control for safety specifications of systems with imperfect information on a partial order in this paper we consider the control problem for uncertain systems with imperfect information in which an output of interest must be kept outside an undesired region the bad set in the output space the state input output and disturbance spaces are equipped with partial orders the system dynamics are either input output order preserving with output in r2 or given by the parallel composition of input output order preserving dynamics each with scalar output we provide necessary and sufficient conditions under which an initial set of possible system states is safe that is the corresponding outputs are steerable away from the bad set with open loop controls a closed loop control strategy is explicitly constructed which guarantees that the current set of possible system states as obtained from an estimator generates outputs that never enter the bad set the complexity of algorithms that check safety of an initial set of states and implement the control map is quadratic with the dimension of the state space the algorithms are illustrated on two application examples a ship maneuver to avoid an obstacle and safe navigation of an helicopter among buildings

a bound on the number of integrators needed to linearize a control system this paper considers the problem of dynamic feedback linearization for nonlinear control systems for a restricted class of dynamic compensators that correspond to adding chains of integrators to the inputs we give an upper bound on the order of the compensator that needs to be considered in the case of 2 input systems we show that this bound is sharp

on minimal compensators for decoupling control abstract the general construction of minimal regular compensators for decoupling a nonlinear system is given by means of vector subspaces which are generated by differential vectors of outputs and states and the minimal dimension of a decoupling compensator is expressed in intrinsic characterization the equivalence relation of all minimal regular compensators is established though these compensators may have different dynamic behavior from each other

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

the differential field associated to a general analytic nonlinear dynamical system a rigorous and detailed construction of the differential field k sub sigma u y associated in a differential algebraic context to a nonlinear system sigma described in state space form with analytic coefficients is presented the field k sub sigma u y represents an input output description of sigma and its study is of key importance in problems concerning the input output behavior of sigma technically the basic step of the construction of k sub sigma u y consists in proving that the differential ideal associated to the state evolution equation of sigma is prime

linearized oscillation theory for a nonlinear nonautonomous delay differential equation oscillation properties of two following equations are compared a scalar nonlinear delay differential equation y t k 1m rk t f k y hk t 0 with rk t o hk t t and a linear delay differential equation x t k 1m rk t x hk t 0 coefficients rk t and delays are not assumed to be continuous as an application explicit oscillation and nonoscillation conditions are established for nonlinear equations arising in population dynamics

a fuzzy flight controller combining linguistic and model based fuzzy control in this paper we address the design of a fuzzy flight controller that achieves stable and robust aggressive manoeuvrability for an unmanned helicopter the fuzzy flight controller proposed consists of a combination of a fuzzy gain scheduler and linguistic mamdani type controller the fuzzy gain scheduler is used for stable and robust altitude roll pitch and yaw control the linguistic controller is used to compute the inputs to the fuzzy gain scheduler i e desired values for roll pitch and yaw at given desired altitude and horizontal velocities the flight controller is obtained and tested in simulation using a realistic nonlinear mimo model of a real unmanned helicopter platform the apid mk

existence of global solutions to nonlinear mixed type functional differential equations abstract the paper considers systems of nonlinear mixed type functional differential equations it aims to find conditions for the existence of global solutions with graphs staying in a prescribed domain a relevant result is proved by schauder tychonoff fixed point technique with illustrative examples shown a linear variant of the derived result is formulated comparisons with known results are discussed and some open problems are formulated

design of a minimal precompensator for the decoupling problem abstract for right invertible linear time invariant systems which cannot be decoupled row by row using regular static state feedback laws we propose a new algorithmic procedure for designing a minimal precompensator leading to a compensated system which can be decoupled by regular static state feedback

asymptotic convergence criteria of solutions of delayed functional differential equations abstract the convergence of all solutions of the scalar equation x f t x t is studied under the main assumption that every constant is its solution the criterion and the sufficient conditions for convergence are proved for the considered classes of equations it is among others proved that all solutions are convergent if and only if there exists at least one increasing and convergent solution as applications criteria for some classes of linear equations as well as for nonlinear equations are obtained some comparisons with already known results are given too

