on the hughes model for pedestrian flow the one dimensional case in this paper we investigate the mathematical theory of hughes model for the ow of pedestrians cf 17 consisting of a nonlinear conservation law for the density of pedestrians coupled with an eikonal equation for a potential modelling the common sense of the task we rst consider an approximation of the original model in which the eikonal equation is replaced by an elliptic approximation for such an approximated system we prove existence and uniqueness of entropy solutions in one space dimension in the sense of kru zkov 21 in which the boundary conditions are posed following the approach of bardos et al 7 we use bv estimates on the density and stability estimates on the potential in order to prove uniqueness furthermore we analyse the evolution of characteristics for the original hughes model in one space dimension and study the behaviour of simple solutions in order to reproduce interesting phenomena related to the formation of shocks and rarefaction waves the characteristic calculus is supported by numerical simulations

design of multivariable feedback systems with stable plant this paper considers in a general algebraic framework the design of a unity feedback multivariable system with a stable plant the method is based on a simple parameterization of the four closed loop transfer functions in terms of p the plant transfer function and q h y 1 u 1 in particular the i o transfer function q h y 2 u 1 pq using the framework of rational transfer functions we show that the closed loop system will be exponentially stable if and only if q is exponentially stable furthermore if both p and q are strictly proper then the controller is also strictly proper the basic result is design theorem 2 an algorithm is given for obtaining strictly proper controllers such that the resulting i o map is decoupled all its poles can be chosen by the designer and the same holds for zeros except of course for the c zeros prescribed by the c zeros of the plant a discussion is included to temper these results by the constraints imposed by noise and plant saturation

on the stabilization of nonlinear systems we extend the applicability of the global q parametrization method of controller design to a large class of unstable nonlinear plants the main result is a two step compensation theorem analogous to that of zames for unstable linear plants if p l e2 rightarrow l e1 is a nonlinear possibly unstable plant and f 0 is any incrementally stable controller such that p 1 p i f 0 p 1 is incrementally stable then the class of controllers f which yields an f g stable closed loop system in the unity feedback configuration for p is globally parametrized by finite gain stable maps q l e1 rightarrow l e2 with f f 0 q i p 1 q 1

on the distribution of dominance in populations of social organisms bumble bees may possess a scalar character called dominance which changes according to certain rules as a result of encounters between pairs of organisms an equation for the distribution of dominance in a population is derived based on a set of plausible axioms the resulting boltzmann like integrodifferential equation is analyzed analytically and or numerically for certain important special cases

on the modelling of crowd dynamics by generalized kinetic models abstract we introduce a new approach for modelling the behavior of pedestrians which borrows techniques from the kinetic theory of rarefied gazes this approach is based on concepts from the kinetic theory for active particles in our modelling of crowd movements pedestrians are regarded as entities whose microscopic states include a geometric variable to denote position a mechanical variable to denote speed and a variable to describe the rate of development of individual strategies that influence the collective dynamics indeed the third variable is introduced to account for the ability of individuals to modify their dynamics according to specific objectives and strategies the equations eventually obtained are a set of nonlinear integro differential equations of vlasov or boltzmann type

realizing rcc8 networks using convex regions rcc8 is a popular fragment of the region connection calculus in which qualitative spatial relations between regions such as adjacency overlap and parthood can be expressed while rcc8 is essentially dimensionless most current applications are confined to reasoning about two dimensional or three dimensional physical space in this paper however we are mainly interested in conceptual spaces which typically are high dimensional euclidean spaces in which the meaning of natural language concepts can be represented using convex regions the aim of this paper is to analyze how the restriction to convex regions constrains the realizability of networks of rcc8 relations first we identify all ways in which the set of rcc8 base relations can be restricted to guarantee that consistent networks can be convexly realized in respectively 1d 2d 3d and 4d most surprisingly we find that if the relation partially overlaps is disallowed all consistent atomic rcc8 networks can be convexly realized in 4d if instead refinements of the relation part of are disallowed all consistent atomic rcc8 relations can be convexly realized in 3d we furthermore show among others that any consistent rcc8 network with 2 n 1 variables can be realized using convex regions in the n dimensional euclidean space

