hybrid systems with time scales and impulses abstract in this paper we describe hybrid systems introducing special time scales and impulsive effects so as to provide a broader perspective for hybrid systems

nonlinear control of constrained linear systems via predictive reference management a method based on conceptual tools of predictive control is described for solving set point tracking problems wherein pointwise in time input and or state inequality constraints are present it consists of adding to a primal compensated system a nonlinear device called command governor cg whose action is based on the current state set point and prescribed constraints the cg selects at any time a virtual sequence among a family of linearly parameterized command sequences by solving a convex constrained quadratic optimization problem and feeds the primal system according to a receding horizon control philosophy the overall system is proved to fulfill the constraints be asymptotically stable and exhibit an offset free tracking behavior provided that an admissibility condition on the initial state is satisfied though the cg can be tailored for the application at hand by appropriately choosing the available design knobs the required online computational load for the usual case of affine constraints is well tempered by the related relatively simple convex quadratic programming problem

a representation of an efficiency equivalent polyhedron for the objective set of a multiple objective linear program abstract associated with the objective set y of a linear k objective minimization problem is the efficiency equivalent polyhedron y y r k since y has the same efficient structure as y and since every extreme point of y is efficient this polyhedron provides a promising avenue for the analysis of the given multiple objective linear program molp however in order to fully explore this avenue a representation of y as a system of linear inequalities is needed in this paper an algorithm is given to construct a matrix h and a vector g such that y has the representation hy g and it is shown that no inequality in this representation is redundant the input data for the algorithm are a finite set of points of y containing the efficient extreme points and a finite set of recession directions for y containing the directions associated with unbounded efficient edges these data which can be obtained using standard molp software packages are used to form a polar polyhedron whose extreme points are precisely what is needed to define h and g

the exact analytic solutions of a nonlinear differential iterative equation abstract this paper is concerned with a second order nonlinear iterated differential equation of the form c 0 x z c 1 x z c 2 x z x p z b x z h z by constructing a convergent power series solution of an auxiliary equation analytic solutions of the original equation are obtained we discuss not only the general case 1 but also the critical case 1 especially when is a root of unity furthermore the exact and explicit analytic solution of the original equation is investigated for the first time such equations are important in both applications and the theory of iterations

connected and alternating vectors polyhedra and algorithms given a graphg v e letas s l be the edge set incidence vectors of its nontrivial connected subgraphs

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

classifications and existence of positive solutions of higher order nonlinear delay differential equations in this paper necessary and sufficient conditions for the existence and classification of positive solutions of the higher order neutral difference equation graphics are obtained where r n 0 p n i greater than or equal to 0 i 1 2 m and f n s 1 s 1 is continuous with respect to n and s j j 1 l c 2003 elsevier inc all rights reserved

analytic solutions of a second order iterative functional differential equation abstract this paper is concerned with a second order iterative functional differential equation x x r z c 0 z c 1 x z c m x m z where r and m are nonnegative integers x 0 z z x 1 z x z x 2 z x x z etc are the iterates of the function x z by constructing a convergent power series solution y z of a companion equation of form 2 y r 1 z y r z y r 1 z y r z y r z 3 i 0 m c i y i z analytic solutions of the form y y 1 z for the original differential equation are obtained

classifications and existence criteria for positive solutions of systems of nonlinear differential equations classification schemes for positive solutions of a class of second order nonlinear differential systems are given in terms of their asymptotic magnitudes and necessary as well as sufficient conditions for the existence of these solutions are also provided

oscillation of certain second order nonlinear differential equations abstract in this paper we consider the second order nonlinear differential equation formula where 0 is any quotient of odd integers a c 1 r 0 q c r r f c r r xf x 0 f x 0 for x 0 some new sufficient conditions for the oscillation of all solutions of are obtained several examples that dwell upon the importance of our results are also included

