semilocal and local convergence of a fifth order iteration with frechet derivative satisfying holder condition the semilocal and local convergence in banach spaces is described for a fifth order iteration for the solutions of nonlinear equations when the frechet derivative satisfies the holder condition the holder condition generalizes the lipschtiz condition the importance of our work lies in the fact that many examples are available which fail to satisfy the lipschtiz condition but satisfy the holder condition the existence and uniqueness theorem is established with error bounds for the solution the convergence analysis is finally worked out on different examples and convergence balls for each of them are obtained these examples include nonlinear hammerstein and fredholm integral equations and a boundary value problem it is found that the larger radius of convergence balls is obtained for all the examples in comparison to existing methods using stronger conditions

performance limitations of non minimum phase systems in the servomechanism problem abstract this paper studies the cheap regulator problem and the cheap servomechanism problem for systems which may be non minimum phase the study extends some well known properties of perfect regulation and the perfect tracking and disturbance rejection of minimum phase systems to non minimum phase systems it is shown that perfect rejection to disturbances applied to the plant input can be achieved no matter whether the system is minimum phase or non minimum phase whereas a fundamental limitation exists in the achievable transient performance of tracking and rejection to disturbances applied to the plant output for a non minimum phase system and that this limitation can be simply and completely characterized by the number and locations of those zeros of the system which lie in the right half of the complex plane furthermore this limitation provides a quantitative measure of the degree of difficulty which is inherent in the control of such non minimum phase systems

local convergence for multi point parametric chebyshev halley type methods of high convergence order we present a local convergence analysis for general multi point chebyshev halley type methods mmchtm of high convergence order in order to approximate a solution of an equation in a banach space setting mmchtm includes earlier methods given by others as special cases the convergence ball for a class of mmchtm methods is obtained under weaker hypotheses than before numerical examples are also presented in this study

a new approach to inversion based feedforward control design for nonlinear systems the finite time transition between stationary setpoints of nonlinear siso systems is considered as a scenario for the presentation of a new design approach for inversion based feedforward control design techniques which are based on a stable system inversion result in input trajectories with pre and or post actuation intervals the presented approach treats the considered transition task as a two point boundary value problem bvp and yields causal feedforward trajectories which are constant outside the transition interval the main idea of this approach is to provide free parameters in the desired output trajectory to solve the bvp of the internal dynamics thereby a standard matlab function can be used for the numerical solution of the bvp feedforward control design techniques are illustrated by simulation results for a simple example

minimum time trajectory generation for constrained linear systems using flatness and b splines in this article we discuss minimum time trajectory generation for input and state constrained continuous time lti systems in the light of the notion of flatness and b splines parametrisation flat systems have the useful property that the input and the state trajectories can be completely characterised by the so called flat output we propose a splines parametrisation for the flat output and the corresponding parametrisations for the performance output the states and the inputs using this parametrisation the problem of minimum time constrained trajectory planning is cast into a feasibility search problem in the splines control point space in which the constraint region is characterised by a polytope a close approximation of the minimum time trajectory is obtained by systematically searching the end time that makes the constraint polytope to be minimally feasible

dynamics of a family of chebyshev halley type methods in this paper the dynamics of the chebyshev halley family is studied on quadratic polynomials a singular set that we call cat set appears in the parameter space associated to the family this set has interesting similarities with the mandelbrot set the parameter space has allowed us to find different elements of the family which have bad convergence properties since periodic orbits and attractive strange fixed points appear in the dynamical plane of the corresponding method

an intrinsic algebraic setting for poles and zeros of linear time varying systems in this paper poles and zeros are defined for linear time varying systems using suitable ground field extensions the definitions of the system poles transmission poles invariant zeros hidden modes etc are given in an intrinsic module based framework and are consistent in the sense that the poles are connected to the stability of the system and the zeros to the zeroing of the output for non zero inputs in particular it is proved that the necessary and sufficient condition for a continuous time system to be exponentially stable is similar to the well known condition in the time invariant case

