a general theorem on local controllability we prove a general sufficient condition for local controllability of a nonlinear system at an equilibrium point earlier results of brunovsky hermes jurdjevic crouch and byrnes sussmann and grossmann are shown to be particular cases of this result also a number of new sufficient conditions are obtained all these results follow from one simple general principle namely that local controllability follows whenever brackets with certain symmetries can be neutralized in a suitable way by writing them as linear combinations of brackets of a lower degree both the class of symmetries and the definition of degree can be chosen to suit the problem

prediction based stabilization of linear systems subject to input dependent input delay of integral type in this paper it is proved that a predictor based feedback controller can effectively yield asymptotic convergence for a class of linear systems subject to input dependent input delay this class is characterized by the delay being implicitly related to past values of the input via an integral model this situation is representative of systems where transport phenomena take place as is frequent in the process industry the sufficient conditions obtained for asymptotic stabilization bring a local result and require the magnitude of the feedback gain to be consistent with the initial conditions scale arguments of proof for this novel result include general halanay inequalities for delay differential equations and build on recent advances of backstepping techniques for uncertain or varying delay systems

index reduction for differential algebraic equations by substitution method abstract differential algebraic equations daes naturally arise in many applications but present numerical and analytical difficulties the index of a dae is a measure of the degree of numerical difficulty in general the higher the index is the more difficult it is to solve the dae therefore it is desirable to transform the original dae into an equivalent dae with lower index in this paper we propose an index reduction method for linear daes with constant coefficients the method is applicable to any dae having at most one derivative per equality in contrast to the other existing methods it does not introduce any additional variables exploiting a combinatorial property of degrees of minors in polynomial matrices we show that the method always reduces the index exactly by one thus the paper exhibits an application of combinatorial matrix theory to numerical analysis of daes

index reduction of differential algebraic equations by differential dixon resultant abstract high index differential algebraic equations daes are ordinary differential equations odes with constraints and arise frequently from many mathematical models of physical phenomenons and engineering fields in this paper we generalize the idea of differential elimination with dixon resultant to polynomially nonlinear daes we propose a new algorithm for index reduction of daes and establish the notion of differential dixon resultant which can provide the differential resultant of the enlarged system of original equations to make use of structure of daes variable pencil technique is given to determine the termination of differentiation moreover we also provide a heuristic method for removing the extraneous factors from differential resultant the experimentation shows that the proposed algorithm outperforms existing ones for many examples taken from the literature

a parallel shortest augmenting path algorithm for the assignment problem abstract we describe a parallel version of the shortest augmenting path algorithm for the assignment problem while generating the initial dual solution and partial assignment in parallel does not require substantive changes in the sequential algorithm using several augmenting paths in parallel does require a new dual variable recalculation method the parallel algorithm was tested on a 14 processor butterfly plus computer on problems with up to 900 million variables the speedup obtained increases with problem size the algorithm was also embedded into a parallel branch and bound procedure for the traveling salesman problem on a directed graph which was test on the butterfly plus on problems involving up to 7 500 cities to our knowledge these are the largest assignment problems and traveling salesman problems solved so far

lie brackets and local controllability a sufficient condition for scalar input systems we develop a general formalism based on exponential lie series which can be used to study control variations we apply the formalism to prove a result conjectured by h hermes that gives a sufficient condition for small time local controllability for single input systems

adaptive control scheme for uncertain time delay systems the paper exposes some of the potential of a recently introduced backstepping transformation for linear uncertain time delay systems to address the classic problems of equilibrium regulation under partial measurements disturbance rejection parameter or delay adaptation for each of these problems an implementable control strategy is proposed it is analyzed through a convergence analysis of infinite dimensional dynamics based on a transport partial differential equation representation of the estimated input delay and the mentioned backstepping transformation the considered controllers contain this representation of the system under the form of a distributed parameter system and use it to determine relevant adaptation strategies an illustration example is proposed

