object trajectory based activity classification and recognition using hidden markov models motion trajectories provide rich spatiotemporal information about an object s activity this paper presents novel classification algorithms for recognizing object activity using object motion trajectory in the proposed classification system trajectories are segmented at points of change in curvature and the subtrajectories are represented by their principal component analysis pca coefficients we first present a framework to robustly estimate the multivariate probability density function based on pca coefficients of the subtrajectories using gaussian mixture models gmms we show that gmm based modeling alone cannot capture the temporal relations and ordering between underlying entities to address this issue we use hidden markov models hmms with a data driven design in terms of number of states and topology e g left right versus ergodic experiments using a database of over 5700 complex trajectories obtained from uci kdd data archives and columbia university multimedia group subdivided into 85 different classes demonstrate the superiority of our proposed hmm based scheme using pca coefficients of subtrajectories in comparison with other techniques in the literature

generalized controller canonical form for linear and nonlinear dynamics a generalized controller canonical form for linear and nonlinear dynamics is proposed it is obtained using the theorem of the primitive element from differential algebra the derivation of the controller form does not apply to multivariable constant linear systems with the transformations all nonlinear dynamics can be exactly linearized by dynamic feedback the main departure from standard theory is that transformations may depend on input derivatives once differential algebraic tools are introduced the proofs of the results are easy

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

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

unsupervised learning of human action categories using spatial temporal words we present a novel unsupervised learning method for human action categories a video sequence is represented as a collection of spatial temporal words by extracting space time interest points the algorithm automatically learns the probability distributions of the spatial temporal words and the intermediate topics corresponding to human action categories this is achieved by using latent topic models such as the probabilistic latent semantic analysis plsa model and latent dirichlet allocation lda our approach can handle noisy feature points arisen from dynamic background and moving cameras due to the application of the probabilistic models given a novel video sequence the algorithm can categorize and localize the human action s contained in the video we test our algorithm on three challenging datasets the kth human motion dataset the weizmann human action dataset and a recent dataset of figure skating actions our results reflect the promise of such a simple approach in addition our algorithm can recognize and localize multiple actions in long and complex video sequences containing multiple motions

global stabilization of a class of invertible mimo nonlinear systems in this paper we consider the class of input affine mimo nonlinear systems which are assumed to be invertible and input output linearizable this class includes as a trivial special case the class of mimo systems possessing a well defined vector relative degree it is shown that if a system in this class is strongly minimum phase in a sense specified in the paper it is globally stabilizable via partial state feedback or semiglobally stabilizable via dynamic output feedback the result substantially broadens the class of nonlinear mimo systems for which global semiglobal stabilization via limited state information is known to be possible

general c means clustering model partitional clustering is an important part of cluster analysis based on various theories numerous clustering algorithms have been developed and new clustering algorithms continue to appear in the literature it is known that occam s razor plays a pivotal role in data based models and partitional clustering is categorized as a data based model however no relation had previously been discovered between occam s razor and partitional clustering as we discuss in this paper the three main contributions of this paper can be summarized as follows 1 according to a novel definition of the mean a unifying generative framework for partitional clustering algorithms called a general c means clustering model gcm is presented and studied and 2 based on the local optimality test of the gcm the connection between occam s razor and partitional clustering is established for the first time as its application a comprehensive review of the existing objective function based clustering algorithms is presented based on gcm 3 under a common assumption about partitional clustering a theoretical guide for devising and implementing clustering algorithm is discovered these conclusions are verified by numerical experimental results

local stabilization of minimum phase nonlinear systems abstract in this note we briefly review the notion of a nonlinear minimum phase system i e a system which when constrained in such a way as to produce zero output evolves with an asymptotically stable dynamics the main purpose of the paper is to show that any minimum phase nonlinear system can always be locally stabilized by smooth state feedback

structure at infinity revisited abstract the structure at infinity of an ordinary differential control system is a finite sequence of increasing integers ending with the differential output rank of the system namely the number of outputs that can be given as arbitrary functions of time when the inputs are unknown its definition and construction originally done for linear systems has been extended to affine nonlinear systems and used in order to study dynamic decoupling or model matching it essentially relies on a state representation the purpose of this paper is to make a critical examination of this concept and to modify it in order to avoid the state representation at the same time we extend it to nonlinear partial differential control systems by exhibiting a link with formal integrability a highly important concept in the formal theory of systems of partial differential equations that cannot be handled by means of a transfer matrix approach many explicit examples will illustrate the main results and the possibility to use computer algebra techniques will be pointed out