some basic structural properties of generalized linear systems abstract this paper shows how to give a kalman state variable realization to generalized linear systems simple characterizations of controllability observability of their duality and of a minimal realization are proposed our techniques based on elementary module theory are applicable to time varying systems as well as constant systems the note ends with a brief discussion of asymptotic observers in the constant case

enlarging the convergence ball of the method of parabola for finding zero of derivatives we present a new technique for enlarging the convergence ball of the method of parabola in order to approximate a zero of derivatives this approach also leads to more precise error estimates on the distances involved than in earlier studies such as hua 1974 ren and wu 2009 and wand 1975 these advantages are obtained under the same computational cost on the lipschitz constants involved as in the earlier studies numerical examples are also given to show the advantages over the earlier work

faster scaling algorithms for general graph matching problems an algorithm for minimum cost matching on a general graph with integral edge costs is presented the algorithm runs in time close to the fastest known bound for maximum cardinality matching specifically let n m and n denote the number of vertices number of edges and largest magnitude of a cost respectively the best known time bound for maximum cardinal ity matching m 0 am the new algorithm for minimum cost matching has time bound 0 in a m n iog n m log nn a slight modification of the new algorithm finds a maximum cardinality matching in 0 fire time other applications of the new algorlthm are given mchrding an efficient implementa tion of christofides traveling salesman approximation algorithm and efficient solutions to update problems that require the linear programming duals for matching

recurrence relations for a newton like method in banach spaces the convergence of iterative methods for solving nonlinear operator equations in banach spaces is established from the convergence of majorizing sequences an alternative approach is developed to establish this convergence by using recurrence relations for example the recurrence relations are used in establishing the convergence of newton s method l b rall computational solution of nonlinear operator equations robert e krieger new york 1979 and the third order methods such as halley s chebyshev s and super halley s v candela a marquina recurrence relations for rational cubic methods i the halley method computing 44 1990 169 184 v candela a marquina recurrence relations for rational cubic methods ii the halley method computing 45 1990 355 367 j a ezquerro m a hernandez recurrence relations for chebyshev type methods appl math optim 41 2000 227 236 j m gutierrez m a hernandez third order iterative methods for operators with bounded second derivative j comput appl math 82 1997 171 183 j m gutierrez m a hernandez recurrence relations for the super halley method comput math appl 7 36 1998 1 8 m a hernandez chebyshev s approximation algorithms and applications comput math appl 41 2001 433 445 10 in this paper an attempt is made to use recurrence relations to establish the convergence of a third order newton like method used for solving a nonlinear operator equation f x 0 where f email protected x y be a nonlinear operator on an open convex subset w of a banach space x with values in a banach space y here first we derive the recurrence relations based on two constants which depend on the operator f then based on this recurrence relations a priori error bounds are obtained for the said iterative method finally some numerical examples are worked out for demonstrating our approach

path following for nonminimum phase systems removes performance limitations we highlight an essential difference between path following and reference tracking for nonminimum phase systems it is well known that in the reference tracking for nonminimum phase systems there exists a fundamental performance limitation in terms of a lower bound on the l sub 2 norm of the tracking error even when the control effort is free we show that this is not the case for the less stringent path following problem where the control objective is to force the output to follow a geometric path without a timing law assigned to it furthermore the same is true even when an additional desired speed assignment is imposed

periodic polynomial interpretation for structural properties of linear periodic discrete time systems the structural properties of linear periodic discrete time systems are analyzed in the periodic polynomial representation it is shown that the classical polynomial approach for linear time invariant systems can be extended to periodic systems new definitions and properties are given in terms of skew polynomial rings and periodic difference algebra necessary and sufficient conditions for the characterization of reachability controllability observability and reconstructibility are given in this framework

flat output characterization for linear systems using polynomial matrices this paper is devoted to the study of linear flat outputs for linear controllable time invariant systems in polynomial matrix form we characterize the transformations expressing the system variables in terms of a linear flat output and derivatives called defining matrices as the kernel of a polynomial matrix an application to trajectory planning is presented showing the usefulness of the present characterization

