principally polarized jacobian j x 0 in this paper we consider curves c with involution without fixed points a c c we let c c tr and denote by n c c the factor map one associates the principally polarized prym variety p where p p c a 1 tr d t and e is algebraically equivalent to 23 the natural question whether the prym variety determines uniquely the pair c tr up to isomorphism has negative answer in general if the genus g of c is 7 for some special loci of curves e g for hyperelliptic c the problem of spotting the pairs c rr which are not determined uniquely by the prym variety is still open some partial results have been obtained in f s k dol do2 del de2 n v in this paper we propose an extension of the prym data p 3 and prove that it determines uniquely up to isomorphism any pair c tr for g 2 our extension originates from the following observation consider the case of c of genus 1 here the involution is a translation t by some point p of order 2 in j c notice that 0 ker nm j c j c the prym variety is equal to 0 there is a classically known data which determines uniquely the pair c tj up to isomorphism see e g m3 c namely one can always represent j c as c z z where z belongs to the upper half plane so that

jamming transition in two dimensional pedestrian traffic abstract jamming transitions of pedestrian traffic are investigated under the periodic boundary condition on the square lattice by the use of the lattice gas model of biased random walkers without the back step the two cases are presented the one with two types of walkers and the other with four types of walkers in the two types of walkers the first is the random walker going to the right and the second is the random walker going up in the four types of walkers the first second third and fourth are respectively the random walkers going to the right left up and down it is found that the dynamical jamming transitions occur at the critical densities the transition points do not depend on the system size for large system but depend strongly on the strength of drift the jamming transitions are compared with that obtained by the cellular automaton model of car traffic

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

observability and controllability for smooth nonlinear systems the definition of a smooth nonlinear system as proposed recently by willems is elaborated as a natural generalization of the more common definitions of a smooth nonlinear input output system mini

exact solutions for a discrete system arising in traffic flow this paper concerns wave propagation in a discrete nonlinear system of equations proposed and studied by g f newell as a model for car following in traffic flow in particular newell found exact solutions for shock waves and related phenomena here exact solutions representing periodic waves and solitary waves are obtained the method relates travelling wave solutions to the toda and kac van moerbeke discrete systems in this and other ways much of the interest is in the general phenomena possible in discrete systems here including also a time lag rather than in just the specific traffic flow setting

phase transition in a difference equation model of traffic flow a difference equation is presented to describe traffic flow on a highway the difference equation model is derived from the optimal velocity models formulated in terms of the differential equations it is compared with the differential equation models we investigate phase transitions among the freely moving phase the coexisting phase in which jams appear and the uniform congested phase the linear stability theory is applied and the neutral stability line is obtained we find the critical point below which no jams appear to derive the modified korteweg de vries equation near the critical point we apply the reductive perturbation method we also compare the nonlinear analysis result with that of the optimal velocity model it is shown that the critical point and the amplitude of the jam are different from those of the optimal velocity model

spatio temporal distribution of escape time in evacuation process abstract we study the escape time distribution of crowd in the evacuation process through an exit from a hall the evacuation process is simulated by the use of the lattice gas model of pedestrian the spatio temporal distribution of escape time is derived the escape time of a person depends highly on the position where the person exists initially within the hall the dependences of the mean value and variance of escape time on the position are calculated it is shown that the mean escape time exhibits a highest value at the front edges the variance of escape time has a highest value at both positions just next door to the exit the dependence of escape time on the exit width is also shown it is found that the escape time exhibits a wide distribution depending on the initial position of people and the exit width

traffic jams granular flow and soliton selection the flow of traffic on a long section of road without entrances or exits can be modeled by continuum equations similar to those describing fluid flow in a certain range of traffic density steady flow becomes unstable against the growth of a cluster or phantom traffic jam which moves at a slower speed than the otherwise homogeneous flow we show that near the onset of this instability traffic flow is described by a perturbed korteweg de vries kdv equation the traffic jam can be identified with a soliton solution of the kdv equation the perturbation terms select a unique member of the continuous family of kdv solitons these results may also apply to the dynamics of granular relaxation

