controlled invariance for discrete time nonlinear systems with an application to the disturbance decoupling problems invariant distributions are defined for discrete time nonlinear control systems and necessary and sufficient conditions are given for their controlled invariance this extends to discrete time systems the basic tool which has been so important in solving the various synthesis problems for continuous time systems to indicate their utility in the discrete time setting they are used to locally solve the disturbance decoupling problem

recursive identification using feedforward neural networks the paper is concerned with the identification of an unknown nonlinear dynamical system when only the inputs and outputs are accessible for measurement under certain assumptions it is shown that generically the system can be realized by a recursive input output model furthermore relying on the approximation properties of neural networks and the existence of effective training algorithms it is demonstrated how an effective identification model can be constructed simulation results are presented to complement the theoretical discussions

implicit discrete time systems and accessibility an intrinsic description for dynamic systems whose evolution along discrete time is governed by nonlinear implicit difference equations in one independent variable and zero order algebraic equations is presented by means of differential geometrical methods where systems are associated with appropriate geometric objects reflecting their dynamics dynamic systems given in implicit form have the peculiarity that they may contain so called hidden restrictions a normal form is presented which is characterized by the circumstances that there are no further restrictions in addition it is illustrated that such a normal form allows for an equivalent system representation in explicit form based on the geometric picture of implicit discrete time systems the qualitative property of accessibility along a fixed trajectory is discussed by applying symmetry groups of discrete time systems and studying invariants of these groups a formal approach is provided that allows us to gather local accessibility criteria successively which can be tested by computer algebra several examples illustrate the results

discrete bipolar universal integrals the concept of universal integral recently proposed generalizes the choquet shilkret and sugeno integrals those integrals admit a discrete bipolar formulation useful in those situations where the underlying scale is bipolar in this paper we propose the concept of discrete bipolar universal integral in order to provide a common framework for bipolar discrete integrals including as special cases the discrete choquet shilkret and sugeno bipolar integrals moreover we provide two different axiomatic characterizations of the proposed discrete bipolar universal integral

multiple positive solutions for multipoint boundary value problems with one dimensional p laplacian abstract in this paper we consider the multiplicity of positive solutions for the one dimensional p laplacian differential equation p u q t f t u u 0 t 0 1 subject to some boundary conditions by means of a fixed point theorem due to avery and peterson we provide sufficient conditions for the existence of multiple positive solutions to some multipoint boundary value problems

ergodic theorems for discrete time stochastic systems using a stochastic lyapunov function sufficient conditions are established under which the law of large numbers and related ergodic theorems hold for nonlinear stochastic systems operating under feedback it is shown that these conditions hold whenever a moment condition is satisfied this may be interpreted as a generalizaton of the martingale property if in addition a stochastic controllability condition holds then it is shown that the underlying distributions governing the system converge to an invariant probability at a geometric rate the key assumption used is that a markov chain with stationary transition probabilities exists that serves as a state process for the closed loop system

controllability to the origin implies state feedback stabilizability for discrete time nonlinear systems abstract the problem of finite time state feedback stabilizability of discrete time nonlinear systems has been considered in this technical communique two assertions have been proved first if the system is n step controllable to the origin then there is a state feedback control law for which the trajectory of the closed loop system converges to the origin in n steps second if the system is asymptotically controllable to the origin and satisfies the controllability rank condition at the origin then there is a state feedback control law for which the trajectory of the closed loop system converges to the origin in finite steps

minimal realization of nonlinear systems described by input output difference equations we consider a general class of nonlinear discrete time systems described by their input output i o relationship we first present the necessary and sufficient conditions for existence of a local observable state space realization of the system and an explicit algorithm for computing it in cases where the i o map and its resulting realization are nonminimal we formulate an algorithm for extracting its minimal realization whenever possible the developed theory and algorithms are illustrated by means of several examples

on uncontrollable discrete time bilinear systems which are nearly controllable in this note for a class of uncontrollable discrete time bilinear systems it is shown that the controllable region nearly covers the whole space while the uncontrollable region is only a hypersurface as a result for almost any initial state and any terminal state of the system the former can be transferred to the latter in addition the two dimensional controllability counterexamples in are generalized to arbitrary finite dimensional cases