immersion of discrete time nonlinear system by regular dynamic state feedback into a linear system necessary and sufficient conditions for local solvability of the title problem around a given trajectory are obtained the proposed conditions are less restrictive than those obtained by lee and marcus for the problem of immersion a nonlinear system into a linear system via static state feedback instrumental in the problem solution is the inversion structure algorithm for a discrete time nonlinear system the solvability conditions are expressed in terms of the inversion algorithm moreover the construction of both the dynamic state feedback and the immersion map relies on this algorithm finally it is shown that for locally right invertible systems the considered problem unlike the problem of immersion via static state feedback is always solvable

asymptotic representation of solutions of equationẏ t β t y t y t τ t abstract in this paper the equation t t y t y t t is considered where c i 1 r i 1 t 1 r 0 t t is an increasing function on i 1 t t i 1 0 c i 1 r results about asymptotic structure and behavior of the solutions of this equation are proved a connection with the equation t c t x t t and the asymptotic representation of its solutions is obtained

dynamic decoupling for right invertible nonlinear systems abstract it is shown that every system with more inputs than outputs that is right invertible in the sense of 5 can be decoupled via a dynamic state feedback that can be computed using a given algorithm this result generalizes the one of 2 and completes the results of 3

on dynamic input output linearization of discrete time nonlinear systems this paper studies the problem of linearizing the input output map of an analytic discrete time nonlinear system locally around a given trajectory necessary and sufficient conditions are given for the existence of a regular dynamic state feedback control law under which the input dependent part of the response of a nonlinear system becomes linear in the input and independent of the initial state the proposed conditions are less restrictive than those obtained by lee and marcus for linearizing the input output map via a static state feedback instrumental in the problem solution is the inversion structure algorithm for a discrete time nonlinear system firstly the solvability conditions are expressed in terms of the inversion algorithm secondly the proof of the existence and construction of the dynamic state feedback compensator relies on this algorithm

decoupling with dynamic compensation for strong invertible affine non linear systems abstract in this paper we tackle for affine non linear systems the morgan problem i e the scalar input scalar output decoupling problem for square systems with dynamic compensation the result provided here theorem 3 1 generalizes that one previously given by wang 1970 for linear systems

a remark on nonlinear accessibility conditions and infinite prolongations the lie rank condition for strong nonlinear accessibility is interpreted via the differential geometry of jets and prolongations of infinite order it yields to a new lie algebraic criterion and to the consideration of first integrals which apply to nonlinear systems in quite general form the latter characterization in particular is valid without distinguishing between the system variables and is independent of time scalings weak accessibility is also considered

sufficient conditions for the existence of global solutions of delayed differential equations the purpose of this contribution is to give sufficient conditions for the existence of global solutions or left semi global solutions for some classes of delayed functional differential equations the principle of monotone sequences is used as a main tool of investigation inequalities for coordinates of global solutions are derived as a consequence of used method examples illustrate the results

noninteracting control with stability for a class of nonlinear systems abstract in this paper we address the problem of noninteracting control with stability for the class of nonlinear square systems for which noninteraction can be achieved without stability by means of invertible static state feedback the use of both static state feedback and dynamic state feedback is investigated we prove that in both cases the asymptotic stabilizability of certain subsystems is necessary to achieve noninteraction and stability we use this and some recent results to state a complete set of necessary and sufficient conditions in order to solve the problem

all pairs shortest paths using bridging sets and rectangular matrix multiplication we present two new algorithms for solving the all pairs shortest paths apsp problem for weighted directed graphs both algorithms use fast matrix multiplication algorithms the first algorithm solves the apsp problem for weighted directed graphs in which the edge weights are integers of small absolute value in o n2 time where satisfies the equation 1 1 1 2 and 1 1 is the exponent of the multiplication of an n n matrix by an n n matrix currently the best available bounds on 1 1 obtained by coppersmith imply that 0 is an error parameter and w is the largest edge weight in the graph after the edge weights are scaled so that the smallest non zero edge weight in the graph is 1 it returns estimates of all the distances in the graph with a stretch of at most 1 e corresponding paths can also be found efficiently