homogeneous lyapunov function for homogeneous continuous vector field the goal of this article is to provide a construction of a homogeneous lyapunov function p associated with a system of differential equations j f x x r n 1 under the hypotheses 1 f c r n vanishes at x 0 and is homogeneous 2 the zero solution of this system is locally asymptotically stable moreover the lyapunov function v x tends to infinity with 1 x i and belongs to c r 0 r n cp with p e as large as wanted as application to the theory of homogeneous systems we present two well known results of robustness in a slightly extended form and with simpler proofs

generalized halanay inequalities and their applications to neural networks with unbounded time varying delays in this brief we discuss some variants of generalized halanay inequalities that are useful in the discussion of dissipativity and stability of delayed neural networks integro differential systems and volterra functional differential equations we provide some generalizations of the halanay inequality which is more accurate than the existing results as applications we discuss invariant set dissipative synchronization and global asymptotic stability for the hopfield neural networks with infinite delays we also prove that the dynamical systems with unbounded time varying delays are globally asymptotically stable

local stabilization and controllability of a class of non triangular nonlinear systems this paper considers the problems of local asymptotic stabilization using continuous static state feedback lcfs and small time local controllability stlc of single input nonlinear systems a specific class of nontriangular systems called the essentially triangular form is introduced for this class of systems sufficient conditions for lcfs and necessary and sufficient conditions for stlc are obtained in particular it is shown that stlc implies lcfs a motivating physical example of the etf system is presented

efficient index reduction algorithm for large scale systems of differential algebraic equations in many mathematical models of physical phenomenons and engineering fields such as electrical circuits or mechanical multibody systems which generate the differential algebraic equations daes systems naturally in general the feature of daes is a sparse large scale system of fully nonlinear and high index to make use of its sparsity this paper provides a simple and efficient algorithm for index reduction of large scale daes system we exploit the shortest augmenting path algorithm for finding maximum value transversal mvt as well as block triangular forms btfs we also present the extended signature matrix method with the block fixed point iteration and its complexity results furthermore a range of nontrivial problems are demonstrated by our algorithm

pryce pre analysis adapted to some dae solvers abstract the ode solver hbt 12 5 of order 12 t nguyen ba h hao h yagoub r vaillancourt one step 5 stage hermite birkho taylor ode solver of order 12 appl math comput 211 2009 313 328 doi 10 1016 j amc 2009 01 043 which combines a taylor series method of order 9 with a runge kutta method of order 4 is expanded into the dae solver hbt 12 5dae of order 12 dormand prince s dp 8 7 13m is also expanded into the dae solver dp 8 7 dae pryce structural pre analysis extended odes and ode first order forms are adapted to these dae solvers with a stepsize control based on local error estimators and a modified pryce algorithm to advance integration hbt 12 5dae uses only the first nine derivatives of the unknown variables as opposed to the first 12 derivatives used by the taylor series method t12dae of order 12 numerical results show the advantage of hbt 12 5dae over t12dae dp 8 7 dae and other known dae solvers

robustness of nonlinear predictor feedback laws to time and state dependent delay perturbations much recent progress has been achieved for stabilization of linear and nonlinear systems with input delays that are long and dependent on either time or the plant state provided the dependence is known in this paper we consider the delay variations as unknown and study robustness of nominal constant delay predictor feedbacks under delay variations that depend on time and the state we show that when the delay perturbation and its rate have sufficiently small magnitude the local asymptotic stability of the closed loop system under the nominal predictor based design is preserved for the special case of linear systems and under only time varying delay perturbations we prove robustness of global exponential stability of the predictor feedback when the delay perturbation and its rate are small in any one of four different metrics we present two examples one that is concerned with the control of a dc motor through a network and one of a teleoperation like system

adaptive backstepping control of uncertain linear systems under unknown actuator delay trajectory tracking of uncertain time delay linear systems by output feedback control is of theoretical importance and practical value in this paper concentrating on a class of linear plants whose relative degree equals to system dimension we develop a lyapunov based control scheme to achieve trajectory tracking despite some classic difficulties including unmeasurable system state unknown plant parameters and unknown input time delay a comprehensive approach combining adaptive backstepping output feedback with prediction based boundary control is employed in the design the stability analysis exhibits the global boundedness of all closed loop system signals and the tracking performance is also guaranteed