on near controllability and stabilizability of a class of discrete time bilinear systems in this paper the near controllability and stabilizability of a class of discrete time bilinear systems are studied a necessary and sufficient condition for the near controllability of the systems is first derived then on the basis of the corresponding near controllability criterion the stabilizability problem of the systems is solved in turn

a parameter free elicitation of the probability weighting function in medical decision analysis an important reason why people violate expected utility theory is probability weighting previous studies on the probability weighting function typically assume a specific parametric form exclude heterogeneity in individual preferences and exclusively consider monetary decision making this study presents a method to elicit the probability weighting function in rank dependent expected utility theory that makes no prior assumptions about the functional form of the probability weighting function we use both aggregate and individual subject data thereby allowing for heterogeneity of individual preferences and we examine probability weighting in a new domain medical decision making there is significant evidence of probability weighting both at the aggregate and at the individual subject level the modal probability weighting function is inverse s shaped displaying both lower subadditivity and upper subadditivity probability weighting is in particular relevant at the boundaries of the unit interval compared to studies involving monetary outcomes we generally find more elevation of the probability weighting function the robustness of the empirical findings on probability weighting indicates its importance ignoring probability weighting in modeling decision under risk and in utility measurement is likely to lead to descriptively invalid theories and distorted elicitations

stochastic dominance and cumulative prospect theory we generalize and extend the second order stochastic dominance condition for expected utility to cumulative prospect theory the new definitions include preferences represented by s shaped value functions inverse s shaped probability weighting functions and loss aversion the stochastic dominance conditions supply a framework to test different features of cumulative prospect theory in the experimental part of the paper we offer a test of several joint hypotheses on the value function and the probability weighting function assuming empirically relevant weighting functions we can reject the inverse s shaped value function recently advocated by levy and levy 2002 in favor of the s shaped form in addition we find generally supporting evidence for loss aversion violations of loss aversion can be explained by subjects using the overall probability of winning as a heuristic

an empirical test of gain loss separability in prospect theory we investigate a basic premise of prospect theory that the valuation of gains and losses is separable in prospect theory gain loss separability implies that a mixed gamble is valued by summing the valuations of the gain and loss portions of that gamble two experimental studies demonstrate a systematic violation of the double matching axiom an axiom that is necessary for gain loss separability we document a reversal between preferences for mixed gambles and the associated gain and loss gambles mixed gamble a is preferred to mixed gamble b but the gain and loss portions of b are preferred to the gain and loss portions of a the observed choice patterns are consistent with a process in which individuals are less sensitive to probability differences when choosing among mixed gambles than when choosing among either gain or loss gambles

a generalized multi point boundary value problem for second order ordinary differential equations let f 0 1 x r 2 r be a function satisfying caratheodory s conditions and e t l 1 0 1 let x i t j 0 1 a i b j r i 1 2 m 2 j 1 2 n 2 0 x 1 x 2 x m 2 1 0 t 1 t 2 t n 2 1 be given this paper is concerned with the problem of existence of a solution for the generalized multi point boundary value problems x t f t x t x t e t 0

global stabilization of discrete time homogeneous systems abstract the feedback stabilization of continuous time r homogeneous systems has been studied by several authors see for instance dayawansa and martin proceedings of the 28th c d c tampa florida december 1989 hermes j differential equations 92 1991 76 89 hermes systems control lett 24 1995 7 11 kawski proceedings of the 27th c d c texas 1988 texas kawski control theory and advanced technology vol 6 mita press tokyo 1996 pp 497 516 sepulchre and aeyels math control signal systems 9 1996 34 58 in kawski analysis of controlled dynamical systems birkhauser basel 1991 kawski proceedings of ifac nolcos 1995 kawski gave an intrinsic concept of homogeneity with respect to general smooth dilations in this note we define the homogeneity of transition maps w r t continuous dilations and we show how one can construct a global stabilizing feedback control for discrete time homogeneous systems which are locally asymptotically stabilizable

the data of levy and levy 2002 prospect theory much ado about nothing actually support prospect theory levy and levy management science 2002 present data that according to their claims violate prospect theory they suggest that prospect theory s hypothesis of an s shaped value function concave for gains and convex for losses is incorrect however all the data of levy and levy are perfectly consistent with the predictions of prospect theory as can be verified by simply applying prospect theory formulas the mistake of levy and levy is that they incorrectly thought that probability weighting could be ignored

