model structure simplification of nonlinear systems via immersion this paper concerns the simplification of model structures of nonlinear systems while preserving their input output maps the basic technique is an immersion of a system which is a mapping of the initial state from the original system to another system of an identical input output map the necessary and sufficient conditions are presented for the immersibility of a given system into a state space representation of such particular structures as rational functions or polynomials with respect to the state the conditions are so mild that many types of nonlinear systems can be represented by rational or polynomial model structures moreover it is also shown that a polynomial state space representation can always be constructed to be at most quadratic with respect to the state

finite dimensional open loop control generators for non linear systems this paper concerns itself with the existence of open loop control generators for non linear continuous time systems the main result is that under relatively mild assumptions on the original system and for each fixed compact subset of the state space there always exists one such generator this is a new system with the property that the controls it produces are sufficiently rich to preserve complete controllability along non singular trajectories general results are also given on the continuity and differentiability of the input to state mapping for various p norms on controls as well as a comparison of various non linear controllability notions

analysis of a predator prey model with modified leslie gower and holling type ii schemes with stochastic perturbation abstract in this paper we consider a predator prey model with modified leslie gower and holling type ii schemes with stochastic perturbation we show there is a unique positive solution to the system with positive initial value and mainly investigate the long time behavior of the system condition for the system to be extinct is given and persistent condition is established at last numerical simulations are carried out to support our results

on flat systems behaviors and observable image representations in this short paper we propose a definition of flatness for systems not necessarily given in input state output representation a flat system is a system for which there exists a mapping such that the manifest system behavior is equal to the image of this mapping and such that the latent variable appearing in this image representation can be written as a function of the manifest variable and its derivatives up to some order for linear differential systems flatness is equivalent to controllability we will generalize the main theorem of levine and nguyen systems control lett 48 2003 69 to general linear differential systems

mappings that preserve pairs of operators with zero triple jordan product abstract let f be a field and n 3 suppose s 1 s 2 m n f contain all rank one idempotents the structure of surjections s 1 s 2 satisfying aba 0 a b a 0 is determined similar results are also obtained for a subsets of bounded operators acting on a complex or real banach space x b the space of hermitian matrices acting on n dimensional vectors over a skew field d c subsets of self adjoint bounded linear operators acting on an infinite dimensional complex hilbert space it is then illustrated that the results can be applied to characterize mappings on matrices or operators such that f aba f a b a for all a b for functions f such as the spectral norm schatten p norm numerical radius and numerical range etc

maps preserving the local spectrum of jordan product of matrices abstract let m n c be the algebra of all n n complex matrices and fix a nonzero vector x 0 c n we show that a map from m n c into itself satisfies t s s t x 0 t s s t x 0 t s m n c if and only if there exists an invertible matrix a m n c such that a x 0 x 0 and t a t a 1 for all t m n c

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

stationary distribution of a stochastic hiv model with two infective stages abstract a stochastic hiv model is studied in this paper using the lyapunov analysis method we provide a sufficient condition for the ergodic stationary distribution of the positive solutions to the model

regular propagators of bilinear quantum systems the present analysis deals with the regularity of solutions of bilinear control systems of the type x a u t b x where the state x belongs to some complex infinite dimensional hilbert space the possibly unbounded linear operators a and b are skew adjoint and the control u is a real valued function such systems arise for instance in quantum control with the bilinear schr o dinger equation for the sake of the regularity analysis we consider a more general framework where a and b are generators of contraction semi groups under some hypotheses on the commutator of the operators a and b it is possible to extend the definition of solution for controls in the set of radon measures to obtain precise a priori energy estimates on the solutions leading to a natural extension of the celebrated noncontrollability result of ball marsden and slemrod in 1982 complementary material to this analysis can be found in hal 01537743v1

asymptotic behaviors of a cell to cell hiv 1 infection model perturbed by white noise abstract in this paper we analyze a mathematical model of cell to cell hiv 1 infection to c d 4 t cells perturbed by stochastic perturbations first of all we investigate that there exists a unique global positive solution of the system for any positive initial value then by using lyapunov analysis methods we study the asymptotic property of this solution moreover we discuss whether there is a stationary distribution for this system and if it owns the ergodic property numerical simulations are presented to illustrate the theoretical results