fulfilling hard constraints in uncertain linear systems by reference managing a method based on conceptual tools of predictive control is described for tackling tracking problems of uncertain linear systems wherein pointwise in time input and or state inequality constraints are present the method consists of adding to a primal compensated system a nonlinear device called predictive reference filter which manipulates the desired reference in order to fulfill the prescribed constraints provided that an admissibility condition on the initial state is satisfied the control scheme is proved to fulfill the constraints as well as stability and set point tracking requirements for all systems whose impulse step responses lie within given uncertainty ranges

probabilistic output admissible set for systems with time varying uncertainties this paper considers time varying uncertain constrained systems and develops a method for computing a probabilistic output admissible poa set this set consists of the initial states probabilistically assured to satisfy the constraint the time invariant counterpart has already been investigated in hatanaka and takaba computations of probabilistic output admissible set for uncertain constrained systems automatica 44 2 2008 to appear we first define the poa set for time varying uncertainties with finite dimensional probability space then we show that an algorithm similar to hatanaka and takaba computations of probabilistic output admissible set for uncertain constrained systems automatica 44 2 2008 to appear provides the poa set also in the time varying case as long as an upper bound of a what we call future output admissibility foa index is available we moreover present two methods for computing the upper bound of the foa index probabilistic and deterministic methods a numerical simulation demonstrates the effectiveness of our algorithm

linear systems with state and control constraints the theory and application of maximal output admissible sets the initial state of an unforced linear system is output admissible with respect to a constraint set y if the resulting output function satisfies the pointwise in time condition y t in y t or 0 the set of all possible such initial conditions is the maximal output admissible set o sub infinity the properties of o sub infinity and its characterization are investigated in the discrete time case it is generally possible to represent o sub infinity or a close approximation of it by a finite number of functional inequalities practical algorithms for generating the functions are described in the continuous time case simple representations of the maximal output admissible set are not available however it is shown that the discrete time results may be used to obtain approximate representations

lie symmetry analysis and exact explicit solutions for general burgers equation in this paper the lie symmetry analysis is performed for the general burgers equation the exact solutions and similarity reductions generated from the symmetry transformations are provided furthermore the all exact explicit solutions and similarity reductions based on the lie group method are obtained some new method and techniques are employed simultaneously such exact explicit solutions and similarity reductions are important in both applications and the theory of nonlinear science

exact complexity certification of active set methods for quadratic programming active set methods are recognized to often outperform other methods in terms of speed and solution accuracy when solving small size quadratic programming qp problems making them very attractive in embedded linear model predictive control mpc applications a drawback of active set methods is the lack of tight bounds on the worst case number of iterations a fundamental requirement for their implementation in a real time system extensive simulation campaigns provide an indication of the expected worst case computation load but not a complete guarantee this paper solves such a certification problem by proposing an algorithm to compute the exact bound on the maximum number of iterations and floating point operations required by a state of the art dual active set qp solver the algorithm is applicable to a given qp problem whose linear term of the cost function and right hand side of the constraints depend linearly on a vector of parameters as in the case of linear mpc in addition a new solver is presented that combines explicit and implicit mpc ideas guaranteeing improvements of the worst case computation time the ability of the approach to exactly quantify memory and worst case computation requirements is tested on a few mpc examples also highlighting when online optimization should be preferred to explicit mpc

analytic solutions for a class of differential equation with delays depending on state abstract in this paper we study existence of analytic solutions of a class of the differential equation with state dependent delays x z j 0 k t 1 c t j z x j z t g z in the complex field c by constructing a convergent power series solution y z of an auxiliary equation of the form y z y z j 0 k t 1 c t j y z y j z t g y z with g 0 c 0 invertible analytic solutions of the form y y 1 z for the original equation are obtained

classifications and existence of positive solutions of higher order nonlinear iterative functional differential equations classification schemes for eventually positive solutions of a class of higher order nonlinear iterative functional differential equations of the form r t x m 1 t f t x t x t x t 0 in the case when ds r s are given in terms of their magnitudes and necessary as well as sufficient conditions for the existence of these positive solutions are also provided