on controllability and near controllability of discrete time inhomogeneous bilinear systems without drift in this paper controllability and near controllability of discrete time inhomogeneous bilinear systems without drift are studied necessary and sufficient conditions for controllability and near controllability of the systems are respectively presented in particular algorithms for computing the control inputs to achieve the transition of a given pair of states for the controllable systems and nearly controllable systems are also provided examples are shown to demonstrate the conceptions and results of the paper

invariant codistributions and the feedforward form for discrete time nonlinear systems the goal of this paper is two fold first given an arbitrary n dimensional discrete time nonlinear dynamical system necessary and sufficient conditions for the existence of a one dimensional invariant codistribution are obtained second it is shown that the previous conditions can be used iteratively to obtain a nested sequence of n invariant codistributions with the properties that each codistribution contains the previous one and the last one coincides with the cotangent bundle of the state manifold as a byproduct necessary and sufficient conditions are obtained for a discrete time nonlinear dynamical system to be equivalent to the so called feedforward form

non linear non interacting control with stability in discrete time a dynamic solution the geometric approach proposed in califano et al nonlinear noninteracting control with stability in discrete time a geometric approach int j control 75 1 pp 11 22 2002 for non linear non interacting control with stability via static state feedback in discrete time is now used to find a dynamic solution for systems characterized by an invertible drift geometric necessary and sufficient conditions are given a constructive procedure for the computation of the dynamic compensator solving the problem is proposed

the effect sampling on linear equivalence and feedback linearization we investigate the effect of sampling on linearization for continuous time systems it is shown that the discretized system is linearizable by state coordinate change for an open set of sampling times if and only if the continuous time system is linearizable by state coordinate change also it is shown that linearizability via digital feedback imposes highly nongeneric constraints on the structure of the plant even if this is known to be linearizable with continuous time feedback for n 2 we show under the assumption of completeness of adfg that if the discretized system is lineariable by state coordinate change and feedback then the continuous time affine complete analytic system is linearizable by state coordinate change only also we suggest a method of proof when n 3

sampled data observer error linearization the effects of time sampling on the solvability conditions for the observer linearization design methodology are investigated it is shown that the class of systems for which this design method can be applied for an open set of sampling times is quite small in particular when the dimension of the state space is two it consists only of those systems that are state equivalent to a linear system the practical implication is that digital implementations of this methodology will have to be approximate

observability of autonomous discrete time non linear systems a geometric approach in this paper the observability of autonomous discrete time systems is studied from a purely differential geometric point of view as with continuous time systems this approach leads to a local canonical form for an observable system a proposal for the generalization of an invariant subspace is made

discrete time transitivity and accessibility analytic systems a basic open question for discrete time nonlinear systems is that of determining when in analogy with the classical continuous time positive form of chow s lemma accessibility follows from transitivity of a natural group action this paper studies the problem and establishes the desired implication for analytic systems in several cases i compact state space ii under a poisson stability condition and iii in a generic sense in addition the paper studies accessibility properties of the controllability sets recently introduced in the context of dynamical systems studies finally various examples and counterexamples are provided relating the various lie algebras introduced in past work

non linear non interacting control with stability in discrete time a geometric framework the aim of the paper is to set the non linear non interacting control problem with stability in discrete time in a correct geometric framework so providing a solution which recalls the continuous approach and to point out the peculiarities of discrete time dynamics geometric necessary and sufficient conditions for the solvability of the problem are given and a constructive method figures out the regular static state feedback solution it is shown that if the given dynamics is feedback equivalent to a decoupled system characterized by an invertible drift the computation of the distributions involved can be carried out in a simple and elegant way the main results are thus proved exhaustively in this case and then generalized to submersive systems

twin solutions to singular dirichlet problems the existence of two nonnegative solutions to dirichlet second order boundary value problems is established in this paper our nonlinearity may be singular at y 0 t 0 and or t 1

existence and iteration of monotone positive solutions for multipoint boundary value problem with p laplacian operator in the paper we obtain the existence of monotone positive solutions and establish acorresponding iterative scheme for the following multipoint boundary value problem with p laplacian operator f p u t q t f t u t 0 0