effect of partition line on jamming transition in pedestrian counter flow abstract the effect of partition line on the pedestrian counter flow is investigated under the open boundaries by using the lattice gas model of biased random walkers there are two types of walkers without the back step the one is the walker going to the right and the other is the walker going to the left the right left walker prefers to move within outside the partition line right walkers interfere with left walkers near the partition line when the density of right walkers increases under a constant value of left walker density the jamming transition between the freely moving phase and the stopped state occurs at a critical density depending on the left walker density the critical density is compared with that without the partition line the partition line has an important effect on the jamming transition

equivalence of nonlinear systems to input output prime forms the problem of transforming nonlinear control systems into input output prime forms is dealt with using state space static state feedback and also output space transformations necessary and sufficient geometric conditions for the solvability of this problem are obtained the results obtained generalize well known results both on feedback linearization as well as input output decoupling of nonlinear systems it turns out that from a computational point of view the output space transformation is the crucial step that is performed by constructing rectifying coordinates for a nested sequence of distributions on the output manifold

clogging transition of pedestrian flow in t shaped channel abstract pedestrian flow is investigated under the open boundaries in a t shaped channel where the branch flow joins the main flow at the junction the pedestrian merging flow is simulated by the use of the lattice gas model of biased random walkers when the main flow rate increases under the constant value of branch flow rate the clogging transitions occur at the main flow or branch flow or both flows it is shown that the dynamical phase transitions depend on both inlet densities the four distinct phases are found the phase diagram is presented for the distinct phases the scaling of saturated flow rate and transition point is shown the flow rate exhibits the universal scaling form

canonical decomposition of non linear systems the construction of a canonical or normal representation for non linear systems similar to the morse canonical form in the linear case is obtained the problem considered consists in particular of studying the existence of generalized transformations that achieve a desired block decoupling such transformations generalize the notions of state transformation state feedback and output injection a sufficient condition is given in terms of a separability condition which in turn is completely characterized by using differential forms and their properties

pedestrian behaviors in a lattice gas model with large maximum velocity abstract in this paper the lattice gas model for pedestrian flow is extended to large maximum velocity v max 1 it is shown that at large v max the critical density corresponding to the maximum flow rate of fundamental diagram is in good agreement with empirical results the counter flow is studied and it is found that with the increase of v max the jam transition threshold decreases this is explained by the attachment rate to jam and detachment rate from jam the fundamental diagram of mixed pedestrian flow is also investigated and the dependence of the flow rate on the ratio of fast pedestrians is simulated finally the counter flow of mixed pedestrians is studied and it is found the more homogeneous the mixed pedestrians are distributed the smaller the jam transition threshold is

feedback linearization of discrete time systems abstract we give necessary and sufficient conditions for a nonlinear discrete time system to be locally linearizable by a change of state coordinates and a feedback the conditions are expressed in terms of controllability distributions associated to the system

on the construction of static stabilizers and static output trackers for dynamically linearizable systems related results and applications it is shown that the property of dynamic linearizability to be understood as linearizability by means of the dynamic extension algorithm implies the existence of static possibly time varying control laws yielding asymptotic output tracking with arbitrary speed of convergence and asymptotic stabilization with a computable bound on the region of attraction similar results hold for systems which are only input output linearizable by means of dynamic state feedback provided that the inverse dynamics possess certain stability properties applications of these results to the problem of regional stabilization of a vtol aircraft is considered together with the tracking problem for a class of flexible joints robots moreover a novel parameterization for flexible joint robots is also proposed

on normal forms of nonlinear systems affine in control the nonlinear equivalences of both finite and infinite zero structures of linear systems have been well understood for single input single output systems and have found many applications in nonlinear control theory the extensions of these notions to multiple input multiple output systems have proven to be highly sophisticated in this paper we propose constructive algorithms for decomposing a nonlinear system that is affine in control these algorithms require modest assumptions on the system and apply to general multiple input multiple output systems that do not necessarily have the same number of inputs and outputs they lead to various normal form representations and reveal the structure at infinity the zero dynamics and the invertibility properties all of which represent nonlinear equivalences of relevant linear system structural properties