exact feedforward linearization based on differential flatness this article deals with the trajectory aspect of differential flatness from a feedforward point of view the notion of exact feedforward linearization based on differential flatness is introduced a differentially flat system to which a nominal feedforward deduced from flatness is applied is equivalent by change of coordinates to a linear multivariable brunovsk form if the initial condition is consistent with the one considered in the design of the nominal trajectory in its second part the new notion states that there exist unique solutions in the vicinity of the desired trajectory when applying a nominal feedforward to the corresponding flat system to the end of stabilizing the desired trajectory the information from the brunovsk form is used to design the combination of the nominal feedforward and an additional feedback part in the case of extended pid controls for the latter stability is proven using a theorem by kelemen thus the overall control structure turns out to be quite simple and e

randomized tilde o m a randomized las vegas algorithm is given for finding the gallai edmonds decomposition of a graph let n denote the number of vertices and let m n denote the number of arithmetic operations for multiplying two n times n matrices the sequential running time i e number of bit operations is within a poly logarithmic factor of m n the parallel complexity is o log n 2 parallel time using a number of processors within a poly logarithmic factor of m n the same complexity bounds suffice for solving several other problems finding a minimum vertex cover in a bipartite graph finding a minimum x y vertex separator in a directed graph where x and y are specified sets of vertices finding the allowed edges i e edges that occur in some maximum matching of a graph finding the canonical partition of the vertex set of an elementary graph the sequential algorithms for problems i ii and iv are las vegas and the algorithm for problem iii is monte carlo the new complexity bounds are significantly better than the best previous ones e g using the best value of m n currently known the new sequential running time is o n2 38 versus the previous best o n2 5 log n or more

continuous time linear predictive control and flatness a module theoretic setting with examples a general flatness based framework for linear continuous time predictive control is presented the mathematical setting which is valid for multivariable systems is provided by the algebraic theory of modules where a controllable system corresponds to a finitely generated free module over a principal ideal ring any basis of this free module is a flat output which yields an easy calculation of the predicted trajectory this formalism permits one to handle non minimum phase systems system constraints and to deal with additive perturbations three concrete case studies namely a dc motor a flexible system and a cement mill are analysed and simulations are given these examples are written in such a way that any reader who is not familiar with module theory may nevertheless grasp the proposed control strategy

finite poles and zeros of linear systems an intrinsic approach several kinds of finite poles and zeros are defined and their relationships are studied in an intrinsic manner some of these definitions are more precise than the usual ones all kinds of multiplicities of an input output decoupling zero are defined here in addition we believe that our approach clarifies those notions and it makes it possible to very concisely establish fundamental relationships between various poles and zeros some new relationships are derived the notions of input output stability and transfer stability are also introduced several examples illustrate the theory

third order iterative methods for operators with bounded second derivative abstract we analyse the classical third order methods chebyshev halley super halley to solve a nonlnnear equation f x 0 where f is an operator defined between two banach spaces until now the convergence of these methods is established assuming that the second derivative f satisfies a lipschitz condition in this paper we prove by using recurrence relations the convergence of these and other third order methods just assuming f is bounded we show examples where our conditions are fulfilled and the classical ones fail

flatness based control of a nonlinear chemical reactor model the nonlinear model of a continuous stirred tank reactor is shown to be flat the flatness permits the design of suitable trajectories on the basis of the explicit stationary solution and the tracking of these trajectories asymptotically using quasi static state feedback linearization a nonlinear local observer with a time varying gain is designed allowing the realisation of the state feedback in the case of partial measurement of the state simulation results illustrate the tracking behavior of the closed loop with the observer

flatness and defect of non linear systems introductory theory and examples we introduce flat systems which are equivalent to linear ones via a special type of feedback called endogenous their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of kalman s controllability the distance to flatness is measured by a non negative integer the defect we utilize differential algebra where flatness and defect are best defined without distinguishing between input state output and other variables many realistic classes of examples are flat we treat two popular ones the crane and the car with n trailers the motion planning of which is obtained via elementary properties of plane curves the three non flat examples the simple double and variable length pendulums are borrowed from non linear physics a high frequency control strategy is proposed such that the averaged systems become flat