asymptotic behaviour of the nonoscillatory solutions of differential equations of second order with delay depending on the unknown function abstract the asymptotic behaviour of the solutions of the differential equations r t x t f t x t x t x t 0 in the case when ds r s is considered

on splitting the area under curves ii two area splitting problems involving real valued functions of a real variable are investigated the second of these is essentially equivalent to finding all functions a c1 0 r with 0 a x x which satisfy the functional differential equation a a x a x x for x 0 r all solutions analytic at x 0 and many which are not are exhibited in closed form

analytic solutions to a class of nonlinear infinite delay differential equations abstract the infinite delay differential equations iddes are studied and the analytic solution of a class of nonlinear iddes is presented based on the characteristics of the reproducing kernel space w 2 0 besides the exact solution is represented in the form of series it is proved that the n term approximation u n x converges to the exact solution u x of the iddes moreover the approximate error of u n x is monotone decreasing the results of experiments showed that the proposed method in this paper is computationally efficient

model predictive control using segregated disturbance feedback this paper proposes a new control parametrization under the model predictive control mpc framework for constrained linear discrete time systems with bounded disturbances the proposed parametrization takes the form of a special piecewise affine disturbance feedback in an effort to reduce conservatism it is a generalization of linear disturbance feedback parametrization introduced in the recent literature numerical computations and stability properties of the resulting mpc problem using the proposed parametrization are discussed when the disturbance set and the problem data satisfy mild assumptions the associated finite horizon optimization can be computed efficiently and exactly the advantage of the proposed parametrization over linear disturbance feedback is illustrated via numerical examples

local analytic solutions of a functional differential equation αz βx z x az bx z in this paper we are concerned with the existence of analytic solution of a functional differential equation email protected z x az bx z where a b a b are four complex numbers we first discuss the existence of analytic solutions for some special cases of the above equation then by reducing the equation with the schroder transformation to the another functional equation with proportional delay an existence theorem is established for analytic solutions of the original equation for the constant l given in the schroder transformation we discuss the case 0 l 1 and l on the unit circle s 1 i e l 1 we study l is at resonance i e at a root of the unity and l is near resonance under the brjuno condition

local analytic solutions of a functional differential equation with a deviating argument depending on the state derivative near resonance this paper is concerned with a functional differential equation x n z 1x az bx z with a deviating argument depending on the state derivative where a b are two complex numbers we first discuss the existence of analytic solutions for some special cases of the above equation then by reducing the equation with the schroder transformation to another functional differential equation with proportional delay an existence theorem is established for analytic solutions of the original equation for the constant l given in the schroder transformation besides the case 0 l 1 we focus on those l on the unit circle s 1 i e l 1 we discuss not only those l s at resonance i e at a root of the unity but also those l near resonance under the brjuno condition

polyhedral polarity defined by a general bilinear inequality letx andy be finite dimensional vector spaces over the real numbers let be a binary relation betweenx andy given by a bilinear inequality the polar of a subsetp ofx is the set of all elements ofy which are related by to all elements ofp the polar of a subset ofy is defined similarly the polar of the polar ofp is called the closure ofp andp is called closed ifp equals its closure we describe the polar of any finitely generated setp as the solution set of a finite system of linear inequalities and describe the closure ofp as a finitely generated set the closed polyhedra are characterized in terms of defining systems of linear inequalities and also in terms of the relationship of the polyhedronp with its recessional cone and with certain subsets ofx andy determined by the relation six classes of bilinear inequalities are distinguished in the characterization of closed polyhedra

lie group classifications and exact solutions for two variable coefficient equations in this paper the lie symmetry analysis and group classifications are performed for two variable coefficient equations the hanging chain equation and the bond pricing equation the symmetries for the two equations are obtained the exact explicit solutions generated from the similarity reductions are presented moreover the exact analytic solutions are considered by the power series method

analytic solutions of a class of iterative functional differential equations analytic solutions are obtained for iterative functional differential equations that are natural extensions of x 1 x x we make use of neutral functional differential equations with proportional delays as well as neutral differential difference equations for achieving our purposes