robust analysis of flatness based control using interval methods in this paper a new approach to the robustness analysis of flatness based tracking controllers using interval methods is proposed this methodology allows us to explicitely determine admissible intervals for the uncertain parameters such that specified error bounds for the state space trajectories are not violated in contrast to earlier approaches no additional controllers have to be considered to take robustness properties into account the presented approach also poses no a priori restrictions on the velocity of the reference trajectory the application of the robustness analysis is demonstrated for a feedforward as well as a feedback tracking controller for the van de vusse type continuous stirred tank reactor cstr

brief transfer equivalence and realization of nonlinear higher order input output difference equations two fundamental modelling problems in nonlinear discrete time control systems are studied using the language of differential forms the discrete time nonlinear single input single output systems to be studied are described by input output i o difference equations i e a high order difference equation relating the input the output and a finite number of their time shifts a new definition of equivalence is introduced which generalizes the notion of transfer equivalence well known for the linear case our definition is based upon the notion of an irreducible differential form of the system and was inspired by the analogous definition for continuous time systems the second problem to be addressed is the realization problem the i o difference equation is assumed to be in the irreducible form so that one can obtain an accessible and observable realization necessary and sufficient conditions are given for the existence of a local state space realization of the irreducible i o difference equation these conditions are formulated in terms of the integrability of certain subspaces of one forms classified according to their relative degree the sufficiency part of the proof gives a constructive procedure up to finding the integrating factors and integration of the set of one forms for obtaining a locally observable and accessible state space system if the system is not in the irreducible form one has first to apply the reduction procedure to transform the system into the irreducible form

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

flatness for linear fractional systems with application to a thermal system this paper is devoted to the study of the flatness property of linear time invariant fractional systems in the framework of polynomial matrices of the fractional derivative operator we give a characterization of fractionally flat outputs and a simple algorithm to compute them we also obtain a characterization of the so called fractionally 0 flat outputs we then present an application to a two dimensional heated metallic sheet whose dynamics may be approximated by a fractional model of order 1 2 the trajectory planning of the temperature at a given point of the metallic sheet is obtained thanks to the fractional flatness property without integrating the system equations the pertinence of this approach is discussed on simulations

quantum control and representation theory a new notion of controllability for quantum systems that takes advantage of the linear superposition of quantum states is introduced we call such a notion von neumann controllability and it is shown that it is strictly weaker than the usual notion of pure state and operator controllability we provide a simple and effective characterization of it by using tools from the theory of unitary representations of lie groups in this sense we are able to approach the problem of control of quantum states from a new perspective that of the theory of unitary representations of lie groups a few examples of physical interest and the particular instances of compact and nilpotent dynamical lie groups are discussed

finite controllability of infinite dimensional quantum systems quantum phenomena of interest in connection with applications to computation and communication often involve generating specific transfers between eigenstates and their linear superpositions for some quantum systems such as spin systems the quantum evolution equation the schrodinger equation is finite dimensional and old results on controllability of systems defined on on lie groups and quotient spaces provide most of what is needed insofar as controllability of non dissipative systems is concerned however in an infinite dimensional setting controlling the evolution of quantum systems often presents difficulties both conceptual and technical in this paper we present a systematic approach to a class of such problems for which it is possible to avoid some of the technical issues in particular we analyze controllability for infinite dimensional bilinear systems under assumptions that make controllability possible using trajectories lying in a nested family of pre defined subspaces this result which we call the finite controllability theorem provides a set of sufficient conditions for controllability in an infinite dimensional setting we consider specific physical systems that are of interest for quantum computing and provide insights into the types of quantum operations gates that may be developed

a constructive condition for dynamic feedback linearization the paper deals with dynamic feedback linearization of continuous time affine systems a constructive procedure based on prolongations is proposed based on necessary geometric conditions the algorithm computes a set of prolongation indices