block decoupling of non linear systems by static measurement feedback in this paper the block input output decoupling problem for non linear systems is stated and solved by static feedback of measured variables only in contrast with standard solutions which assume that the full state is available for feedback

zeros at infinity for affine nonlinear control systems a definition of zeros at infinity for affine nonlinear control systems is proposed the definition is local which means that we exclude certain singularities we argue the reasonableness of our definition by showing its relevance to the problem of nonlinear decoupling in particular we give a necessary and sufficient condition for the solvability of the general regular decoupling problem for affine systems in terms of the zeros at infinity

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

invertibility of switched nonlinear systems this article addresses the invertibility problem for switched nonlinear systems affine in controls the problem is concerned with reconstructing the input and switching signal uniquely from given output and initial state we extend the concept of switch singular pairs introduced recently to nonlinear systems and develop a formula for checking if the given state and output form a switch singular pair a necessary and sufficient condition for the invertibility of switched nonlinear systems is given which requires the invertibility of individual subsystems and the nonexistence of switch singular pairs when all the subsystems are invertible we present an algorithm for finding switching signals and inputs that generate a given output in a finite interval when there is a finite number of such switching signals and inputs detailed examples are included to illustrate these newly developed concepts

warped k means an algorithm to cluster sequentially distributed data many devices generate large amounts of data that follow some sort of sequentiality e g motion sensors e pens eye trackers etc and often these data need to be compressed for classification storage and or retrieval tasks traditional clustering algorithms can be used for this purpose but unfortunately they do not cope with the sequential information implicitly embedded in such data thus we revisit the well known k means algorithm and provide a general method to properly cluster sequentially distributed data we present warped k means wkm a multi purpose partitional clustering procedure that minimizes the sum of squared error criterion while imposing a hard sequentiality constraint in the classification step we illustrate the properties of wkm in three applications one being the segmentation and classification of human activity wkm outperformed five state of the art clustering techniques to simplify data trajectories achieving a recognition accuracy of near 97 which is an improvement of around 66 over their peers moreover such an improvement came with a reduction in the computational cost of more than one order of magnitude

minimality of dynamic input output decoupling for nonlinear systems in this note we study the strong dynamic input output decoupling problem for nonlinear systems using an algebraic theory for nonlinear control systems we obtain for a dynamic input output decouplable nonlinear system a compensator of minimal dimension that solves the decoupling problem

multilevel image coding with hyperfeatures histograms of local appearance descriptors are a popular representation for visual recognition they are highly discriminant with good resistance to local occlusions and to geometric and photometric variations but they are not able to exploit spatial co occurrence statistics over scales larger than the local input patches we present a multilevel visual representation that remedies this the starting point is the notion that to detect object parts in images in practice it often suffices to detect co occurrences of more local object fragments this can be formalized by coding image patches against a codebook of known fragments or a more general statistical model and locally histogramming the resulting labels to capture their co occurrence statistics local patch descriptors are converted into somewhat less local histograms over label occurrences the histograms are themselves local descriptor vectors so the process can be iterated to code ever larger assemblies of object parts and increasingly abstract or semantic image properties we call these higher level descriptors hyperfeatures we formulate the hyperfeature model and study its performance under several different image coding methods including k means based vector quantization gaussian mixtures and combinations of these with latent dirichlet allocation we find that the resulting high level features provide improved performance in several object image and texture image classification tasks

special coordinate basis for multivariable linear systems finite and infinite zero structure squaring down and decoupling abstract a special coordinate basis for multivariable linear systems is introduced here several fundamental properties of linear systems regarding controllability stabiliza bility observability detectability invariant zeros decoupling zeros infinite zero structure effect of feedback on zero structure squaring down diagonal and triangular decoupling etc can be directly displayed in terms of the special coordinate basis moreover connections between the special coordinate basis and the important invariant subspaces of the geometric theory of linear systems are established

almost disturbance decoupling for single input single output nonlinear systems the almost disturbance decoupling problem for nonlinear single input single output systems is addressed by using singular perturbation methods and high gain feedback sufficient conditions and the explicit high gain nonlinear state feedback in solvable cases are given they generalize both previous almost results for linear systems and exact ones for nonlinear systems the necessity of the conditions is discussed in particular an example is given where the main structural condition is not satisfied and the high gain control designed on the basis of linear approximations fails to achieve almost disturbance decoupling for the original system