temporal dimension and transition out of chaos abstract a real time process could evolve governed by difference differential equations we introduce this possibility of discrete continuous evolution in the well known unidimensional logistic equation searching for new behaviour an extension to general hybrid equations is proposed

lie symmetry analysis optimal systems and exact solutions to the fifth order kdv types of equations abstract in this paper the lie symmetry analysis is performed on the fifth order kdv types of equations which arise in modeling many physical phenomena the similarity reductions and exact solutions are obtained based on the optimal system method then the exact analytic solutions are considered by using the power series method

construction of quasi periodic solutions of state dependent delay differential equations by the parameterization method ii analytic case abstract we construct analytic quasi periodic solutions of a state dependent delay differential equation with quasi periodically forcing we show that if we consider a family of problems that depends on one dimensional parameters with some non degeneracy conditions there is a positive measure set of parameters for which the system admits analytic quasi periodic solutions the main difficulty to be overcome is the appearance of small divisors and this is the reason why we need to exclude parameters our main result is proved by a nash moser fast convergent method and is formulated in the a posteriori format of numerical analysis that is given an approximate solution of a functional equation which satisfies some non degeneracy conditions we can find a true solution close to it this is in sharp contrast with the finite regularity theory developed in 18 we conjecture that the exclusion of parameters is a real phenomenon and not a technical difficulty more precisely for generic families of perturbations the quasi periodic solutions are only finitely differentiable in open sets in the complement of parameters set

local analytic solution of a second order functional differential equation with a state derivative dependent delay abstract this paper is concerned with a second order functional differential equation x z 1 x az bx z with a state derivative dependent delay by reducing the equation to another functional differential equation with proportional delay an existence theorem is established for analytic solutions of the original equation and systematic methods for deriving explicit solutions are also given we not only prove the convergence of the formal solution under the diophantine condition i e eigenvalues is far from unit roots but also make progresses without the diophantine condition i e the convergence is equivalent to the well known small divisor problems

projection free parallel quadratic programming for linear model predictive control a key component in enabling the application of model predictive control mpc in fields such as automotive aerospace and factory automation is the availability of low complexity fast optimisation algorithms to solve the mpc finite horizon optimal control problem in architectures with reduced computational capabilities in this paper we introduce a projection free iterative optimisation algorithm and discuss its application to linear mpc the algorithm originally developed by brand for non negative quadratic programs is based on a multiplicative update rule and it is shown to converge to a fixed point which is the optimum an acceleration technique based on a projection free line search is also introduced to speed up the convergence to the optimum the algorithm is applied to mpc through the dual of the quadratic program qp formulated from the mpc finite time optimal control problem we discuss how termination conditions with guaranteed degree of suboptimality can be enforced and how the algorithm

the functional differential equation x t x x t abstract a classification of the solutions of the functional differential equation x t x x t is given and it is proved that every solution either vanishes identically or is strictly monotonie for monotonically increasing solutions existence and uniqueness of the solution x are proved with the condition x t0 x0 where t0 x0 is any given pair of reals in some specified subset of r 2 every monotonically increasing solution is thus obtained it is analytic and depends analytically on t0 and x0 only for t0 x0 1 is the question of analyticity still open

existence of solutions for a mixed type differential equation with state dependence abstract in this paper we study a general n dimensional mixed type differential equation with state dependence many known works give the existence of solutions with the so called return condition in this paper without requiring the return condition we prove a non local existence of solutions by using a technique of compactification and the dependence of the maximum of functions on the size of their domains we apply our result to differential equations with iterates

lie symmetry analysis and exact solutions for the short pulse equation abstract in this paper the lie symmetry analysis and the generalized symmetry method are performed for a short pulse equation spe the symmetries for this equation are given for the traveling wave solutions the exact parametric representations are investigated to guarantee the existence of the above solutions all parameter conditions are determined furthermore the exact analytic solutions are obtained by using the power series method