robust h sub spl infin control for a class of cascaded nonlinear systems this paper is concerned with the problem of robust h sub spl infin control for a class of nonlinear systems with parameter uncertainty the system under consideration is composed of two cascaded subsystems a zero input asymptotically stable nonlinear one and a linearizable one which is controllable the uncertain parameters are from a known compact set and are allowed to enter the system nonlinearly based on a lyapunov approach a nonlinear static state feedback controller is designed such that the l sub 2 gain of the closed loop system is below a prespecified value for all admissible uncertainties furthermore the closed loop system is shown to be robust input to state stable under some conditions

difference algebra and system identification the framework of differential algebra especially ritt s algorithm has turned out to be a useful tool when analyzing the identifiability of certain nonlinear continuous time model structures this framework provides conceptually interesting means to analyze complex nonlinear model structures via the much simpler linear regression models one difficulty when working with continuous time signals is dealing with white noise in nonlinear systems in this paper difference algebraic techniques which mimic the differential algebraic techniques are presented besides making it possible to analyze discrete time model structures this opens up the possibility of dealing with noise unfortunately the corresponding discrete time identifiability results are not as conclusive as in continuous time in addition an alternative elimination scheme to ritt s algorithm will be formalized and the resulting algorithm is analyzed when applied to a special form of the nfir model structure

jordan triple maps abstract let a be a standard operator algebra on a banach space of dimension 1 and b be an algebra over the field of rational numbers let k be a non zero rational number in this note we prove that if a bijection a b satisfies kaba k a b a for all a b a or k abc cba k a b c c b a for all a b c a then is additive

paradigms and puzzles in the theory of dynamical systems a self contained exposition is given of an approach to mathematical models in particular to the theory of dynamical systems the basic ingredients form a triptych with the behavior of a system in the center and behavioral equations with latent variables as side panels the author discusses a variety of representation and parametrization problems in particular questions related to input output and state models the proposed concept of a dynamical system leads to a new view of the notions of controllability and observability and of the interconnection of systems in particular to what constitutes a feedback control law the final issue addressed is that of system identification it is argued that exact system identification leads to the question of computing the most powerful unfalsified model

nonholonomic motion planning steering using sinusoids methods for steering systems with nonholonomic c onstraints between arbitrary configurations are investigated suboptimal trajectories are derived for systems that are not in canonical form systems in which it takes more than one level of bracketing to achieve controllability are considered the trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level a class of systems that can be steered using sinusoids claimed systems is defined conditions under which a class of two input systems can be converted into this form are given

dynamics of a stochastic cell to cell hiv 1 model with distributed delay abstract in this paper we consider a stochastic cell to cell hiv 1 model with distributed delay firstly we show that there is a global positive solution of this model before exploring its long time behavior then sufficient conditions for extinction of the disease are established moreover we obtain sufficient conditions for the existence of an ergodic stationary distribution of the model by constructing a suitable stochastic lyapunov function the stationary distribution implies that the disease is persistent in the mean finally we provide some numerical examples to illustrate theoretical results

stationary distribution of a stochastic staged progression hiv model with imperfect vaccination abstract in this paper we study a stochastic staged progression hiv model with imperfect vaccination we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model by using the stochastic lyapunov analysis method

global stability and stochastic permanence of a non autonomous logistic equation with random perturbation abstract this paper discusses a randomized non autonomous logistic equation d n t n t a t b t n t d t t d b t where b t is a 1 dimensional standard brownian motion in d q jiang n z shi a note on non autonomous logistic equation with random perturbation j math anal appl 303 2005 164 172 the authors show that e 1 n t has a unique positive t periodic solution e 1 n p t provided a t b t and t are continuous t periodic functions a t 0 b t 0 and 0 t a s 2 s d s 0 we show that this equation is stochastically permanent and the solution n p t is globally attractive provided a t b t and t are continuous t periodic functions a t 0 b t 0 and min t 0 t a t max t 0 t 2 t by the way the similar results of a generalized non autonomous logistic equation with random perturbation are yielded