exponential solutions of equation ẏ t β t y t δ y t τ abstract asymptotic behaviour of solutions of first order differential equation with two deviating arguments of the form y t t y t y t is discussed for t a criterion for representing solutions in exponential form is proved as consequences inequalities for such solutions are given connections with known results are discussed and a sufficient condition for existence of unbounded solutions generalizing previous ones is derived an illustrative example is considered too

on the inversion of a class of nonlinear systems this paper deals with the inversion problem of affine square multi input multi output mimo nonlinear systems it presents a new algorithm unifying the construction of the inverse of a dynamical system with a regular or a singular characteristic matrix this algorithm is based on the determination of a projector on the fibre bundle of the state space and incorporates a regularization of the singular case it has the advantage of avoiding the input derivatives numerical examples are given to illustrate the proposed approach

dynamic input output decoupling of nonlinear control systems the problem of dynamic input output decoupling of nonlinear control systems is studied based on an analytic algorithm the authors obtain necessary and sufficient conditions for the solvability of this problem the solution of the problem is constructed by applying a series of simple precompensations and linking maps some interesting connections with other approaches in nonlinear control theory are discussed the authors also give a few simple examples to illustrate the methods used

sharing information for the all pairs shortest path problem we improve the time complexity of the all pairs shortest path apsp problem for special classes of directed graphs one is a nearly acyclic directed graph and the other is a directed graph with limited edge costs the common idea for speed up is information sharing by n single source shortest path sssp problems that are solved for apsp we measure the degree of acyclicity by the size r of a given set of feedback vertices if r is small the given graph can be considered to be nearly acyclic we consider this parameter r in addition to the traditional parameters of the number of vertices n and that of edges m in the first part we improve the existing time complexity of o mn r 3 for the all pairs shortest path problem to o mn rnlogn this complexity is equal to or better than the previous one for all values of r under a reasonable assumption of m n in the second part we deal with a directed graph with non negative integer edge costs bounded by c we show the all pairs shortest path apsp problem can be solved in o mn n 2log c n time with the data structure of cascading bucket system we use the traditional computational model such that comparison addition operations on distance data and random access with o logn bits can be done in o 1 time also the graph is not separated meaning m n 1

l2 perturbation of a linear delay differential equation abstract in this paper we present an asymptotic formula for the solutions of the nonautonomous delay differential equation t a 0 a t x t b 0 b t x t assuming that it is an l 2 perturbation of the autonomous equation t a 0 x t b 0 x t our theorem is an essential generalization of the corresponding result in the classical book by r bellman and k l cooke the proof is based on a new result on the asymptotic constancy of the solutions of a linear delay equation

approximate linearization of nonlinear control systems abstract the paper address the problem of approximate linearization of a nonlinear control system by state feedback or dynamic feedback the main result proved is that if the fast k d relative degrees are equal to each other then the input output response of a nonlinear control system can be linearized to degree k any system having linear d relative degree can be linearized to any degree by dynamic feedbacks one example of signal tracking using dynamic feedback linearization method to improve the performance is also given

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

a sufficient condition for nonlinear noninteracting control with stability via dynamic state feedback a sufficient condition is given to solve the problem of achieving local noninteracting control with asymptotic stability via dynamic state feedback for a nonlinear affine system the condition which is automatically satisfied in the case of linear systems although only sufficient is helpful in overcoming some of the geometric obstructions pointed out in the literature an example in which the author assumptions are satisfied is given clearly showing how to construct a decoupling and stabilizing dynamic state feedback and how the condition can weaken the requirement that the p dynamics be locally asymptotically stable

an intrinsic sufficient condition for regular decoupling abstract this paper introduces an intrinsic regularity property namely regular invertibility which requires that a sequence of vector spaces has constant dimension after a certain order thus allowing some degeneracies in the beginning it corresponds to the system and its tangent having the same defect using the constant rank theorem this property is shown to be sufficient condition for regular decoupling