analytic solutions of an iterative functional differential equation this paper is concerned with a functional differential equation x z 1 x az bx z where a b are two complex numbers by constructing a convergent power series solution y z of a auxiliary equation of the form b 2y z y m 2z ay mz my mz ay z analytic solutions of the form 1b y my 1 z az for the original differential equation are obtained

exact and explicit solutions for a nonlinear extended iterative differential equation abstract this paper is concerned with a nonlinear iterative functional differential equation x z 1 x p z bx z by constructing a convergent power series solution of an auxiliary equation analytic solutions of the original equation are obtained we discuss not only in the general case but also in critical cases especially for given in schroder transformation is a root of the unity and in case h4 we dealt with the equation under the brjuno condition which is weaker than the diophantine condition moreover the exact and explicit solution of the original equation has been investigated for the first time such equations are important in both applications and the theory of iterations

brief paper a predictive controller with artificial lyapunov function for linear systems with input state constraints this paper copes with the problem of satisfying input and or state hard constraints in set point tracking problems stability is guaranteed by synthesizing a lyapunov quadratic function for the system and by imposing that the terminal state lies within a level set of the function procedures to maximize the volume of such an ellipsoidal set are provided and interiorpoint methods to solve on line optimization are considered

analytic solutions of a second order iterative functional differential equation abstract this paper is concerned with a second order iterative functional differential equation x z x m z 2 its analytic solutions are discussed by locally reducing the equation to another functional differential equation with proportional delays 2 y z y z y z y z y z 3 y m z 2 and by constructing a convergent power series solutions for the latter equation

smooth solutions of a nonhomogeneous iterative functional differential equation with variable coefficients using the fixed point theorems of banach and schauder in this paper we discuss the existence uniqueness and stability of smooth solutions of a nonhomogeneous iterative functional differential equation with variable coefficients

existence of analytic solutions of an iterative functional equation abstract this paper is concern analytic solutions of an iterative functional equation of the form f p z q f z h f z z c byconstructing a convergent power series solution of an auxiliary equation g 2 z p z h g z p z z c analytic solutions of the original equation are obtained we discuss not only these appeared in the auxiliary equation at the hyperbolic case 0

polarities given by systems of bilinear inequalities we extend the concept of polar pairs of cones to polyhedra using binary relations given by systems of bilinear inequalities in particular we consider those which give natural generalizations of the theory of blocking and antiblocking of fulkerson these extensions preserve the important relations between vertices and facets of polar pairs

analytic solutions of a second order iterative functional differential equation this paper is concerned with an iterative functional differential equationc 1x z c 2x z c 3x z x az bx z with the delay depends on the argument of the unknown function and the state derivative by reducing the equation with the schroder transformation to another functional differential equation without iteration of the unknown function we give existence of its local analytic solutions which extend the known results in related literature

the brjuno functions and their regularity properties we show that various possible versions of the brjuno function based on different kinds of continued fraction developments are all equivalent and we study their regularity l p bmo and holder properties through a systematic analysis of the functional equation which they fulfill

a multiparametric quadratic programming algorithm with polyhedral computations based on nonnegative least squares model predictive control mpc is one of the most successful techniques adopted in industry to control multivariable systems under constraints on input and output variables to circumvent the main drawback of mpc i e the need to solve a quadratic program qp on line to compute the control action explicit mpc was proposed in the past to precompute the control law off line using multiparametric qp mpqp the resulting form of the mpc law is piecewise affine which is extremely easy to code can be computed online by simple arithmetic operations and requires a maximum number of iterations that can be exactly determined a priori on the other hand the offline computations to solve the mpqp problem require detecting emptiness full dimensionality and minimal hyperplane representations of polyhedra and other computational geometric operations while most of the existing methods solve such operations via linear programming the approach proposed in this paper relies on a nonnegative least squares nnls solver that is very simple to code and fast to execute in addition the new approach exploits qp duality to identify and construct critical regions and to handle degeneracy issues