non integrability of the optimal control problem for n level quantum systems we study the problem of optimal laser induced population transfer in n level quantum systems this problem can be represented as an energy optimal control problem related to a sub riemannian problem on and it is known boscain chambrion charlot gauthier that for n 2 and n 3 the hamiltonian system associated with the pontryagin maximum principle pmp is integrable we will show that this changes completely for specifically for n 4 we will prove that the adjoint equation of the pmp does not possess any meromorphic first integral independent of the hamiltonian on the levels of the casimir functions this implies that the system is not b integrable for any in proving our nonintegrability results we will use differential galois theory

decoupling theory of general multivariable analytic non linear systems in this paper the decoupling problem of the general muitivariable analytic nonlinear system of the form xdot x u y h x u is discussed where the state space is a real analytic manifold sufficient and necessary conditions for decoupling by state feedback combined with compensation and state feedback only are represented a sufficient and necessary condition for stable decoupling is also derived for decouplable systems the synthesis procedure is represented

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

on differential systems with quadratic impulses and their applications to lagrangian mechanics this paper is concerned with the basic dynamics and a class of variational problems for control systems of the form text e qquad dot x f t x u g t x u dot u h t x u dot u 2 these systems have impulsive character due to the presence of the time derivative dot u of the control it is shown that trajectories can be well defined when the controls u are limits in a suitable weak sense of sequences u n contained in the sobolev space w 1 2 roughly speaking one can say that in this case the dot u n tend to the square root of a measure actually this paper shows that the system e is essentially equivalent to an affine impulsive system of the form dot x f x g x v h x dot w where v in l 2 and dot w is a nonnegative radon measure not smaller than v 2 this provides a characterization of the closure of the set of trajectories of e as the controls u range inside a fixed ball of w 1 2 the existence of generalized optimal controls for va

local exact controllability of a one dimensional nonlinear schrodinger equation we consider a one dimensional nonlinear schrodinger equation modeling a bose einstein condensate in an infinite square well potential box this is a nonlinear control system in which the state is the wave function of the bose einstein condensate and the control is the length of the box we prove that local exact controllability around the ground state associated with a fixed length of the box holds generically with respect to the chemical potential mu i e up to an at most countable set of mu values the proof relies on the linearization principle and the inverse mapping theorem as well as ideas from analytic perturbation theory

hybrid adaptive control laws solving a path following problem for non holonomic mobile manipulators in this paper a general solution to the path following problem for mobile manipulators with non holonomic mobile platform has been presented new proposed control algorithms for mobile manipulators with fully known dynamics or with parametric uncertainty in the dynamics take into considerations the kinematics as well as the dynamics of the non holonomic mobile manipulator the convergence of the control algorithms is proved using the lasalle s invariance principle

preservers of local spectrum of matrix jordan triple products abstract let m n be the space of n n complex matrices and for a nonzero vector e c n and t m n let t e denote the local spectrum of t at e maps on m n which preserve the local spectrum of jordan triple product of matrices at e in a sense that t s t e t s t e t s m n are characterized with no surjectivity assumption on them

additivity of jordan maps on standard operator algebras abstract in this paper we prove that a bijective map form a a standard operator algebra on a banach space of dimension 1 onto a ring that satisfies ab ba a b b a a b a is additive

preservers of radial unitary similarity functions on products of operators abstract let s be a subset of the algebra l h of all bounded linear operators on an infinite dimensional complex hilbert space h and let f s 0 be a radial unitary similarity invariant function under some assumption on s and f characterizations are obtained for surjective maps on s satisfying f t s f t s t s s where the binary operation stands for the product or the jordan semi triple product on operators analogous descriptions are obtained for the finite dimensional case without the surjectivity assumption on

on dynamic feedback linearization abstract we address the problem of transforming a nonlinear multi input system into a linear controllable one via nonsingular dynamic feedback and extended state space diffeomorphism we show that in the single input case if a system is dynamic feedback linearizable it is also static feedback linearizable we then give sufficient conditions for a class of multi input systems to be dynamic feedback linearizable all three dimensional systems with two controls and a controllable linear approximation about the origin are shown to belong to such a class