stabilization by output feedback of multivariable invertible nonlinear systems in this paper the problem of global stabilization of a rather general class of mimo nonlinear systems is addressed the systems considered in the paper are invertible have a trivial zero dynamics and possess a normal form in which certain multipliers are functions of the state vector of a special kind while special structural dependence of such multipliers on the components state vector has been exploited before in the context of achieving stabilization via full state feedback though the novelty in the approach of this paper is that a peculiar structure is identified which happens to be intimately related to the property of uniform complete observability thus making the design of observers possible and to the property of uniform invertibility relations never established before in the literature as a result for this class of mimo nonlinear systems a dynamic output feedback law can be designed yielding semiglobal and even global under appropriate assumptions asymptotic stability

asymptotic model matching for nonlinear systems this paper investigates the problem of designing a compensating control law for a square invertible nonlinear plant so that the response of the closed loop system asymptotically matches that of a prescribed driven nonlinear model a set of necessary conditions for achieving asymptotic model matching is established one of these involves the stability properties for subdynamics which are common to every model matching closed loop these subdynamics called the fixed dynamics are intrinsically characterized based on these results a new set of sufficient conditions for achieving asymptotic model matching is given the interrelation between the minimum phase and vector relative degree properties of a plant and a matchable model are studied

the asymptotic bounds of solutions of linear delay systems abstract our aim is to obtain conditions under which every solutionyof the vector functional differential equation formula can be estimated in terms of a solution of a scalar functional equation formula wherea x is a suitable real positive function andbis a suitable real negative constant moreover ifb x is diagonal matrix we derive more precise estimates ofyin terms of a solution of a vector functional equation formula where the elements ofa x are formed by the absolute values of the corresponding elements ofa x these asymptotic results enable us to obtain sharp estimates of solutions of certain linear delay systems

generalized state variable representation for a simplified crane description recent theoretical advances in nonlinear systems theory insist on the relevance of dynamics where control derivatives appear we discuss here a simplified model of a crane which exhibits such a description

necessary conditions for asymptotic tracking in nonlinear systems in the literature it has been shown that if a single input single output analytic nonlinear plant 1 has a well defined relative degree and 2 is minimum phase it is possible to achieve asymptotic tracking for an open set of output trajectories containing the origin in c sup n 0 spl infin the space of n times continuously differentiable functions taking values in r when either of these sufficient conditions is not met various authors have investigated approximate analytic solutions discontinuous solutions and solutions for restricted sets of trajectories in this paper it is shown that conditions 1 and 2 are necessary for the existence of an analytic compensator which yields asymptotic tracking for an open set of output trajectories analogous results are established for multi input multi output systems

a new approach to the structure at infinity of nonlinear systems abstract zeros at infinity for nonlinear systems are defined by using differential algebra this approach can be viewed as a nonlinear generalization of silverman s structure algorithm the connection with the problem of inverting input output systems is briefly described

approximate decoupling and asymptotic tracking for mimo systems this paper presents an algorithm for approximate input output decoupling of nonlinear mimo systems that are either numerically ill posed or exhibit nearly singular behavior in the application of decoupling algorithms although the systems considered are regular so that the exact decoupling algorithms are applicable in this case they require inversion of an ill conditioned matrix and yield high gain feedback solutions that may result in actuator saturation and cancellation of high frequency zeros the approximate algorithms of this paper are numerically robust and provide solutions that do not cancel far off right half plane zeros this latter characteristic is especially valuable when some of the far off right half plane zeros are unstable the algorithms are inspired by and are generalizations of some examples in the flight control literature

a note on the invertibility of nonlinear input output differential systems abstract a new conceptual framework employing differential algebra is proposed for solving the long standing problem of inverting nonlinear input output differential systems simple characterizations of left and right invertibility are given which rest upon an invariant integer which for constant linear systems turns out to be the rank of the transfer matrix