parameter free elicitation of utility and probability weighting functions this paper proposes a two step method to successively elicit utility functions and decision weights under rank dependent expected utility theory and its more descriptive version cumulative prospect theory the novelty of the method is that it is parameter free and thus elicits the whole individual preference functional without imposing any prior restriction this method is used in an experimental study to elicit individual utility and probability weighting functions for monetary outcomes in the gain and loss domains concave utility functions are obtained for gains and convex utility functions for losses the elicited weighting functions satisfy upper and lower subadditivity and are consistent with previous parametric estimations the data also show that the probability weighting function for losses is more elevated than for gains

the probability weighting function a probability weighting finction w p is a prominent feature of several non expected utility theories including prospect theoiy and rank dependent models empirical esti mates indicate that w p is regressive first w p p then iv p p s shaped first concave then convex and asymmetrical intersecting the diagonal at about 1 3 the paper states axioms for several w p forms including the compound invariant w p exp ln p 1 0 a 1 which is regressive s shaped and with an invariant fixed point and inflection point at i e 37 the common ratio effect allais 1953 refers to the obselvation that the more risky of two simple prospects becomes relatively more attractive when the probability of winning is reduced by equal proportion in both prospects thus a person who prefers a sure gain of 100 000 over a coin toss for 300 000 or nothing might also prefer a one in a million lottery ticket for 300 000 over a two in a million lottery ticket for 100 000 this contradicts expected utility but not common sense there is a world of difference between certainty and a 50 50 shot the difference between one or two chances in a million is negligible the example has all the force and simplicity of classical arguments for nonlinear utility where the utility interval from say 10 and 20 is taken as self evidently greater than the utility interval from 1 000 010 and 1 000 020 both arguments appeal directly to our intuitions about numbers a major point of difference is that the money argument involves a constant money intelval and the probability argument a constant probability ratio a minor difference is that in the money domain a constant interval has less impact as the numbers get larger while in the probability domain a constant ratio has less impact as the numbers get smaller putting the two demonstrations side by side like this raises an interesting question namely whether an account of nonlinearity in probabilities can be somehow adapted from classical utility theory modulo a log transformation converting statements about probability ratios into statements about utility intervals indeed in their seminal paper on prospect theory kahneman and tversky 1979 explained the common ratio effect by means of a nonlinear transformation of probabilities into decision weights p w p with log w

simple sufficient conditions for reachability of discrete time polynomial systems we consider reachability of discrete time polynomial systems the reachability of such systems can be interpreted as the surjectivity of the polynomial mappings defined by the systems for a polynomial mapping between suitable spaces of the same dimensions it has been shown that the injectivity of the mapping also implies the surjectivity by utilizing this fact we derive sufficient conditions for the reachability of the polynomial systems which essentially check the injectivity of the polynomial mappings

on controllability near controllability controllable subspaces and nearly controllable subspaces of a class of discrete time multi input bilinear systems abstract this paper considers a class of discrete time multi input inhomogeneous bilinear systems the structure of such systems is most close to linear time invariant systems but they own a strong property that is if the systems are uncontrollable they can still be nearly controllable necessary and sufficient conditions for controllability and near controllability of the systems are established by using a classical decomposition furthermore a geometric characterization is given for the systems such that controllable subspaces and nearly controllable subspaces are derived and characterized similar results on controllability are also obtained for the continuous time counterparts of the systems finally examples are provided to demonstrate the conceptions and results of this paper

remarks on universal nonsingular controls for discrete time systems for analytic discrete time systems it is shown that uniform forward accessibility implies the generic existence of universal nonsingular control sequences a particular application is given by considering forward accessible systems on compact manifolds for general systems it is proved that the complement of the set of universal sequences of infinite length is of the first category for classes of systems satisfying a descending chain condition and in particular for systems defined by polynomial dynamics forward accessibility implies uniform forward accessibility

existence and iteration of positive solutions for a multipoint one dimensional p laplacian boundary value problem abstract in this paper we study the existence and iteration of positive solutions for the one dimensional p laplacian differential equation p u t q t f t u t u t 0 t 0 1 subject to the following multipoint boundary condition u 0 i 1 n 2 i u i u 1 i 1 n 2 i u i by applying a monotone iterative method we not only obtain the existence of positive solutions for the problem but also establish iterative schemes for approximating the solutions