algebraic algorithms for matching and matroid problems we present new algebraic approaches for two well known combinatorial problems nonbipartite matching and matroid intersection our work yields new randomized algorithms that exceed or match the efficiency of existing algorithms for nonbipartite matching we obtain a simple purely algebraic algorithm with running time o n omega where n is the number of vertices and omega is the matrix multiplication exponent this resolves the central open problem of mucha and sankowski 2004 for matroid intersection our algorithm has running time o nr omega 1 for matroids with n elements and rank r that satisfy some natural conditions

on the semi local convergence of halley s method under a center lipschitz condition on the second frechet derivative abstract we expand the applicability of halley s method for solving nonlinear equations in a banach space setting we assume the existence of the center lipschitz condition on the second frechet derivative of the operator involved instead of lipschitz condition used extensively in the literature 1 2 4 5 the center lipschitz condition is satisfied in many interesting cases where the lipschitz condition is not satisfied 3 4 6 7 13 we show that the semi local convergence theorem established in x b xu y h ling semilocal convergence for halley s method under weak lipschitz condition appl math comput 215 2009 3057 3067 is not true a new semi local convergence theorem is established for halley s method under the same condition our results are illustrated using a nonlinear hammerstein integral equation of the second kind where our convergence criteria are satisfied but convergence criteria in earlier studies such as 1 2 are not satisfied

continuous time non linear flatness based predictive control an exact feedforward linearisation setting with an induction drive example a general flatness based framework for non linear continuous time predictive control is presented it extends the results of fliess and marquez 2000 to the non linear case the mathematical setting which is valid for multivariable systems is provided by the theory of flatness based exact feedforward linearisation introduced by the authors hagenmeyer and delaleau 2003b thereby differential flatness does not only yield an easy calculation of the predicted trajectories considering the respective system constraints but allows to use simple linear feedback parts in a two degree of freedom control structure moreover this formalism permits one to handle non minimum phase systems and furthermore to deal with parameter uncertainties and exogenous perturbations respective robustness analysis tools are available finally an induction drive example is discussed in detail and experimental results for this fast electro mechanical system are presented

finding all maximally matchable edges in a bipartite graph we consider the problem of finding all maximally matchable edges in a bipartite graph g v e i e all edges that are included in some maximum matching we show that given any maximum matching in the graph it is possible to perform this computation in linear time o n m where n v and m e hence the time complexity of finding all maximally matchable edges reduces to that of finding a single maximum matching which is o n 1 2m hopcroft and karp 12 or o n logn 1 2m for dense graphs with m q n 2 alt et al 2 this time complexity improves upon that of the best known algorithms for the problem which is o nm costa 5 for bipartite graphs and carvalho and cheriyan 6 for general graphs other algorithms for solving that problem are randomized algorithms due to rabin and vazirani 15 and cheriyan 3 the runtime of which is o n 2 3 7 6 our algorithm apart from being deterministic improves upon that time complexity for bipartite graphs when m o n r and r 1 876 in addition our algorithm is elementary conceptually simple and easy to implement

nonlinear model predictive control of a wave energy converter based on differential flatness parameterisation abstractthis paper presents a fast constrained optimization approach which is tailored for nonlinear model predictive control of wave energy converters wec the advantage of this approach relies on its exploitation of the differential flatness of the wec model this can reduce the dimension of the resulting nonlinear programming problem nlp derived from the continuous constrained optimal control of wec using pseudospectral method the alleviation of computational burden using this approach helps to promote an economic implementation of nonlinear model predictive control strategy for wec control problems the method is applicable to nonlinear wec models nonconvex objective functions and nonlinear constraints which are commonly encountered in wec control problems numerical simulations demonstrate the efficacy of this approach