a nonregular solution of the nonlinear dynamic disturbance decoupling problem with an application to a complete solution of the nonlinear model matching problem the nonregular dynamic disturbance decoupling problem for nonlinear control systems is introduced a local solution is given by means of a constructive algorithm that is based on singh s algorithm and the clamped dynamics algorithm further studied is the nonlinear model matching problem that is defined as follows given a nonlinear control system to be referred to as the plant and another nonlinear control system to be referred to as the model can a compensator for the plant be found in such a way that the input output behavior of the compensated plant matches that of the model by proving that the solvability of the nonlinear model matching problem is equivalent to the solvability of an associated nonregular dynamic disturbance decoupling problem a complete local solution of this problem can be established

global state and feedback equivalence of nonlinear systems the problem of finding global state space transformations and global feedback of the form u t x t to transform a given nonlinear system xdot f x g x u to a controllable linear system on rn or on an open subset of rn is considered here we give a complete set of differential geometric conditions which are equivalent to the existence of a solution to the above problem

use of observers for the inversion of nonlinear maps abstract in this paper we deal with the problem of the inversion of nonlinear maps the first contribution of the paper is the definition in a formal framework of some problems related to map inversion which are already present in the literature for instance in the robotics area and in observer theory the second and the main contribution consists in the solution of such problems by means of observers for which some structures are proposed for the state estimation of a time varying nonlinear system associated with the given map and reference trajectory

stable inversion for nonlinear systems abstract there have been two recent major developments in output tracking for nonlinear systems and our first main contribution is to relate these under appropriate assumptions we show that the bounded solution of the partial differential equation of isidori and byrnes for each trajectory of an exosystem must be given by an integral representation formula of devasia chen and paden under restrictive hypotheses devasia chen and paden develop a picard process that converges to the solution of the integral equation this solution to the integral equation is also a bounded solution to a dynamical equation driven by the desired outputs in aircraft applications our nonlinear systems are perturbations of pure feedback systems with outputs and we find a solution to the stable inversion problem i e finding bounded controls and bounded state trajectories in response to bounded output signals in two steps the first step ignores the perturbation error and computes the major part of the desired control and corresponding state trajectory the second step computes the remaining control and states by finding a noncausal and stable solution to an error driven dynamical equation in other words the method of devasia chen and paden is applied to an error system and not to the full system this two step procedure is the second main contribution of this paper throughout this paper it is assumed that our nonlinear systems have vector relative degree

on implicit systems of differential equations abstract this article considers implicit systems of differential equations the implicit systems that are considered are given by polynomial relations on the coordinates of the indeterminate function and the coordinates of the time derivative of the indeterminate function for such implicit systems of differential equations we are concerned with computing algebraic constraints such that on the algebraic variety determined by the constraint equations the original implicit system of differential equations has an explicit representation our approach is algebraic although there have been a number of articles that approach implicit differential equations algebraically all such approaches have relied heavily on linear algebra the approach of this article is different we have no linearity requirements at all instead we rely on algebraic geometry in particular we use birational mappings to produce an explicit system the methods developed in this article are easily implemented using various computer algebra 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

a maximum variance cluster algorithm we present a partitional cluster algorithm that minimizes the sum of squared error criterion while imposing a hard constraint on the cluster variance conceptually hypothesized clusters act in parallel and cooperate with their neighboring clusters in order to minimize the criterion and to satisfy the variance constraint in order to enable the demarcation of the cluster neighborhood without crucial parameters we introduce the notion of foreign cluster samples finally we demonstrate a new method for cluster tendency assessment based on varying the variance constraint parameter

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

observability and controllability for smooth nonlinear systems the definition of a smooth nonlinear system as proposed recently by willems is elaborated as a natural generalization of the more common definitions of a smooth nonlinear input output system mini

an efficient sequential clustering method abstract a new method for the sequential clustering of data that gives better results compared to the conventional sequential clustering method is presented in this paper this method utilizes certainty factors and it is independent of the technique used for data representation and or distance computation examples are given for cases where the data are represented as feature vectors as well as strings of symbols syntactic patterns