risk aversion in cumulative prospect theory this paper characterizes the conditions for strong risk aversion and second order stochastic dominance for cumulative prospect theory strong risk aversion implies a convex weighting function for gains and a concave one for losses it does not necessarily imply a concave utility function the latter does follow if the weighting functions are continuous by investigating the exact relationship between loss aversion and strong risk aversion a natural index for the degree of loss aversion is derived

commutative algebraic methods for controllability of discrete time polynomial systems abstractin this paper we consider controllability of discrete time polynomial systems first we present a forward accessibility local reachability condition that can be verified in finite time in contrast to conventional conditions second we give a backward accessibility local controllability condition for an invertible system and a condition to verify invertibility finally we derive sufficient conditions to test whether the forward accessible system is reachable and to test the backward accessible system is controllable

triple positive solutions to third order three point bvp with increasing homeomorphism and positive homomorphism in this paper we investigate the existence of triple positive solutions for nonlinear differential equations boundary value problems with increasing homeomorphism and positive homomorphism operator by using fixed point theorems in cones we establish results on the existence of three positive solutions with suitable growth conditions imposed on the nonlinear term as applications two examples are given to demonstrate our result the conclusions in this paper essentially extend and improve the known results

on controllability of discrete time bilinear systems by near controllability abstract in this paper controllability of discrete time bilinear systems is studied by applying a recent result on near controllability a new sufficient condition for controllability of the systems is presented where controllability is proved by approximation with near controllability the new condition is algebraically verifiable and is hence easy to apply compared with a classical result on controllability of discrete time bilinear systems which can be effective even when the classical result does not work furthermore the control inputs to achieve the transition of the systems between any given pair of states are approximately computable according to near controllability therefore near controllability can be used to not only better characterize the system properties but also prove controllability with computable control inputs the new condition is then generalized to derive similar results on controllability and near controllability of the systems finally examples are given to illustrate the results of this paper

from chronological calculus to exponential representations of continuous and discrete time dynamics a lie algebraic approach in this paper formal exponential representations of the solutions to nonautonomous nonlinear differential equations are derived it is shown that the chronological exponential admits an ordinary exponential representation the exponent being given by an explicitly computable lie series expansion the results are then used to describe controlled dynamics dynamics under sampling and forced discrete time dynamics the study emphasizes the role of lie algebra techniques in nonlinear control theory and specifies structural similarities between nonautonomous differential equations dynamics under sampling and forced discrete time dynamics up to hybrid ones

on the solvability of polynomial systems arising in control we consider a compactification of a general system of polynomial equations in weighted projective space and give some sufficient conditions about the solvability of a polynomial system over c and r we also prove that for generic linear subspaces the inverse eigenvalue problem with perturbations in the linear subspace always has n solutions

on small controllability and controllability of a class of nonlinear systems in this paper small controllability and controllability of a class of nonlinear systems are studied both the discrete time case and continuous time case are considered by proposing an implicit function approach sufficient conditions for the systems respectively to be small controllable and controllable are obtained examples are also provided to illustrate the results of the paper

multiple positive solutions for the one dimensional singular p laplacian we consider the following boundary value problem f p y q t f y 0 p 1 t 0 1 with y 0 y 1 0 or y 0 y 1 0 using a fixed point theorem for operators on a cone we provide sufficient conditions for the existence of multiple at least three positive solutions to the above boundary value problem an example is also included to illustrate the importance of the result obtained

existence of solutions for weighted p t laplacian system multi point boundary value problems abstract this paper investigates the existence of solutions for weighted p t laplacian system multi point boundary value problems our method is based on leray schauder s degree we give the existence of solutions when the nonlinearity term f t satisfies sub p growth condition or general growth condition respectively moreover the existence of nonnegative and positive solutions has been discussed

investigating generalisations of expected utility theory using experimental data a number of generalizations of the expected utility preference functional are estimated using experimentally generated data involving 100 pairwise choice questions repeated on two separate occasions likelihood ratio tests are conducted to investigate the statistical superiority of the various generalizations and the akaike information criterion is used to distinguish between them the economic superiority of the various generalizations is also explored and the paper concludes that for many subjects the superiority of several of the generalizations is not established copyright 1994 by the econometric society

on accessibility conditions for state space nonlinear control systems on homogeneous time scales abstract an algebraic formalism for nonlinear control systems defined on homogeneous time scales is introduced this formalism is based on the forward backward shifts delta and nabla operators of differential one forms and vector fields the accessibility conditions for considered control systems both in terms of vector fields and one forms are presented