index reduction in differential algebraic equations using dummy derivatives a new index reduction algorithm for daes is developed in the usual manner parts of the dae are differentiated analytically and appended to the original system for each additional equation a derivative is selected to be replaced by a new algebraic variable called a dummy derivative the resulting augmented system is at most index 1 but no longer overdetermined the dummy derivatives are not subject to discretization their purpose is to annihilate part of the dynamics in the dae leaving only what corresponds to the dynamics of a state space form no constraint stabilization is necessary in the subsequent numerical treatment numerical tests indicate that the method yields results with an accuracy comparable to that obtained for the corresponding state space ode

compensation of transport actuator dynamics with input dependent moving controlled boundary we introduce and solve the stabilization problem of a transport partial differential equation pde nonlinear ordinary differential equation ode cascade in which the pde state evolves on a domain whose length depends on the boundary values of the pde state itself in particular we develop a predictor feedback control design which compensates such transport pde dynamics we prove local asymptotic stability of the closed loop system in the c 1 norm of the pde state employing a lyapunov like argument and introducing a backstepping transformation we also highlight the relation of the pde ode cascade to a nonlinear system with input delay that depends on past input values and present the predictor feedback control design for this representation as well

on the relation between local controllability and stabilizability for a class of nonlinear systems the problem of local stabilizability of locally controllable nonlinear systems is considered it is well known that contrary to the linear case local controllability does not necessarily imply stabilizability a class of nonlinear systems for which local controllability implies local asymptotic stabilizability using continuous static state feedback is described as for this class of systems the well known hermes controllability condition is necessary and sufficient for local controllability

least squares completions for nonlinear differential algebraic equations a method has been proposed for numerically solving lower dimensional nonlinear higher index differential algebraic equations for which more classical methods such as backward differentiation or implicit runge kutta may not be appropriate this method is based on solving nonlinear dae derivative arrays using nonlinear singular least squares methods the theoretical foundations generality and limitations of this approach remain to be determined this paper carefully examines several key aspects of this approach the emphasis is on general results rather than specific results based on the structure of various applications

adding an integrator for the stabilization problem abstract we study the relationship between the following two properties p1 the system x f x y y v is locally asymptotically stabilizable and p2 the system x f x u is locally asymptotically stabilizable where x r n y r dayawansa martin and knowles have proved that these properties are equivalent if the dimension n 1 here using the so called control lyapunov function approach a we propose another more constructive and somewhat simpler proof of dayawansa martin and knowles s result b we show that in general p1 does not imply p2 for dimensions n larger than 1 c we prove that p2 implies p1 if some extra assumptions are added like homogeneity of the system by using the latter result recursively we obtain a sufficient condition for the local asymptotic stabilizability of systems in a triangular form

delay identification for a class of nonlinear systems abstractthe problem of state estimation for nonlinear systems with unknown state delays is still an open problem in this paper we propose to add a delay identifier to suitable high gain observers in order to achieve simultaneous estimation of state and delay in the case of one constant delay in the state we provide sufficient conditions to guarantee the exponential convergence to zero of the errors globally with respect to the initial choice of the system state variables and locally with respect to the initial delay estimation we validate the method through an example concerning chaotic oscillators

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

signature methods for the assignment problem the signature of a dual feasible basis of the assignment problem is an n vector whose ith component is the number of nonbasic activities of type i j this paper uses signatures to describe a method for finding optimal assignments that terminates in at most n 1n 2 2 pivot steps and takes at most on3 work

delay robustness of linear predictor feedback without restriction on delay rate robustness is established for the predictor feedback for linear time invariant systems with respect to possibly time varying perturbations of the input delay with a constant nominal delay the prior results have addressed qualitatively constant delay perturbations robustness of stability in l 2 norm of actuator state and delay perturbations with restricted rate of change robustness of stability in h 1 norm of actuator state the present work provides simple formulas that allow direct and accurate computation of the least upper bound of the magnitude of the delay perturbation for which the exponential stability in supremum norm on the actuator state is preserved while the prior work has employed lyapunov krasovskii functionals constructed via backstepping the present work employs a particular form of small gain analysis two cases are considered the case of measurable possibly discontinuous time varying perturbations and the case of constant perturbations