brief paper asymptotic rejection of asymmetric periodic disturbances in output feedback nonlinear systems this paper deals with asymptotic rejection of periodic disturbances which may have asymmetric basic wave patterns this class of disturbances covers asymmetric wave forms in the half period such as alternating sawtooth wave form some disturbances which are generated from nonlinear oscillation such as van de pol oscillators as well as disturbances with symmetric half period wave forms such as sinusoidal disturbances and triangular disturbances etc the systems considered in this paper can be transformed to the nonlinear output feedback form the amplitude and phase of the disturbances are unknown the novel concept of integral phase shift is introduced together with the newly introduced half period integration operator to investigate the invariant properties of asymmetric periodic disturbances they are used for the estimation of unknown disturbances in the systems together with observer design techniques to deal with nonlinearity the proposed control design with the disturbance estimation asymptotically rejects the unknown disturbance and ensures the overall stability of the system

on the sliding mode control of multivariable nonlinear systems sliding mode control of multivariable nonlinear systems is addressed from the perspective of linear differential algebra for a special but large class of linearizable systems known as differentially flat systems essential orders and differential flatness are shown to be a relevant concept and a sensible requirement respectively associated with the possibilities of designing static or dynamical sliding mode multivariable feedback regulators for nonlinear systems

output feedback disturbance decoupling in nonlinear systems the problem of disturbance decoupling by means of output feedback is addressed the notion of conditioned invariance is reconsidered in a linear algebraic framework using this geometric notion a necessary and sufficient condition respectively necessary condition is obtained for solving the disturbance decoupling problem by quasi static output feedback respectively the disturbance decoupling problem by dynamic output feedback dddpo the necessary conditions for dddpo which are derived are weaker than the existing ones a sufficient condition for the disturbance decoupling problem by static output feedback is given as well

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

equivalence of nonlinear systems to input output prime forms the problem of transforming nonlinear control systems into input output prime forms is dealt with using state space static state feedback and also output space transformations necessary and sufficient geometric conditions for the solvability of this problem are obtained the results obtained generalize well known results both on feedback linearization as well as input output decoupling of nonlinear systems it turns out that from a computational point of view the output space transformation is the crucial step that is performed by constructing rectifying coordinates for a nested sequence of distributions on the output manifold

output input stability implies feedback stabilization abstract we study the recently introduced notion of output input stability which is a robust variant of the minimum phase property for general smooth nonlinear control systems this paper develops the theory of output input stability in the multi input multi output setting we show that output input stability is a combination of two system properties one related to detectability and the other to left invertibility for systems affine in controls we derive a necessary and sufficient condition for output input stability which relies on a global version of the nonlinear structure algorithm this condition leads naturally to a globally asymptotically stabilizing state feedback strategy for affine output input stable systems

canonical decomposition of non linear systems the construction of a canonical or normal representation for non linear systems similar to the morse canonical form in the linear case is obtained the problem considered consists in particular of studying the existence of generalized transformations that achieve a desired block decoupling such transformations generalize the notions of state transformation state feedback and output injection a sufficient condition is given in terms of a separability condition which in turn is completely characterized by using differential forms and their properties

mining mid level features for image classification mid level or semi local features learnt using class level information are potentially more distinctive than the traditional low level local features constructed in a purely bottom up fashion at the same time they preserve some of the robustness properties with respect to occlusions and image clutter in this paper we propose a new and effective scheme for extracting mid level features for image classification based on relevant pattern mining in particular we mine relevant patterns of local compositions of densely sampled low level features we refer to the new set of obtained patterns as frequent local histograms or flhs during this process we pay special attention to keeping all the local histogram information and to selecting the most relevant reduced set of flh patterns for classification the careful choice of the visual primitives and an extension to exploit both local and global spatial information allow us to build powerful bag of flh based image representations we show that these bag of flhs are more discriminative than traditional bag of words and yield state of the art results on various image classification benchmarks including pascal voc

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

feedback linearization of discrete time systems abstract we give necessary and sufficient conditions for a nonlinear discrete time system to be locally linearizable by a change of state coordinates and a feedback the conditions are expressed in terms of controllability distributions associated to the system

on the construction of static stabilizers and static output trackers for dynamically linearizable systems related results and applications it is shown that the property of dynamic linearizability to be understood as linearizability by means of the dynamic extension algorithm implies the existence of static possibly time varying control laws yielding asymptotic output tracking with arbitrary speed of convergence and asymptotic stabilization with a computable bound on the region of attraction similar results hold for systems which are only input output linearizable by means of dynamic state feedback provided that the inverse dynamics possess certain stability properties applications of these results to the problem of regional stabilization of a vtol aircraft is considered together with the tracking problem for a class of flexible joints robots moreover a novel parameterization for flexible joint robots is also proposed