quadratic forms and approximate feed back linearization in discrete time quadratic feedback linearization is discussed for discrete time systems i e approximate feedback linearization up to the second order with respect to input and state variables after introducing in discrete time two equivalence classes invariant under quadratic static state feedback and diffeomorphism two canonical quadratic representations are proposed then it is shown that any nonlinear discrete time dynamics which are controllable in their first approximations can be linearized up to the second order under dynamic feedback the results stated here can be considered as the general discrete time analogues of the continuous time ones kang and krener 1992

reversible linear and nonlinear discrete time dynamics it is shown that any causal discrete time system can be realized with a reversible or invertible state variable representation this bridges the gap with continuous time where flows always satisfy this property and settles an old debate on the relevance of invertibility in nonlinear discrete dynamics as the result applies to the linear case it is shown how the classic approach should be slightly modified and several examples of the benefits that can be obtained are given difference algebra is employed for nonlinear systems it leads to a most elegant characterization of causality which enables reversibility to be demonstrated module theory suffices in the linear case which is supplemented by elementary matrix manipulations

three positive fixed points of nonlinear operators on ordered banach spaces we generalize the fixed point theorem of leggett williams which is a theorem giving conditions that imply the existence of three fixed points of an operator defined on a cone in a banach space we then show how to apply our theorem to prove the existence of three positive solutions to a second order discrete boundary value problem 2001 elsevier science ltd all rights reserved

identification and control of a nonlinear discrete time system based on its linearization a unified framework this paper presents a unified theoretical framework for the identification and control of a nonlinear discrete time dynamical system in which the nonlinear system is represented explicitly as a sum of its linearized component and the residual nonlinear component referred to as a higher order function this representation substantially simplifies the procedure of applying the implicit function theorem to derive local properties of the nonlinear system and reveals the role played by the linearized system in a more transparent form under the assumption that the linearized system is controllable and observable it is shown that 1 the nonlinear system is also controllable and observable in a local domain 2 a feedback law exists to stabilize the nonlinear system locally and 3 the nonlinear system can exactly track a constant or a periodic sequence locally if its linearized system can do so with some additional assumptions the nonlinear system is shown to have a well defined relative degree delay and zero dynamics if the zero dynamics of the linearized system is asymptotically stable so is that of the nonlinear one and in such a case a control law exists for the nonlinear system to asymptotically track an arbitrary reference signal exactly in a neighborhood of the equilibrium state the tracking can be achieved by using the state vector for feedback or by using only the input and the output in which case the nonlinear autoregressive moving average narma model is established and utilized these results are important for understanding the use of neural networks as identifiers and controllers for general nonlinear discrete time dynamical systems

on the finiteness of accessibility test for nonlinear discrete time systems it is shown that for two large subclasses of discrete time nonlinear systems analytic systems defined on a compact state space and rational systems the minimum length r for input sequences ca

formulas relating kl stability estimates of discrete time and sampled data nonlinear systems abstract we provide an explicit kl stability or input to state stability iss estimate for a sampled data nonlinear system in terms of the kl estimate for the corresponding discrete time system and a k function describing inter sample growth it is quite obvious that a uniform inter sample growth condition plus an iss property for the exact discrete time model of a closed loop system implies uniform iss of the sampled data nonlinear system our results serve to quantify these facts by means of comparison functions our results can be used as an alternative to prove and extend results in 1 or extend some results in 4 to a class of nonlinear systems finally the formulas we establish can be used as a tool for some other problems which we indicate

analysis and stabilization for networked linear hyperbolic systems of rationally dependent conservation laws in this paper for a networked linear hyperbolic partial differential equations pdes system of conservation laws the propagation periods of which are rationally dependent with coupled boundary conditions we propose a novel approach to analyze its controllability and observability in addition we propose a design method of a stabilizing controller where a boundary input with boundary valued feedback is considered first we characterize the control properties such as controllability of such a pde system in terms of the corresponding ones of a finite dimensional discrete time system defined on the boundaries of the pde system which is derived by fully exploiting the method of characteristics since the obtained discrete time system is low dimensional its analysis is relatively easier next we propose a design method of a stabilizing controller based on this discrete time system finally numerical simulations are presented to show that the proposed method is effective