controllability of quantum harmonic oscillators it is proven in a previous paper that any modal approximation of the one dimensional quantum harmonic oscillator is controllable we prove here that contrary to such finite dimensional approximations the original infinite dimensional system is not controllable its controllable part is of dimension 2 and corresponds to the dynamics of the average position more generally we prove that for the quantum harmonic oscillator of any dimension similar lacks of controllability occur whatever the number of control is the controllable part still corresponds to the average position dynamics we show with the quantum particle in a moving quadratic potential that some physically interesting motion planning questions can be however solved

flatness based control of a single qubit gate this work considers the open loop control problem of steering a two level quantum system from any initial to any final condition the model of this system evolves on the state space having two inputs that correspond to the complex amplitude of a resonant laser field a symmetry preserving flat output is constructed using a fully geometric construction and quaternion computations simulation results of this flatness based open loop control are provided

distributed nonlinear control of mobile autonomous multi agents abstract this paper studies the distributed nonlinear control of mobile autonomous agents with variable and directed topology a new distributed nonlinear design scheme is presented for multi agent systems modeled by double integrators with the new design the outputs of the controlled agents asymptotically converge to each other as long as a mild connectivity condition is satisfied moreover the velocity derivative of the output of each agent can be restricted to be within any specified neighborhood of the origin which is of practical interest for systems under such physical constraint the new design is still valid if one of the agents is a leader and the control objective is to achieve leader following as an illustration of the generality and effectiveness of the presented methodology the formation control of a group of unicycle mobile robots with nonholonomic constraints is revisited instead of assuming the point robot model the unicycle model is transformed into two double integrators by dynamic feedback linearization and the proposed distributed nonlinear design method is used to overcome the singularity problem caused by the nonholonomic constraint by properly restricting the velocities simulation results are included to illustrate the theoretical results

controllability of networks of spatially one dimensional second order pdes an algebraic approach we discuss controllability of systems that are initially given by boundary coupled pdes of second order these systems may be described by modules over particular rings of distributions and ultradistributions with compact support arising from the solution of the cauchy problem of the pde under consideration with data on the time axis we show that those rings are bezout domains this property is utilized in order to derive algebraic and trajectory related controllability results

on the problem of quantum control in infinite dimensions in the framework of bilinear control of the schrodinger equation it has been proved that the reachable set has a dense complement in hence in this setting exact quantum control in infinite dimensions is not possible on the other hand it is known that there is a simple choice of operators which when applied to an arbitrary state generate dense orbits in hilbert space compatibility of these two results is established in this paper and in particular it is proved that the closure of the reachable set of bilinear control is dense in the requirements for controllability in infinite dimensions are also related to the properties of the infinite dimensional unitary group

a structurally flat triangular form based on the extended chained form in this paper we present a structurally flat triangular form which is based on the extended chained form we provide a complete geometric characterisation of the proposed triangular form in terms

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

stability and hopf bifurcation in a model of gene expression with distributed time delays in this paper we consider the effect of distributed time delays on dynamics of a mathematical model of gene expression both the weak and strong delay kernels are discussed sufficient conditions for the local stability of the unique equilibrium are obtained taking the average delay as a bifurcation parameter we investigate the direction of the hopf bifurcations and the stability of the bifurcating periodic solutions by using the method of multiple time scales finally numerical simulation is carried out to illustrate our theoretical results it shows both subcritical and supercritical hopf bifurcations can happen

vibrational control of a class of nonlinear systems by nonlinear multiplicative vibrations vibrational control is a nonclassical control principle which proposes a utilization of zero mean parametric excitation of a dynamical system for control purposes this paper extends nonlinear vibrational control theory developed in 8 9 to systems controlled by nonlinear multiplicative vibrations condition for partial vibrational stabilization with respect to a component of a steady state vector the choice of stabilizing vibrations and the transient motions are discussed for a certain practically important class of nonlinear vibrationally controlled systems the application of the results is demonstrated on the example of a catalytic reactor using a combination of numerical and analytical techniques