on normal forms of nonlinear systems affine in control the nonlinear equivalences of both finite and infinite zero structures of linear systems have been well understood for single input single output systems and have found many applications in nonlinear control theory the extensions of these notions to multiple input multiple output systems have proven to be highly sophisticated in this paper we propose constructive algorithms for decomposing a nonlinear system that is affine in control these algorithms require modest assumptions on the system and apply to general multiple input multiple output systems that do not necessarily have the same number of inputs and outputs they lead to various normal form representations and reveal the structure at infinity the zero dynamics and the invertibility properties all of which represent nonlinear equivalences of relevant linear system structural properties

algorithms for model based gaussian hierarchical clustering agglomerative hierarchical clustering methods based on gaussian probability models have recently shown promise in a variety of applications in this approach a maximum likelihood pair of clusters is chosen for merging at each stage unlike classical methods model based methods reduce to a recurrence relation only in the simplest case which corresponds to the classical sum of squares method we show how the structure of the gaussian model can be exploited to yield efficient algorithms for agglomerative hierarchical clustering

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

a robust approach for object matching and classification using partial dominant orientation descriptor this paper introduces a novel approach to measure the correspondence between objects and exploit it for object and image classification tasks using the proposed partial dominant orientation descriptor pdod in particular the object is represented by a set of stable and informative key locations sampled using difference of gaussian the proposed pdod at each extracted key location takes into account the position and partially computes the dominant orientation of other key locations relative to it thus offering a global distinctive and discriminative characterization this allows us to learn features that are largely invariant to common image transformations including changes in object colors and textures the correspondence in between two objects is performed by finding for each key location in one object the key location in the other object that has the most similar descriptor object classification proceeds by assigning the most relevant category that has maximally similar stored prototype objects to the query object using k nearest neighbors algorithm with adaptive object distance for efficiency we further investigate pdod for image classification by developing powerful image representations based on the popular bag of words model the extensive experiments demonstrate that the proposed approach greatly improves the matching and classification results while achieving the state of the art performances on several challenging benchmark datasets the obtained results suggest also broader applicability to other classification modalities we propose a novel descriptor for complex object matching and classification the proposed descriptor combines both local and global properties of interest points the proposed descriptor is highly distinctive and insensitive to common image transformations adaptive object distance is proposed to measure the similarity between objects we compare our approach with many existing methods and we achieve the state of the art performances on several benchmarks

global stabilization of partially linear composite systems a linear stabilizable nonlinear asymptotically stable cascade system is globally stabilizable by smooth dynamic state feedback if a the linear subsystem is right invertible and weakly minimum phase and b the only linear variables entering the nonlinear subsystem are the output and the zero dynamics corresponding to this output both of these conditions are coordinate free and there is freedom of choice for the linear output variable this result generalizes several earlier sufficient conditions for stabilizability moreover the weak minimum phase condition for the linear subsystem cannot be relaxed unless a growth restriction is imposed on the nonlinear subsystem

generalized normal form and stabilization of non linear systems this paper considers the normal form of non linear control systems first we propose a generalized relative degree relative degree vector for non linear single respectively multiple input control system which is called the point relative degree respectively point relative degree vector for the systems without output the concepts of essential relative degree respectively essential relative degree vector and the essential point relative degree respectively essential point relative degree vector are defined unlike the classical definition which requires regularity the point relative degree vector is always well defined using these new concepts the generalized normal form is obtained its relationship with the jacobian linearization is investigated using it a straightforward computation algorithm is provided to achieve the generalized normal form based on the generalized normal form we prove that with an additional condition if the zero dynamics is stable the overall system is stabil

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

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

the nonlinear interactor and its application to input output decoupling the solvability of the input output decoupling problem via pure dynamic state feedback a special type of dynamic compensator without zeros at infinity is investigated a necessary and sufficient condition for the solvability of this problem is established in terms of a nonlinear interactor a new concept in the theory of nonlinear control

trading the stability of finite zeros for global stabilization of nonlinear cascade systems analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a stable nonlinear system it is shown that the instability of the zeros of the linear system can be traded with the stability of the nonlinear system up to a limit fixed by the growth properties of the cascade interconnection term below this limit global stabilization is achieved by smooth static state feedback beyond this limit various examples illustrate that controllability of the cascade may be lost making it impossible to achieve large regions of attractions