on the numerical solutions of second order macroscopic models of pedestrian flows the main target of this paper is focused on the numerical simulation of macroscopic models two dimensional hyperbolic conservation law of pedestrian flows therefore finite volume methods can be used to discretize the equations actually the algorithms that have been used are particularly suited for solving hyperbolic problems moreover simulations using first order accurate numerical solvers and first godunov type schemes s k godunov a finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics mathematik sbornik 47 1959 271 290 have been developed this article is motivated by recent research activity focused on the problem of modelling systems of the living matter

global parametrization of feedback systems with nonlinear plants for unity feedback systems with a plant p and controller c we show that given a nonlinear stable p the class of all controller stabilizing the feedback system is globally parametrized by a stable map q we also show how q is useful in studying the effects of modeling errors on the stability

a convex characterization of multidimensional linear systems subject to sqi constraints this technical note proposes a convex characterization of the set of all stable closed loop linear systems that are obtained from a given plant which may be multidimensional by interconnecting it in feedback with controllers that satisfy a certain pre selected constraint we take an approach that is particularly useful when a doubly coprime factorization of the plant is difficult to obtain and a stable stabilizing controller may not exist the plant is not strongly stabilizable or when one may be difficult to find most related work requires one of these we adopt the so called coordinate free approach which unlike youla s parametrization does not rely on a doubly coprime factorization of the plant we show that if constraints which satisfy a condition called strong quadratic invariance sqi are imposed on the controllers then the set of all stable closed loop multidimensional linear systems has a convex representation and norm optimal control problems can be cast in convex form although the sqi condition is in general slightly stronger than quadratic invariance qi which was developed in related work they are equivalent for common classes of problems arising in decentralized control

a logic framework for reasoning with movement based on fuzzy qualitative representation abstract we present a logic approach to reason with moving objects under fuzzy qualitative representation this way we can deal both with qualitative and quantitative information and consequently to obtain more accurate results the proposed logic system is introduced as an extension of propositional dynamic logic this choice on the one hand simplifies the theoretical study concerning soundness completeness and decidability on the other hand provides the possibility of constructing complex relations from simpler ones and the use of a language very close to programming languages

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

spatial reasoning in a fuzzy region connection calculus although the region connection calculus rcc offers an appealing framework for modelling topological relations its application in real world scenarios is hampered when spatial phenomena are affected by vagueness to cope with this we present a generalization of the rcc based on fuzzy set theory and discuss how reasoning tasks such as satisfiability and entailment checking can be cast into linear programming problems we furthermore reveal that reasoning in our fuzzy rcc is np complete thus preserving the computational complexity of reasoning in the rcc and we identify an important tractable subfragment moreover we show how reasoning tasks in our fuzzy rcc can also be reduced to reasoning tasks in the original rcc while this link with the rcc could be exploited in practical reasoning algorithms we mainly focus on the theoretical consequences in particular using this link we establish a close relationship with the egg yolk calculus and we demonstrate that satisfiable knowledge bases can be realized by fuzzy regions in any dimension

computing improved optimal solutions to max min flexible constraint satisfaction problems abstract the formal framework for decision making in a fuzzy environment is based on a general max min bottleneck like optimization problem proposed by zadeh it is also the basis for extending the constraint satisfaction paradigm of artificial intelligence to accommodating flexible or prioritized constraints this paper surveys refinements of the ordering of solutions supplied by the max min formulation namely the discrimin partial ordering and the leximin complete preordering a general algorithm is given which computes all maximal solutions in the sense of these relations it also sheds light on the structure of the set of best solutions moreover classes of problems for which there is a unique best discrimin and leximin solution are exhibited namely continuous problems with convex domains and so called isotonic problems noticeable examples of such problems are fuzzy linear programming problems and fuzzy pert like scheduling problems

lqg controller synthesis with plant and noise spectral uncertainties in this paper we consider the problem of robust controller synthesis with plant and noise spectral uncertainties in lqg optimal systems we frame an algorithm for synthesizing the robust controller to minimize the least favourable cost functional j via specifying the weighting matrices q and r the wiener hopf technique in the lqg optimal system the saddle point theory and a property of the contractive operator are employed to solve this problem

on the complexity of qualitative spatial reasoning a maximal tractable fragment of the region connection calculus the computational properties of qualitative spatial reasoning have been investigated to some degree however the question for the boundary between polynomial and np hard reasoning problems has not been addressed yet in this paper we explore this boundary in the region connection calculus rcc 8 we extend bennett s encoding of rcc 8 in modal logic based on this encoding we prove that reasoning is np complete in general and identify a maximal tractable subset of the relations in rcc 8 that contains all base relations further we show that for this subset path consistency is sufficient for deciding consistency