nonregular feedback linearization a nonsmooth approach in this note we address the problem of exact linearization via nonsmooth nonregular feedback a criterion of nonregular static state feedback linearizability is presented for a class of nonlinear affine systems with two control inputs and its application to nonholonomic systems is briefly discussed

flatness based extremum seeking control over periodic orbits in this note an extremum seeking controller is developed to steer a periodic system to orbits that maximize a functional of interest for a class of differentially flat nonlinear systems the problem is posed as a real time optimal trajectory generation problem in which the optimal orbit is computed using an extremum seeking approach using the flatness property of the dynamics the original dynamic optimization problem is transformed to a parameterized optimization problem which can be solved in real time to approximate the optimal orbit the control algorithm provides tracking of the optimal orbit a drug delivery control problem is considered to demonstrate the application of the technique

minimal time for the bilinear control of schrodinger equations abstract we consider a quantum particle in a potential v x x r n subject to a spatially homogeneous time dependent electric field e t which plays the role of the control under generic assumptions on v this system is approximately controllable on the l 2 r n c sphere in sufficiently large times t as proved by boscain caponigro chambrion and sigalotti 2012 in the present article we show that this approximate controllability result is false in small time as a consequence the result by boscain et al is in some sense optimal with respect to the control time t

on persistent excitations for the identification of switched linear dynamical systems over finite fields this paper discusses the issue of the persistent excitation pe conditions in the context of identification for dynamical systems defined over a finite field the work is motivated by the fact that the asymptotical property of the pe conditions for dynamical systems defined over the field of real numbers is no longer valid in the case of systems defined over finite fields the special class of switched linear discrete time systems for which the mode is assumed to be unknown is considered a necessary and sufficient condition that provides the minimum amount of data required for the identification is first proposed next a necessary condition is derived that gives the structural condition the system must satisfy regardless of the availability of data finally some computational aspects are discussed and examples are given to illustrate the validity of the proposed results

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

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

flatness of switched linear discrete time systems this note is devoted to flatness for switched linear discrete time systems for this class of hybrid systems algebraic conditions are derived to check whether a given output is flat then a feedforward flatness based control strategy for trajectory tracking is proposed

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

nilpotentization of the kinematics of the n trailer system at singular points and motion planning through the singular locus we propose in this paper a constructive procedure that transforms locally even at singular configurations the kinematics of a car towing trailers into kumpera ruiz normal form this construction converts the non holonomic motion planning problem into an algebraic problem the resolution of a system of polynomial equations which we illustrate by steering the two trailer system in a neighbourhood of singular configurations we show also that the n trailer system is a universal local model for all goursat structures and that all goursat structures are locally nilpotentizable

functional reproducibility of general multivariable analytic non linear systems in this paper the functional reproducibility of a general multivariable analytic nonlinear system of the form x f x u y h x u will be discussed where the state space is a real analytic manifold a general inversion algorithm is presented for the system a sufficient and necessary condition for the functional reproducibility of the system is derived the construction of a right inverse system is also included

preservers of pseudo spectral radius of operator products abstract let h be an infinite dimensional complex hilbert space and let l h be the algebra of all bounded linear operators on h for e 0 and t l h let r e t denote the e pseudo spectral radius of t we characterize surjective maps on l h which satisfy r e t s r e t s for all t s l h we also obtain analogous result for the finite dimensional case without the surjectivity assumption on

jordan triple multiplicative surjective maps on b h abstract let h be a hilbert space and b h be the algebra of all bounded linear operators on h in this paper we obtain a structure theorem of maps preserving the jordan triple zero product on b h then this is applied to give a full characterization of a surjective map b h b h satisfying a b a a b a