numerical solution of the optimal periodic control problem using differential flatness optimal periodic control opc is of interest in many engineering applications in practice the numerical solution of the opc problem has been found to be quite challenging in this note we present a method which uses differential flatness for the solution of opc problems the opc problem is reformulated using the flatness of the underlying dynamical system to eliminate the differential equations and the periodicity constraints resulting in simpler and generally more efficient computation the effect of point wise constraints and the analytical computation of the jacobian matrix are also discussed the approach is demonstrated using two examples

model free control model free control and the corresponding intelligent pid controllers ipids which already had many successful concrete applications are presented here for the first time in an unified manner where the new advances are taken into account the basics of model free control is now employing some old functional analysis and some elementary differential algebra the estimation techniques become quite straightforward via a recent online parameter identification approach the importance of ipis and especially of ips is deduced from the presence of friction the strange industrial ubiquity of classic pid s and the great difficulty for tuning them in complex situations is deduced via an elementary sampling from their connections with ipids several numerical simulations are presented which include some infinite dimensional systems they demonstrate not only the power of our intelligent controllers but also the great simplicity for tuning them

recurrence relations for the super halley method in this paper we give sufficient conditions in order to assure the convergence of the super halley method in banach spaces we use a system of recurrence relations analogous to those given in the classical newton kantorovich theorem or those given for chebyshev and halley methods by different authors 1998 elsevier science ltd all rights reserved

third order convergence theorem by using majorizing function for a modified newton method in banach space abstract following the ideas of frontini and sormani we present a modified newton method in banach space which is used to solve the nonlinear operator equation we establish the newton kantorovich convergence theorem for the modified newton method with third order convergence in banach space by using majorizing function we also get the error estimate finally two examples are provided to show the application of our theorem

modified chebyshev s method free from second derivative for non linear equations in this paper we present some new modifications of chebyshev s method free from second derivative the order of convergence of the new methods is three per iteration the methods require two evaluations of the function and one evaluation of its first derivative the convergence of the new methods for the case of multiple roots is also discussed numerical examples show that the new methods have definite practical utility

enlarging the convergence domain in local convergence studies for iterative methods in banach spaces in this work we introduce a new form of setting the general assumptions for the local convergence studies of iterative methods in banach spaces that allows us to improve the convergence domains specifically a local convergence result for a family of higher order iterative methods for solving nonlinear equations in banach spaces is established under the assumption that the frechet derivative satisfies the lipschitz continuity condition for some values of the parameter these iterative methods are of fifth order the importance of our work is that it avoids the usual practice of boundedness conditions of higher order derivatives which is a drawback for solving some practical problems the existence and uniqueness theorem that establishes the convergence balls of these methods is obtained we have considered a number of numerical examples including a nonlinear hammerstein equation and computed the radii of the convergence balls it is found that the radius of convergence ball obtained by our approach is much larger when compared with some other existing methods the global convergence properties of the family are explored by analyzing the dynamics of the corresponding operator on complex quadratic polynomials

a remark on willems trajectory characterization of linear controllability abstract willems trajectory characterization of linear controllability is related to some module theoretic property

lmis for constrained polynomial interpolation with application in trajectory planning we consider an open loop trajectory planning problem for linear systems with bound constraints originating from saturations or physical limitations using an algebraic approach and results on positive polynomials we show that this control problem can be cast into a constrained polynomial interpolation problem admitting a convex linear matrix inequality lmi formulation

time varying linear systems and invariants of system equivalence in the paper we consider time varying systems with coefficients depending mero morphically on time in differential operator representations these systems are described by matrices over a skew polynomial ring with coefficients in the field of real meromorphic functions different kinds of indices controllability minimal geometric and dynamical are introduced and it is proved that they essentially coincide the input module and the formal transfer matrix are defined and used for an algebraic description of time varying systems a characterization of system equivalence is given in these terms and also a complete list of invariants of similarity for time varying state space systems