on the cauchy problem for macroscopic model of pedestrian flows abstract in this paper we discuss the limit behavior of hyperbolic systems of conservation laws with stiff relaxation terms to the local systems as the relaxation time tends to zero the prototype is crowd models derived from crowd dynamics according to macroscopic scaling when the flow of crowds is supposed to satisfy the paradigms of continuum mechanics under an appropriate structural stability condition the asymptotic expansion is obtained when one assumes the existence of a smooth solution to the equilibrium system in this case the local existence of a classical solution is also shown

a unifying approach to temporal constraint reasoning abstract we present a formalism disjunctive linear relations dlrs for reasoning about temporal constraints dlrs subsume most of the formalisms for temporal constraint reasoning proposed in the literature and is therefore computationally expensive we also present a restricted type of dlrs horn dlrs which have a polynomial time satisfiability problem we prove that most approaches to tractable temporal constraint reasoning can be encoded as horn dlrs including the ord horn algebra by nebel and burckert and the simple temporal constraints by dechter et al thus dlrs is a suitable unifying formalism for reasoning about temporal constraints

an algebraic theory for design of controllers for linear multivariable systems part ii feedback realizations and feedback design the study of general linear multivariable systems with possibly different controlled and measured outputs is continued in this part of the paper the structure matrices defined in part i are used to solve the feedback realization problem feedback realizable transfer functions are then used to solve problems of regulator type it is shown that the solutions to problems like disturbance deeoupling output regulation and pole placement are all special cases of the solution to a more general problem finally it is shown how the results of part i and part ii can be combined to solve problems of servo type and of regulator type simultaneously

generalized region connection calculus the region connection calculus rcc is one of the most widely referenced system of high level qualitative spatial reasoning rcc assumes a continuous representation of space this contrasts sharply with the fact that spatial information obtained from physical recording devices is nowadays invariably digital in form and therefore implicitly uses a discrete representation of space recently galton developed a theory of discrete space that parallels rcc but question still lies in that can we have a theory of qualitative spatial reasoning admitting models of discrete spaces as well as continuous spaces in this paper we aim at establishing a formal theory which accommodates both discrete and continuous spatial information and a generalization of region connection calculus is introduced grcc the new theory takes two primitives the mereological notion of part and the topological notion of connection rcc and galton s theory for discrete space are both extensions of grcc the relation between continuous models and discrete ones is also clarified by introducing some operations on models of grcc in particular we propose a general approach for constructing countable rcc models as direct limits of collections of finite models compared with standard rcc models given rise from regular connected spaces these countable models have the nice property that each region can be constructed in finite steps from basic regions two interesting countable rcc models are also given one is a minimal rcc model the other is a countable sub model of the continuous space r 2

a fuzzy sets theoretic approach to approximate spatial reasoning relational composition based reasoning has become the most prevalent method for qualitative reasoning since allen s 1983 work on temporal intervals underlying this reasoning technique is the concept of a jointly exhaustive and pairwise disjoint set of relations systems of relations such as rcc5 and rcc8 were originally developed for ideal regions not subject to imperfections such as vagueness or fuzziness which are found in many applications in geographic analysis and image understanding this paper however presents a general method for classifying binary topological relations involving fuzzy regions using the rcc5 or the rcc8 theory our approach is based on fuzzy set theory and the theory of consonant random set some complete classifications of topological relations between fuzzy regions are also given furthermore two composition operators on spatial relations between fuzzy regions are introduced in this paper these composition operators provide reasonable relational composition based reasoning engine for spatial reasoning involving fuzzy regions

solving conflicts in information merging by a flexible interpretation of atomic propositions although many techniques for merging conflicting propositional knowledge bases have already been proposed most existing work is based on the idea that inconsistency results from the presence of incorrect pieces of information which should be identified and removed in contrast we take the view in this paper that conflicts are often caused by statements that are inaccurate rather than completely false suggesting to restore consistency by interpreting certain statements in a flexible way rather than ignoring them completely in accordance with this view we propose a novel approach to merging which exploits extra logical background information about the semantic relatedness of atomic propositions several merging operators are presented which are based on different formalizations of this background knowledge ranging from purely qualitative approaches related to possibilistic logic to quantitative approaches with a probabilistic flavor both syntactic and semantic characterizations are provided for each merging operator and the computational complexity is analyzed