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

on the computation of π flat outputs for linear time varying differential delay systems abstract we introduce a new definition of flatness for linear differential delay systems with time varying coefficients we characterize and 0 flat outputs and provide an algorithm to efficiently compute such outputs we present an academic example of motion planning to discuss the pertinence of the approach

dynamics of a novel nonlinear stochastic sis epidemic model with double epidemic hypothesis abstract in this paper we propose new mathematical models with nonlinear incidence rate and double epidemic hypothesis then we dedicate to develop a method to obtain the threshold of the stochastic sis epidemic model to this end first we investigate the stability of the equilibria of the deterministic system and obtain the conditions for the extinction and the permanence of two epidemic diseases second we explore and obtain the threshold of a stochastic sis system for the extinction and the permanence in mean of two epidemic diseases the results show that a large stochastic disturbance can cause infectious diseases to go to extinction in other words the persistent infectious disease of a deterministic system can become extinct due to the white noise stochastic disturbance this implies that the stochastic disturbance is conducive to epidemic diseases control to illustrate the performance of the theoretical results we present a series of numerical simulations of these cases with respect to different noise disturbance coefficients

optimal control strategy for an impulsive stochastic competition system with time delays and jumps abstract driven by both white and jump noises a stochastic delayed model with two competitive species in a polluted environment is proposed and investigated by using the comparison theorem of stochastic differential equations and limit superior theory sufficient conditions for persistence in mean and extinction of two species are established in addition we obtain that the system is asymptotically stable in distribution by using ergodic method furthermore the optimal harvesting effort and the maximum of expectation of sustainable yield esy are derived from hessian matrix method and optimal harvesting theory of differential equations finally some numerical simulations are provided to illustrate the theoretical results

rank invariants of nonlinear systems a linear algebraic framework for the analysis of rank properties of nonlinear systems is introduced this framework gives a high level interpretation of several existing algorithms built around the recursive computation of certain algebraic ranks associated with right invertibility left invertibility and dynamic decoupling furthermore it can be used to establish links between these algorithms and the differential algebraic approach as well as to solve some static and dynamic noninteracting control problems

pseudospectral methods for optimal motion planning of differentially flat systems the article presents some preliminary results on combining two new ideas from nonlinear control theory and dynamic optimization we show that the computational framework facilitated by pseudospectral methods applies quite naturally and easily to fliess implicit state variable representation of dynamical systems the optimal motion planning problem for differentially flat systems is equivalent to a classic bolza problem of the calculus of variations we exploit the notion that derivatives of flat outputs given in terms of lagrange polynomials at legendre gauss lobatto points can be quickly computed using pseudospectral differentiation matrices additionally the legendre pseudospectral method approximates integrals by gauss type quadrature rules the application of this method to the two dimensional crane model reveals how differential flatness may be readily exploited

absolute equivalence and dynamic feedback linearization abstract elie cartan s results on absolute equivalence of differential systems are shown to imply a generalization of a recent result on dynamic feedback linearization of scalar control systems

flatness of semilinear parabolic pdes a generalized cauchy kowalevski approach a generalized cauchy kowalevski approach is proposed for flatness based trajectory planning for boundary controlled semilinear systems of partial differential equations pdes in a one dimensional spatial domain for this the ansatz presented in trajectory planning for boundary controlled parabolic pdes with varying parameters on higher dimensional spatial domains t meurer and a kugi ieee trans autom control vol 54 no 8 pp 1854 1868 aug 2009 using formal integration is generalized towards a unified design framework which covers linear and semilinear pdes including rather broad classes of nonlinearities arising in applications in addition an efficient semi numerical solution of the implicit state and input parametrizations is developed and evaluated in different scenarios simulation results for various types of nonlinearities and a tubular reactor model described by a system of semilinear reaction diffusion convection equations illustrate the applicability of the proposed method

a pendulum theorem we consider n linked pendulums which are inverted and balanced on top of one another and establish a general theorem which shows how they may be stabilized by small vertical oscillations of the support

null controllability of the heat equation using flatness we derive in a direct and rather straightforward way the null controllability of the n dimensional heat equation in a bounded cylinder with boundary control at one end of the cylinder we use the so called flatness approach which consists in parameterizing the solution and the control by the derivatives of a flat output this yields an explicit control law achieving the exact steering to zero replacing the involved series by partial sums we obtain a simple numerical scheme for which we give explicit error bounds numerical experiments demonstrate the relevance of the approach