dead beat controllability of polynomial systems symbolic computation approaches state and output dead beat controllability tests for a very large class of polynomial systems with rational coefficients may be based on the quantifier elimination by partial cylindrical algebraic decomposition qepcad symbolic computation program the method is unified for a very large class of systems and can handle one or two sided control constraints families of minimum time state output dead beat controllers are obtained the computational complexity of the test is prohibitive for general polynomial systems but by constraining the structure of the system we may beat the curse of complexity a computationally less expensive algebraic test for output dead beat controllability for a class of odd polynomial systems is presented necessary and sufficient conditions are given they are still very difficult to check therefore a number of easier to check sufficient conditions are also provided the latter are based on the grobner basis method and qepcad it is shown on a subclass of odd polynomial systems how it is possible to further reduce the computational complexity by exploiting the structure of the system

involutive flows and discretization errors for nonlinear driftless control systems in a continuous time nonlinear driftless control system an involutive flow is a composition of input profiles that does not excite any lie bracket such flow composition is trivial as it correspo

on sampled data models for nonlinear systems models for deterministic continuous time nonlinear systems typically take the form of ordinary differential equations to utilize these models in practice invariably requires discretization in this paper we show how an approximate sampled data model can be obtained for deterministic nonlinear systems such that the local truncation error between the output of this model and the true system is of order spl delta sup r 1 where spl delta is the sampling period and r is the system relative degree the resulting model includes extra zero dynamics which have no counterpart in the underlying continuous time system the ideas presented here generalize well known results for the linear case we also explore the implications of these results in nonlinear system identification

reachability and steering of rolling polyhedra a case study in discrete nonholonomy rolling a ball on a plane is a standard example of nonholonomy reported in many textbooks and the problem is also well understood for any smooth deformation of the surfaces for nonsmoothly deformed surfaces however much less is known although it may seem intuitive that nonholonomy is conserved think e g to polyhedral approximations of smooth surfaces current definitions of nonholonomy are inherently referred to systems described by ordinary differential equations and are thus inapplicable to such systems in this paper we study the set of positions and orientations that a polyhedral part can reach by rolling on a plane through sequences of adjacent faces we provide a description of such reachable set discuss conditions under which the set is dense or discrete or has a compound structure and provide a method for steering the system to a desired reachable configuration robustly with respect to model uncertainties based on ideas and concepts encountered in this case study and in some other examples we provide we turn back to the most general aspects of the problem and investigate the possible generalization of the notion of kinematic nonholonomy to nonsmooth discrete and hybrid dynamical systems to capture the essence of phenomena commonly regarded as nonholonomic at least two irreducible concepts are to be defined of internal and external nonholonomy which may coexist in the same system these definitions are instantiated by examples

linearization of discrete time systems by exogenous dynamic feedback it is shown that a discrete time system may be linearizable by exogenous dynamic feedback even if it cannot be linearized by endogenous feedback this property is completely unexpected and constitutes a fundamental difference with respect to the continuous time case the notion of exogenous linearizing output is introduced it is shown that existence of an exogenous linearizing output is a sufficient condition for dynamic linearizability necessary and sufficient conditions for the existence of an exogenous linearizing output are provided the results of the paper are obtained using transformal operator matrices the properties of such operators are studied the theory is applied to the exact discrete time model of a mobile robot showing that the above mentioned property concerns not only academic examples but also physical systems

on the observer design in discrete time abstract the paper deals with the equivalence under coordinates change and output transformation of a discrete time nonlinear system to observer canonical forms necessary and sufficient conditions for local equivalence to these forms are given

existence of multiple positive solutions for one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for one dimensional p laplacian p u f t u 0 t 0 1 subject to the boundary value conditions p u 0 i 1 n 2 a i p u i u 1 i 1 n 2 b i u i where p s s p 2 s p 1 i 0 1 with 0 1 2 n 2 1 and a i b i satisfy a i b i 0 0 i 1 n 2 a i 1 and i 1 n 2 b i 1 using a fixed point theorem for operators on a cone we provide sufficient conditions for the existence of multiple at least three positive solutions to the above boundary value problem