numerical simulation of a continuum model for bi directional pedestrian flow an algorithm for an extended reactive dynamic user equilibrium model of pedestrian counterflow as a continuum is developed it is based on a cell centered high resolution finite volume scheme with a fast sweeping method for an eikonal type equation on an orthogonal grid a high order total variation diminishing runge kutta method is adopted for the time integration of semi discrete equations the numerical results demonstrate the rationality of the model and efficiency of the algorithm some crowd pedestrian flow phenomena such as dynamic lane formation in bi directional flow are observed which are helpful for a global comprehension of pedestrian dynamics also the model can be utilized with different potential applications

traffic jamming on hexagonal lattice abstract a traffic model on hexagonal lattice is studied the moving objects are modeled as biased random walkers on hexagonal lattice the hexagonal lattice traffic model is an extension of the square lattice traffic model proposed by muramatsu et al physica a 267 1999 487 the hexagonal and square models are compared it is found that hexagonal and square models have a phase transition from freely moving state to jammed state at a critical density the critical density of hexagonal model is greater than that of square model when the drift of moving objects is high the difference between the critical densities of hexagonal and square models decreases when the drift decreases

scaling of pedestrian channel flow with a bottleneck abstract pedestrian channel flow at a bottleneck is investigated under the open boundaries by using the lattice gas model of biased random walkers it is shown that a dynamical phase transition occurs from the free flow to the choking flow at a critical density pc with increasing density the flow rate saturates at higher density than the critical density in the choking flow region a scaling behavior is found as follows the saturated flow rate js scales as js d0 93 0 02 and the critical density pc scales as pc d w 1 16 0 02 where d is the width of the bottleneck and w is the width of channel the plot of the rescaled flow rate against the rescaled density collapses onto a single curve

derivation and empirical validation of a refined traffic flow model abstract the gas kinetic foundation of fluid dynamic traffic equations suggested in previous papers d helbing physica a 219 1995 375 and 391 is further refined by applying the theory of dense gases and granular materials to the boltzmann like traffic model by paveri fontana it is shown that despite the phenomenologically similar behaviour or ordinary and granular fluids the relations for these cannot directly be transferred to vehicular traffic the dissipative and anisotropic interactions of vehicles as well as their velocity dependent space requirements lead to a considerably different structure of the macroscopic traffic equations also in comparison with the previously suggested traffic flow models as a consequence the instability mechanisms of emergent density waves are different crucial assumptions are validated by empirical traffic data and essential results are illustrated by figures

a mathcal b invariant distributions and disturbance decoupling of nonlinear systems the concept of a b invariant subspaces has resulted in a unified approach to many of the basic structural properties of time invariant linear systems w m wonham lecture notes in economics and mathematical systems vol 101 springer verlag new york 1974 the purpose of this paper is to introduce the more general notion of a mathcal b invariant distributions on differentiable manifolds and to use this idea to study the disturbance decoupling problem for a class of nonlinear systems which evolve on real analytic manifolds

asymptotic stabilization of minimum phase nonlinear systems how a class of multivariable nonlinear systems can be stabilized about an equilibrium via smooth state feedback is shown more precisely conditions under which for every compact set of initial states it is possible to design a feedback law which drives to the equilibrium all initial states in this compact set are described the theory includes the development of globally defined transformations of the system equations to their global normal form

a higher order macroscopic model for bi direction pedestrian flow abstract in this paper a higher order macroscopic model for bi direction pedestrian flow is presented to investigate macroscopic crowd patterns of bi direction pedestrian movement for each group the macroscopic model consists of two dimensional euler equations with relaxation and an eikonal type equation the magnitude of the desired velocity is described by an empirical relation between density and speed while its direction is chosen to minimize the total instantaneous walking cost which satisfies a reactive user equilibrium assignment pattern the dynamic model is numerically solved by a splitting technique and a cell centered finite volume method on an orthogonal grid typical numerical examples of bi direction pedestrian flow walking in a channel are designed to validate the rationality of the dynamic model and the effectiveness of the numerical algorithm