analytic solutions of an iterative functional differential equation abstract this paper is concerned with an iterative functional differential equation x x r z c 0 z c 1 x z c 2 x x z c m x m z where r and m are nonnegative integers x 0 z z x 1 z x z x 3 z x x x z etc are the iterates of the function x z and j 0 m c j 0 by constructing a convergent power series solution y z of a companion equation of the form y r 1 z y r z j 0 m c j y j z analytic solutions of the form y y 1 z for the original differential equation are obtained

transient response improvement of feedback control systems using hybrid reference control by means of the internal model principle an approach to improve the performance of a stabilised closed loop continuous time linear system based on manipulation of the reference signal is developed a change in the reference signal is equivalent to implementing an instantaneous change via the choice of a decision vector in the state of the reference signal model and the analysis of the proposed approach called hybrid reference control hrc system is then shown to be equivalent to the analysis of a linear impulsive dynamical system conditions for asymptotic stability and convergence of the output tracking error for a hrc system are expressed in term of conditions on the decision vectors conditions are then derived which guarantee that the hrc system leads to an improved transient performance compared to a conventional closed loop control system in particular it is shown how decision vectors are chosen so that a hrc system results in a deadbeat response

a unified framework for hybrid control model and optimal control theory we propose a very general framework that systematizes the notion of a hybrid system combining differential equations and automata governed by a hybrid controller that issues continuous variable commands and makes logical decisions we first identify the phenomena that arise in real world hybrid systems then we introduce a mathematical model of hybrid systems as interacting collections of dynamical systems evolving on continuous variable state spaces and subject to continuous controls and discrete transitions the model captures the identified phenomena subsumes previous models yet retains enough structure to pose and solve meaningful control problems we develop a theory for synthesizing hybrid controllers for hybrid plants in all optimal control framework in particular we demonstrate the existence of optimal relaxed and near optimal precise controls and derive generalized quasi variational inequalities that the associated value function satisfies we summarize algorithms for solving these inequalities based on a generalized bellman equation impulse control and linear programming

systems with persistent disturbances predictive control with restricted constraints predictive regulation of linear discrete time systems subject to unknown but bounded disturbances and to state control constraints is addressed an algorithm based on constraint restrictions is presented and its stability properties are analysed

analytic solutions of a second order nonautonomous iterative functional differential equation abstract in this paper a second order nonautonomous iterative functional differential equation is considered by reducing the equation with the schroder transformation to another functional differential equation without iteration of the unknown function we give existence of its local analytic solutions we first discuss the case that the constant given in the schroder transformation does not lie on the unit circle in c and the case that the constant lies on the circle but fulfills the diophantine condition then we further study the case that the constant is a unit root in c but the diophantine condition is offended finally we investigate analytic solutions of the form of power functions

a b spline based pseudo inversion approach for constrained optimal output transition the contribution of this paper is to propose a new method for the continuous time optimal output transition problem under constraints on the control effort the new method situates in the recently

analytic solutions of an iterative functional differential equation abstract this paper is concerned with an iterative functional differential equation x z x m z where x m z x x x z is the m th iterate of the function x z by constructing a convergent power series solution y z of a companion equation of the form y z y z y m z analytic solutions of the form y y 1 z for the original differential equation are obtained

local invertible analytic solutions for an iterative differential equation related to a discrete derivatives sequence abstract in this paper we are concerned with the existence of analytic solutions of a class of iterative differential equation f z 1 k f 1 z a 1 f 2 z a 2 f n z a n in the complex field c where k c 0 a i r f i z denotes ith iterate of f z i 1 2 n the above equation is closely related to a discrete derivatives sequence f m see y f s petermann jean luc remy ilan vardi discrete derivative of sequences adv in appl math 27 2001 562 584 we first give the existence of analytic solutions of the form of power functions for such an equation then by constructing a convergent power series solution y z of an auxiliary equation of the form x z k x z x z a 1 x 2 z a 2 x n z a n invertible analytic solutions of the form f z x x 1 z for the original equation are obtained we discuss not only the constant at resonance i e at a root of the unity but also those near resonance near a root of the unity under the brjuno condition