a lie backlund approach to equivalence and flatness of nonlinear systems a new system equivalence relation using the framework of differential geometry of jets and prolongations of infinite order is studied in this setting two systems are said to be equivalent if any variable of one system may be expressed as a function of the variables of the other system and of a finite number of their time derivatives this is a lie backlund isomorphism the authors prove that although the state dimension is not preserved the number of input channels is kept fixed they also prove that a lie backlund isomorphism can be realized by an endogenous feedback the differentially flat nonlinear systems introduced by the authors 1992 via differential algebraic techniques are generalized and the new notion of orbitally flat systems is defined they correspond to systems which are equivalent to a trivial one with time preservation or not the endogenous linearizing feedback is explicitly computed in the case of the vtol aircraft to track given reference trajectories with stability

fast matrix rank algorithms and applications we consider the problem of computing the rank of an m n matrix a over a field we present a randomized algorithm to find a set of r rank a linearly independent columns in o vav p r field operations where vav denotes the number of nonzero entries in a and

a modification of newton method with third order convergence in this paper we present a new modification of newton method for solving non linear equations analysis of convergence shows that the new method is cubically convergent per iteration the new method requires two evaluations of the function and one evaluation of its first derivative thus the new method is preferable if the computational costs of the first derivative are equal or more than those of the function itself its practical utility is demonstrated by numerical examples

newton type methods on riemannian manifolds under kantorovich type conditions one of the most studied problems in numerical analysis is the approximation of nonlinear equations using iterative methods in the last years attention has been paid in studying newton s method on manifolds in this paper we generalize this study considering some newton type iterative methods a characterization of the convergence under kantorovich type conditions and optimal estimates of the error are found using normal coordinates the order of convergence is derived the sufficient semilocal convergence criteria are weaker and the majorizing sequences are tighter for the special cases of simplified newton and newton methods than in earlier studies such as argyros 2004 2007 2008 6 8 12 and kantorovich and akilov 1964 32

feedforward control design for finite time transition problems of non linear mimo systems under input constraints a new approach is presented for the feedforward control design of non linear systems with the application to finite time setpoint transitions under input constraints this contribution extends recently presented results for the siso case to non linear quadratic mimo systems the inversion based design treats the transition task as a two point boundary value problem bvp defined in the input output coordinates of the considered system for its solvability free parameters are provided in ansatz functions for the highest output derivatives this concept allows the direct incorporation of input constraints within the formulation of the bvp the resulting bvp with free parameters can be solved e g with a standard matlab function the load transport of an overhead crane serves as an example to illustrate the concept

a linear differential operator approach to flatness based tracking for linear and non linear systems this contribution presents a flatness based solution to the tracking for linear systems in differential operator representation since the differential operator representation is a flat system representation tracking controllers can easily be designed using dynamic output feedback then the differential operator approach for flatness based tracking of linear systems is extended to non linear systems the design of the resulting linear time varying dynamic output feedback controller is based on a linearization about the trajectory which directly yields the differential operator representation different from the non linear flatness based controller design the new approach uses linear methods both in stabilizing the tracking and in computing the output feedback controller the proposed design procedure assures exact tracking in the steady state when no disturbances are present a simple example demonstrates the design of a dynamic output feedback controller for the tracking of a non linear system

path following for linear systems with unstable zero dynamics a constructive solution to the path following problem for mimo linear systems with unstable zero dynamics is developed while the original control variable steers the system output along the path the path parameter q is used as an additional control to stabilize zero dynamics with a feedback law which is nonlinear due to the path constraint a sufficient condition for solvability of the path following problem is given in terms of the geometric properties of the path when this condition is satisfied an arbitrary small l 2 norm of path following error can be achieved thus avoiding performance limitations of the standard reference tracking problem imposed by unstable zero dynamics

third order family of methods in banach spaces recently parida and gupta p k parida d k gupta recurrence relations for a newton like method in banach spaces j comput appl math 206 2007 873 877 used rall s recurrence relation approach from 1961 to approximate roots of nonlinear equations by developing several methods the latest of which is free of second derivative and it is of third order in this paper we use an idea of kou and li j s kou y t li modified chebyshev s method free from second derivative for non linear equations appl math comput 187 2007 1027 1032 and modify the approach of parida and gupta obtaining yet another third order method to approximate a solution of a nonlinear equation in a banach space we give several applications to our method