cellular automaton simulation of pedestrian counter flow considering the surrounding environment this paper presents a cellular automaton model without step back to simulate the pedestrian counter flow in a channel the consideration of the surrounding environment when people make judgments on moving directions is added to a random walker model also without step back two types of walkers the right walkers going to the right and the left walkers going to the left are taken into account the characteristics of counterflow are clarified influences of the different interaction radius values and system sizes on movement are studied phase transition from free moving to jamming is observed with the increase of entrance density it is found that the critical entrance density p c at the transition point does not depend on the system size when the interaction radius value is large simulation results are represented as a comparison with the random walker model

delay effect on phase transitions in traffic dynamics a dynamical model of traffic is proposed to take into account the effect of acceleration delay in the limit of no delay the model reproduces the optimal velocity model of traffic when the delay is small it is shown that the phase transition among the freely moving phase the coexisting phase and the uniform congested phase occurs below the critical point above the critical point no phase transition occurs the value a c of the critical point increases with increasing delay time 1 b where a is the friction coefficient or sensitivity parameter when the delay time is longer than frac 1 2 the critical point disappears and the phase transition always occurs the linear stability theory and nonlinear analysis are applied the critical point predicted by the linear stability theory agrees with the simulation result the modified korteweg de vries kdv equation is obtained from the nonlinear analysis near the critical point the phase separation line obtained from the modified kdv equation is consistent with the simulation result

an improved model of passenger merging in a y shaped passage abstract during the merging process in a y shaped passage the walking direction of pedestrians changes which can cause crowding and decrease the efficiency of walking facilities based on an analysis of interactions among pedestrians this study conducts a series of merging simulations with an improved social force model isfm to investigate the influences of various walking parameters of pedestrians in a y shaped passage first we construct an isfm by adding a centripetal force to analyze pedestrian turning behaviors based on the basic social force model bsfm second we define simulation scenes with different angles 30 60 and 90 and branch passage widths 2 m 3 m and 4 m walking behavior parameters such as the walking speed traversal time and population density in the branch passages are analyzed the results show that as the width of the branch passage increases the traversal time decreases and throughput increases the turning angle has little influence on the results but as the angle decreases pedestrian speeds sharply fluctuate in the merging area thereby increasing the blockage probability and prolonging the traversal time finally relationships between the branch passage width and traversal time and the merging angle and speed fluctuations are proposed

jamming transition in pedestrian counter flow a lattice gas model with biased random walkers is presented to mimic the pedestrian counter flow in a channel under the open boundary condition of constant density there are two types of walkers without the back step the one is the random walker going to the right and the other is the random walker going to the left it is found that a dynamical jamming transition from the freely moving state at low density to the stopped state at high density occurs at the critical density the transition point is given by pc 0 45 0 01 not depending on the system size the transition point depends on the strength of drift and decreases with increasing drift also we present the extended model to take into account the traffic rule in which a pedestrian walks preferably on the right hand side of the channel

gas kinetic derivation of navier stokes like traffic equations macroscopic traffic models have recently been severely criticized to base on lax analogies only and to have a number of deficiencies therefore this paper shows how to construct a logically consistent fluid dynamic traffic model from basic laws for the acceleration and interaction of vehicles these considerations lead to the gas kinetic traffic equation of paveri fontana its stationary and spatially homogeneous solution implies equilibrium relations for the fundamental diagram the variance density relation and other quantities which are partly difficult to determine empirically paveri fontana s traffic equation allows the derivation of macroscopic moment equations which build a system of non closed equations this system can be closed by the well proved method of chapman and enskog which leads to euler like traffic equations in zeroth order approximation and to navier stokes like traffic equations in first order approximation the latter are finally corrected for the finite space requirements of vehicles it is shown that the resulting model is able to withstand the above mentioned criticism