trajectory planning for boundary controlled parabolic pdes with varying parameters on higher dimensional spatial domains the flatness based design of a feedforward tracking control is considered for the solution of the trajectory planning problem for a boundary controlled diffusion convection reaction system with spatially and temporally varying parameters defined on a 1 les m dimensional parallelepipedon with the nonlinear input being restricted to a m 1 dimensional hyperplane for this an implicit state and input parametrization in terms of a basic output is determined via a volterra type integral equation with operator kernel by recursively computing successive series coefficients a series solution of the integral equation is obtained whose absolute and uniform convergence is verified by restricting the system parameters and the basic output to a certain but broad gevrey class hence prescribing an admissible desired trajectory for the basic output directly yields the feedforward control by evaluating the input parametrization this results in a systematic procedure for trajectory planning and feedforward control design for boundary controlled parabolic distributed parameter systems defined on higher dimensional domains

local factorization of trajectory lifting morphisms for single input affine control systems trajectory preserving and lifting maps have been implicitly used in many recursive or hierarchical control design techniques well known systems theoretic concepts such as differential flatness or more recent ones such as simulation and bisimulation can be also understood through the trajectory lifting maps they define in this paper we initiate a study of trajectory preserving and lifting maps between affine control systems our main result shows that any trajectory lifting map between two single input control affine systems can be locally factored as the composition of two special trajectory lifting maps a projection onto a quotient system followed by a differentially flat output with respect to another control system we use this decomposition result to show that under mild regularity conditions trajectory preserving maps between single input affine control systems also lift trajectories as an additional application of the main result we also show how the hierarchical stabilization method known as back stepping can be used based on the existence of a trajectory preserving and lifting map having a feedback stabilizable control system as codomain

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

local controllability and non controllability for a 1d wave equation with bilinear control abstract we consider a linear wave equation on the interval 0 1 with bilinear control and neumann boundary conditions we study the controllability of this nonlinear control system locally around a constant reference trajectory we prove that the following results hold generically for every t 2 this system is locally controllable in h 3 h 2 in time t with controls in l 2 0 t r for t 2 this system is locally controllable up to codimension one in h 3 h 2 in time t with controls in l 2 0 t r the reachable set is locally a non flat submanifold of h 3 h 2 with codimension one for every t 2 this system is not locally controllable more precisely the reachable set with controls in l 2 0 t r is contained in a non flat submanifold of h 3 h 2 with infinite codimension the proof of these results relies on the inverse mapping theorem and second order expansions

trajectory control and interconnection of 1d and nd systems in this paper we examine the relationship between control viewed as concatenation of trajectories and control viewed as interconnection of systems we show that for one dimensional linear time invariant systems the ability to obtain a given subsystem by regular interconnection a prerequisite for any feedback type structure is equivalent to the ability to drive any trajectory into that subsystem however in the case of multidimensional systems the former is a stronger property than the latter trajectory controllability can however be expressed as a regular interconnection of behaviors in an extended variable space by introducing latent or auxiliary variables this leads as a by product to the notion of controlling a system by means of latent variables

regularity and lyapunov stabilization of weak entropy solutions to scalar conservation laws we consider the problem of lyapunov boundary stabilization of the weak entropy solution to a scalar conservation law with strictly convex flux in one dimension of space around a uniform equilibrium we show that for a specific class of boundary conditions the solution to the initial boundary value problem for an initial condition with bounded variations can be approximated arbitrarily closely in the l 1 norm by a piecewise smooth solution with finitely many discontinuities the constructive method we present designs explicit boundary conditions in this class which guarantee lyapunov stability of the weak entropy solution to the initial boundary value problem we show how the greedy control obtained by maximizing the decrease of the natural lyapunov function may fail to asymptotically stabilize and a brute force control generates unbounded variation of traces we then design a stabilizing control which avoid oscillations and propose a nonlocal technique depending on time and the whole initial datum which optimizes the convergence time controllers performance is illustrated on numerical benchmarks using the godunov scheme