control of transport pde nonlinear ode cascades with state dependent propagation speed in this paper we deal with the control of a transport partial differential equation nonlinear ordinary differential equation pde nonlinear ode cascade system in which the transport coefficient depends on the ode state we develop a pde based predictor feedback boundary control law which compensates the transport dynamics of the actuator and guarantees global asymptotic stability of the closed loop system the stability proof is based on an infinite dimensional backstepping transformation and a lyapunov like argument the relation of the pde ode cascade with a state dependent propagation speed to an ode system with a state dependent input delay which is defined implicitly via an integral of past values of the ode state is also highlighted and the corresponding equivalent predictor feedback design is presented together with an alternative proof of global asymptotic stability of the closed loop system based on the construction of a lyapunov functional the practical relevance of our control framework is illustrated in an example that is concerned with the control of a metal rolling process

compensation of actuator dynamics governed by quasilinear hyperbolic pdes we present a methodology for stabilization of general nonlinear systems with actuator dynamics governed by a certain class of quasilinear first order hyperbolic pdes since for such pde ode cascades the speed of propagation depends on the pde state itself which implies that the prediction horizon cannot be a priori known analytically the key design challenge is the determination of the predictor state we resolve this challenge and introduce a pde predictor feedback control law that compensates the transport actuator dynamics due to the potential formation of shock waves in the solutions of quasilinear first order hyperbolic pdes which is related to the fundamental restriction for systems with time varying delays that the delay rate is bounded by unity we limit ourselves to a certain feasibility region around the origin and we show that the pde predictor feedback law achieves asymptotic stability of the closed loop system providing an estimate of its region of attraction our analysis combines lyapunov like arguments and iss estimates since it may be intriguing as to what is the exact relation of the cascade to a system with input delay we highlight the fact that the considered pde ode cascade gives rise to a system with input delay with a delay that depends on past input values defined implicitly via a nonlinear equation the developed control design methodology is applied to the control of vehicular traffic flow at distant bottlenecks

compensation of input delay that depends on delayed input abstract for nonlinear systems we develop a pde based predictor feedback control design which compensates actuator dynamics governed by a transport pde with outlet boundary value dependent propagation velocity global asymptotic stability under the predictor feedback control law is established assuming spatially uniform strictly positive transport velocity the stability proof is based on a lyapunov like argument and employs an infinite dimensional backstepping transformation that is introduced an equivalent representation of the transport pde nonlinear ode cascade via a nonlinear system with an input delay that is defined implicitly through an integral of the past input is also provided and the equivalent predictor feedback control design for the delay system is presented the validity of the proposed controller is illustrated applying a predictor feedback bang bang boundary control law to a pde model of a production system with a queue consistent simulation results are provided that support the theoretical developments

technical communique robust stabilization of uncertain input delayed systems using reduction method this paper concerns a robust stabilization problem that arises when applying the so called reduction method to multiple input delayed systems with parametric uncertainties a robust stabilizing controller that can be constructed easily by solving convex problems in terms of linear matrix inequalities is presented numerical examples are provided to show that in many cases the proposed controller is less conservative and easier to obtain than the existing controllers

nonsmooth stabilization of a class of nonlinear cascaded systems a global nonsmooth stabilization scheme is presented for a class of nonlinear cascaded systems with uncontrollable linearization a stepwise constructive control methodology is proposed for the driving subsystem by using the adding a power integrator technique under suitable conditions and based on homogeneous properties it is proved that the stabilization of the driving subsystem implies the stabilization of the overall cascaded system due to the versatility of the adding a power integrator technique and homogeneous properties the proposed controller not only can be used to stabilize the cascaded system asymptotically but also is able to lead to an interesting result of finite time stabilization under appropriate conditions

differential algebraic equations of index 1 may have an arbitrarily high structural index it is shown that the structural index of a linear differential algebraic equation dae with constant coefficients and with index 1 may be arbitrarily high contrary to a previous result from the literature this demonstrates that pantelides algorithm applied to daes of index 1 may perform an arbitrarily high number of iterations and differentiations