brief paper computations of probabilistic output admissible set for uncertain constrained systems this paper considers uncertain constrained systems and develops two algorithms for computing a probabilistic output admissible poa set which is a set of initial states probabilistically assured to satisfy the constraint the first algorithm is inspired by an existing randomized sequential technique the second algorithm alleviates the computational effort based on heuristics the present algorithms terminate in a finite number of iterations and provide a poa set additionally we can obtain information on the size of the resulting set a posteriori a numerical simulation demonstrates the applicability of the poa set to a control system design scheme

analysis of zeno behaviors in a class of hybrid systems this note investigates conditions for existence of zeno behaviors where a system undergoes an unbounded number of discrete transitions in a finite length of time in a class of hybrid systems zeno behavior occurs for example when a controller unsuccessfully attempts to satisfy an invariance specification by switching the system among different configurations faster and faster two types of zeno systems are investigated 1 strongly zeno systems where all runs of the system are zeno and 2 weakly zeno systems where only some runs of the system are zeno for constant rate and bounded rate hybrid systems and some nonlinear generalizations necessary and sufficient conditions for both zenoness and strong zenoness are derived the analysis is based on studying the trajectory set of a certain equivalent continuous time system that is associated with the dynamic equations of the hybrid system the relation between the possibility of existence of zeno behaviors in a system and the problem of existence of non zeno safety controllers that keep the system in a specified region of its operating space is also examined it is shown that in certain zeno systems a minimally interventive safety controller may not exist even if a safety controller exists disproving a conjecture made earlier in the literature

on neutral functional differential equations with proportional delays abstract in this paper we develop a comprehensive theory on the well posedness of the initial value problem for the neutral functional differential equation y t ay t i 1 b i y q i t i 1 c i y p i t t 0 y 0 y 0 and the asymptotic behaviour of its solutions we prove that the existence and uniqueness of solutions depend mainly on the coefficientsci i 1 2 and on the smoothness of functions in the solution space as far as the asymptotic behaviour of analytic solutions is concerned thecihave little effect we prove that if re a 0 then the solutiony t either grows exponentially or is polynomial the most interesting result is that if re a 0 anda 0 then the asymptotic behaviour of the solution depends mainly on the characteristic equation a i 1 b i q i 0 these results can be generalized to systems of equations finally we present some examples to illustrate the change of asymptotic behaviour in response to the variation of some parameters the main idea used in this paper is to express the solution in either dirichlet or dirichlet taylor series form

local invertible analytic solution of a functional differential equation with deviating arguments depending on the state derivative abstract this paper is concerned with a functional differential equation of the form x z 1 x a z b x z with the distinctive feature that the argument of the unknown function depends on the state derivative where a b are two complex numbers by reducing the equation with the schroder transformation to another functional differential equation with proportional delay we give existence of its local invertible analytic solutions we discuss not only that the constant given in schroder transformation at resonance i e at a root of the unity but also those near resonance near a root of the unity under the brjuno condition

oscillatory behavior of solutions of certain second order nonlinear differential equations abstract in this paper some simple inequalities are used to offer sufficient conditions for the oscillation of all solutions of the differential equation formula where 0 p q with p q odd integers or p even and q odd integers several examples which dwell upon the importance of our results are also included

survey paper set invariance in control the properties of positively invariant sets are involved in many different problems in control theory such as constrained control robustness analysis synthesis and optimization in this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems

technical communique min max predictive control strategies for input saturated polytopic uncertain systems a novel robust predictive controller for input saturated ltv discrete time systems with polytopic model uncertainties is presented the solution is based on the minimization at each time instant of an upper bound of the worst case infinite horizon quadratic cost under the constraint of steering the set valued future state evolutions emanating from the current state into a feasible and positive invariant set a condition on the initial state is given that suffices to ensure problem solvability for all subsequent time instants under the latter the proposed predictive controller is proved to robustly asymptotically stabilize the input saturated ltv polytopic system