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

immersion and invariance adaptive control of linear multivariable systems abstract we show in this paper that it is possible to globally adaptively stabilize linear multivariable systems with reduced prior knowledge of the high frequency gain in particular we relax the restrictive nongeneric symmetry condition usually required to solve this problem instrumental for the establishment of our result is the use of the new immersion and invariance approach to adaptive control recently proposed in the literature the controllers obtained with this technique are not certainty equivalent though smooth and without projections or overparameterizations and the resulting lyapunov functions contain cross terms between the plant states and the parameter errors

asymptotic stabilization of minimum phase nonlinear systems how a class of multivariable nonlinear systems can be stabilized about an equilibrium via smooth state feedback is shown more precisely conditions under which for every compact set of initial states it is possible to design a feedback law which drives to the equilibrium all initial states in this compact set are described the theory includes the development of globally defined transformations of the system equations to their global normal form

on the solvability of the regulator equations for a class of nonlinear systems regulator equations arise in studying the output regulation problem for nonlinear systems the solvability of the regulator equations is the necessary condition for that of the output regulation problem it has been shown under various assumptions that the solvability of the regulator equations can be reduced to that of a center manifold equation defined by the zero dynamics of a composite system consisting of the plant and exosystem in this paper we further show that for a quite general class of nonlinear systems the solvability of the regulator equations can be reduced to that of a center manifold equation if the relative degree of the composite system at the origin exists

a mathcal b invariant distributions and disturbance decoupling of nonlinear systems the concept of a b invariant subspaces has resulted in a unified approach to many of the basic structural properties of time invariant linear systems w m wonham lecture notes in economics and mathematical systems vol 101 springer verlag new york 1974 the purpose of this paper is to introduce the more general notion of a mathcal b invariant distributions on differentiable manifolds and to use this idea to study the disturbance decoupling problem for a class of nonlinear systems which evolve on real analytic manifolds

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

output input stability and minimum phase nonlinear systems this paper introduces and studies the notion of output input stability which represents a variant of the minimum phase property for general smooth nonlinear control systems the definition of output input stability does not rely on a particular choice of coordinates in which the system takes a normal form or on the computation of zero dynamics in the spirit of the input to state stability philosophy it requires the state and input of the system to be bounded by a suitable function of the output and derivatives of the output modulo a decaying term depending on initial conditions the class of output input stable systems thus defined includes all affine systems in global normal form whose internal dynamics are input to state stable and also all left invertible linear systems whose transmission zeros have negative real parts as an application we explain how the new concept enables one to develop a natural extension to nonlinear systems of a basic result from linear adaptive control

a modified algorithm for invertibility in nonlinear systems the algorithm of hirschorn 1 for the construction of inverses of nonlinear systems is modified and new sufficient conditions for invertibility and inverse system for a larger class of systems are obtained for the systems which do not satisfy the invertibility conditions a characterization of input space on which the input output map is injective is derived

a polynomial approach to discrete time non linear system controllability this paper uses a polynomial approach to present a necessary and sufficient condition for local controllability of single input single output siso discrete time non linear systems the condition is presented in terms of common factors of a non commutative polynomial expression this extends the result on controllability of linear systems and the recent result on controllability of continuous time non linear systems to expose controllability of discrete time non linear systems in the input output framework the controllability condition yields a finite step computing procedure for examining controllability of discrete time input output non linear systems

a unifying framework for global regulation via nonlinear output feedback from iss to iiss this paper presents a unifying framework for the problem of robust global regulation via output feedback for nonlinear systems with integral input to state stable inverse dynamics subject to possibly unknown control direction the contribution of the paper is two fold firstly we consider the problem of global regulation instead of global asymptotic stabilization gas for systems with generalized dynamic uncertainties it is shown by an elementary example that gas is not solvable using conventional smooth output feedback secondly we reduce the stability requirements for the disturbance and demand relaxed assumptions for the system using our framework most of the known classes of output feedback form systems are broadened in several directions unmeasured states and unknown parameters can appear nonlinearly restrictive matching and growth assumptions are removed the dynamic uncertainty satisfies the weaker condition of sontag s integral input to state stability and the sign of high frequency gain may be unknown a constructive strategy is proposed to design a dynamic output feedback control law that drives the state to the origin while keeping all other closed loop signals bounded