on existence of multiple positive solutions for ϕ laplacian multipoint boundary value abstract in this paper we consider the following multipoint boundary value problem with one dimensional laplacian x t q t f t x t x t 0 t 0 1 x 0 i 1 n 2 i x i x 1 i 1 n 2 i x i where is an odd and increasing homeomorphism i 0 1 with 0 1 2 n 2 1 i and i are nonnegative constants and f t x t x t is continuous and allowed to change sign by fixed point theorems we obtain new results on the existence of at least three positive solutions of this boundary value problem which includes and improves some related results in the relevant literature

feedback linearization of sampled data systems it is shown that feedback linearizability of a continuous time system can be destroyed through the introduction of the usual sample and hold devices a method whereby a feedback linearizable discrete time model can be recovered is given

curvature of the probability weighting function when individuals choose among risky alternatives the psychological weight attached to an outcome may not correspond to the probability of that outcome in rank dependent utility theories including prospect theory the probability weighting function permits probabilities to be weighted nonlinearly previous empirical studies of the weighting function have suggested an inverse s shaped function first concave and then convex however these studies suffer from a methodological shortcoming estimation procedures have required assumptions about the functional form of the value and or weighting functions we propose two preference conditions that are necessary and sufficient for concavity and convexity of the weighting function empirical tests of these conditions are independent of the form of the value function we test these conditions using preference ladders a series of questions that differ only by a common consequence the concavity convexity ladders validate previous findings of an s shaped weighting function concave up to p 0 40 and convex beyond that probability the tests also show significant nonlinearity away from the boundaries 0 and 1 finally we fit the ladder data with weighting functions proposed by tversky and kahneman tversky amos daniel kahneman 1992 advances in prospect theory cumulative representation of uncertainty j risk and uncertainty5 297 323 and prelec prelec dra en 1995 the probability weighting function unpublished paper

nonnegative solutions to nonlocal boundary value problems for systems of second order differential equations dependent on the first order derivatives abstract in this paper we consider nonlocal boundary value problems for systems of second order differential equations with dependence on the first order derivatives and deviating arguments by using a fixed point theorem due to avery and peterson sufficient conditions are obtained that guarantee the existence of at least three nonnegative solutions to such problems we investigate our problem both for delayed and advanced arguments i i and also for the case when i t i t t t 0 1 in all cases arguments i i can change the character on 0 1 so in some subinterval i of 0 1 they can be delayed in i and advanced in 0 1 i some remarks concern also the case when differential equations do not depend on the first order derivatives examples illustrate some results

new insights on the analysis of nonlinear time delay systems application to the triangular equivalence in this paper we present recent advances towards an algebraic framework for the analysis and control of nonlinear systems with delays we show the usefulness of these results by applying them to obtain a constructive characterization of the equivalence of a given system to the so called triangular form

gain loss separability and coalescing in risky decision making this experiment tested two behavioral properties of risky decision making gain loss separability gls and coalescing cumulative prospect theory cpt implies both properties but the transfer of attention exchange tax model violates both original prospect theory satisfies gls but may or may not satisfy coalescing depending on whether editing rules are assumed a configural form of cpt proposed by wu and markle wu g a b markle 2004 an empirical test of gain loss separability in prospect theory working paper 06 25 04 graduate school of business university of chicago violates gls but satisfies coalescing new tests were designed and conducted to test these theories against specific predictions of a tax model this model used parameters estimated from previous data together with simple new assumptions to extend tax to gambles with negative and mixed consequences contrary to all three forms of prospect theory systematic violations of both coalescing and gls were observed violations of gls were confirmed by analyses of individual data patterns by means of an error model in which each choice can have a different rate of error without estimating any parameters from the new data the tax model predicted the majority choices in the new data fairly well correctly predicting when modal choices would violate gls when they would satisfy it and when indifference would be observed

internally exponentially stable non linear discrete time non interacting control via static feedback the problem of discrete time block non interacting control with internal exponential stability is treated by identifying the linearized fixed modes common to every non interactive closed loop a necessary condition for achieving an exponentially stable solution to the problem is provided also through a special decomposition of the given system a sufficient condition is obtained owing to peculiarities intrinsic to discrete time non linear systems the development of the solution is not completely parallel to that of the solution for the class of continuous time systems

controllability of nonlinear discrete time systems a lie algebraic approach this paper presents a geometric study of controllability for discrete time nonlinear systems various accessibility properties are characterized in terms of lie algebras of vector fields some of the results obtained are parallel to analogous ones in continuous time but in many respects the theory is substantially different and many new phenomena appear