a canonical dynamic extension for noninteraction with stability for affine nonlinear square systems we study the problem of noninteracting control with stability via dynamic feedback for continuous affine nonlinear square systems given a system which may not be decouplable via static state feedback but is decouplable via dynamic feedback a canonical dynamic extension is constructed we show that every dynamic extension contains this canonical one hence the mix dynamics as defined by wagner of the canonical extension is contained in every other dynamic extension following wagner s result the stability of this mix dynamics is necessary for noninteraction with internal stability the results in this paper show that under some regularity assumptions in the investigation of noninteraction with stability one can assume without loss of generality that the system is decouplable via static state feedback

multi objective optimal trajectory design and tracking with non periodic tracking transition switching for non minimum phase linear systems abstractin this paper the problem of trajectory design and tracking of non periodic tracking transition switching for non minimum phase linear systems is considered such a problem exists in various applications where the output trajectory consists of application dependent tracking sessions and to be designed transition sessions the challenge arises when multiple control objectives are considered including the smooth transition from one output tracking session to the next one without large oscillations during the transition smooth tracking transition switching without inducing pre and or post switching oscillations input energy minimisation without saturation under amplitude constraint and furthermore minimisation of the overall transition time the proposed approach extends the previous work that attained smooth output transition and smooth tracking transition switching to further achieve amplitude constrained input energy minimisation and transition time minimisation first the constrained inp

global approximate output tracking for nonlinear systems addresses the global output tracking problem for nonlinear systems with singular points for nonlinear systems which satisfy a suitable observability condition the authors identify a class of smooth output trajectories which the system can track using continuous open loop controls this class includes all output trajectories generated by smooth state feedback they then study the problem of approximate output tracking using discontinuous time varying feedback controllers given a smooth output trajectory for which exact tracking is possible the authors construct a discontinuous feedback controller which achieves robust tracking of the desired output trajectory in the face of perturbations finally it is shown that their results can be applied to the control of a chain system and some numerical results are presented to illustrate the performance of their controller

fixed modes and nonlinear noninteracting control with stability the existence of a fixed internal dynamics inherent to the noninteraction requirement is identified when unstable this represents an obstruction to the achievement of noninteracting control with stability by means of static state feedback remarkably whenever one leaves the class of linear systems this obstruction cannot in general be removed by dynamic state feedback

approximation by regular input output maps the authors study approximate dynamic input output linearization in the sense of j hauser et al 1989 for multiinput multioutput mimo nonlinear systems which exhibit singularities in the dynamic extension process

positive solutions of the equation ẋ t c t x t τ in the critical case abstract the equation t c t x t is considered in the critical case for it the asymptotic behavior of dominant and subdominant solutions is studied a generalization is made and connections with known results are discussed

convergence in asymptotically autonomous functional differential equations in this paper we consider linear and nonlinear perturbations of a linear autonomous functional differential equation which has infinitely many equilibria we give sufficient conditions under which the solutions of the perturbed equation tend to the equilibria of the unperturbed equation at infinity as a consequence we obtain sufficient conditions for systems of delay differential equations to have asymptotic equilibrium

algebraic theory on shortest paths for all flows abstract we consider a shortest path problem for a directed graph with edges labeled with a cost and a capacity the problem is to push flow f from a specified source to all other vertices with the minimum cost for all f values if there are t capacity values we can solve the single source shortest path problem t times for all capacity values in o t m t n log n time which is o m 2 when t m we improve this time to o c m n if edge costs are non negative integers bounded by c for the all pairs problem we give a simple floyd like algorithm with complexity o min t c n n 3 better than the best known o t c 1 843 n 2 843 for certain ranges of t and c

global dynamics of one class of nonlinear nonautonomous systems with time varying delays abstract a class of nonautonomous systems of nonlinear delay differential equations was studied via construction of matrix inequalities and comparison techniques the results for the nonautonomous systems with time varying delays are novel e g the global stability of differential equations with nonlinear casual volterra operators is considered for the first time in the literature criteria obtained for permanence and global attractivity are explicit and hence are convenient for applying verifying in practice we illustrate applications of the results obtained to the nonautonomous and asymptotically autonomous nicholson type models