high gain feedback in non linear control systems abstract high gain state and output feedback are investigated for non linear control systems with a single additive input by using singular perturbation techniques classical approximation results tihonov like theorems in singular perturbation theory are extended to non linear control systems by defining a composite additive control strategy a control dependent fast equilibrium manifold and non linear change of coordinates those tools and an appropriate change of coordinates show that high gain state feedback and variable structure control systems can be equivalently used for approximate non linearity compensation in feedback linearizable systems next the effect of high gain output feedback is shown to be related to the strong invertibility property and the relative order of invertibility for strongly invertible systems the slow reduced subsystem coincides with the dynamics of the inverse system when zero input is applied and with the unobservable dynamics when a certain input output feedback linear

controllability on principal fibre bundles with compact structure group abstract in this paper we consider the controllability problem for systems defined on principal fibre bundles in which the set of associated vector fields is invariant under the action of the structure group and projects down on to a set of vector fields on the base space it is shown that if the system is accessible and the structure group is compact then the system is controllable if and only if the system is controllable when projected onto the base space the connection between these systems and systems admitting symmetries generated by free and proper group actions is described and various examples are given relating to systems on homogeneous spaces

differential geometric methods in variable structure control this article presents a differential geometric approach for the design of sliding modes in non linear variable structure feedback systems coordinate free characterizations of local existence conditions for sliding regimes and a geometric reformulation of some of its most salient features are presented the approach uses basic notions from differential geometry involving vector fields distributions and 1 forms both single and multiple input cases are treated with some illustrative examples

a new class of orthonormal symmetric wavelet bases using a complex allpass filter this paper considers the design of the whole sample symmetric wss paraunitary filterbanks composed of a single complex allpass filter and gives a new class of real valued orthonormal symmetric wavelet bases first the conditions that the complex allpass filter has to satisfy are derived from the symmetry and orthonormality conditions of wavelets and its transfer function is given to satisfy these conditions second the paraunitary filter banks are designed by using the derived transfer function from the viewpoints of the regularity and frequency selectivity a new method for designing the proposed paraunitary filterbanks with a given degrees of flatness is presented the proposed method is based on the formulation of a generalized eigenvalue problem by using the remez exchange algorithm therefore the filter coefficients can be easily obtained by solving the eigenvalue problem and the optimal solution is attained through a few iterations furthermore both the maximally flat and minimax solutions are also included in the proposed method as two specific cases the maximally flat filters have a closed form solution without any iteration finally some design examples are presented to demonstrate the effectiveness of the proposed method

mathematical properties of the jpeg2000 wavelet filters the legall 5 3 and daubechies 9 7 filters have risen to special prominence because they were selected for inclusion in the jpeg2000 standard we determine their key mathematical features riesz bounds order of approximation and regularity holder and sobolev we give approximation theoretic quantities such as the asymptotic constant for the l sup 2 error and the angle between the analysis and synthesis spaces which characterizes the loss of performance with respect to an orthogonal projection we also derive new asymptotic error formulae that exhibit bound constants that are proportional to the magnitude of the first nonvanishing moment of the wavelet the daubechies 9 7 stands out because it is very close to orthonormal but this turns out to be slightly detrimental to its asymptotic performance when compared to other wavelets with four vanishing moments

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

quotients of fully nonlinear control systems in this paper we introduce and study quotients of fully nonlinear control systems our definition is inspired by categorical definitions of quotients as well as recent work on abstractions of affine control systems we show that quotients exist under mild regularity assumptions and characterize the structure of the quotient state input space this allows one to understand how states and inputs of the quotient system are related to states and inputs of the original system we also introduce a notion of projectability which turns out to be equivalent to controlled invariance this allows one to regard previous work on symmetries partial symmetries and controlled invariance as leading to special types of quotients we also show the existence of quotients that are not induced by symmetries or controlled invariance such decompositions have a potential use in a theory of hierarchical control based on quotients

approximate reduction of dynamic systems abstract the reduction of dynamic systems has a rich history with many important applications related to stability control and verification reduction of nonlinear systems is typically performed in an exact manner as is the case with mechanical systems with symmetry which unfortunately limits the type of systems to which it can be applied the goal of this paper is to consider a more general form of reduction termed approximate reduction in order to extend the class of systems that can be reduced using notions related to incremental stability we give conditions on when a dynamic system can be projected to a lower dimensional space while providing hard bounds on the induced errors i e when it is behaviourally similar to a dynamic system on a lower dimensional space these concepts are illustrated on a series of examples

model based data assessment for terrestrial carbon processes implications for sampling strategy in face experiments the value of different types of data in the estimation of different carbon transfer parameters is investigated a carbon accounting model is used with different observation operators to generate data the effectiveness of the inversion is assessed by observing relative errors of estimators and likelihood ratios it is demonstrated that for an observation operator that relative errors vary widely with the sample test problems an effective strategy to test types of data is to test the effectiveness of corresponding observation operators on an ensemble of sample problems for which parameters are selected from the space of admissible parameters the selection is carried out under the assumption that the test parameters themselves are random variables uniformly distributed over the space of admissible parameters

optimal control of systems possessing symmetries it is shown that a symmetry in an optimization problem induces a decomposition of the optimal feedback control law into factors one factor can be calculated algebraically and depends only on the symmetry the other factor corresponds to a lower dimensional optimization problem this gives a priori information about the structure of the optimal feedback control law and indicates a possibly more efficient method for optimizing such systems

controllability and observability for affine nonlinear hamiltonian systems it is shown that an affine nonlinear hamiltonian system is controllable if and only if it is observable in the sense that strong accessibility implies local weak observability and vice versa furthermore it is shown that a nonminimal hamiltonian system can be reduced to a locally weakly observable and strongly accessible system in such a way that the reduced system is again hamiltonian

grassmannian central projection and output feedback pole assignment of linear systems a sufficient rank condition for arbitrary pole assignability by static output feedback of m input p output linear systems of mcmillan degree n mp is given this condition is easy to check and is satisfied by the generic system an effective computational method to compute the feedback laws assigning any self conjugate set of closed loop poles is also given

on the representation of operators in bases of compactly supported wavelets this paper describes exact and explicit representations of the differential operators d n dx n n 1 2 cdots in orthonormal bases of compactly supported wavelets as well as the representations of the hilbert transform and fractional derivatives the method of computing these representations is directly applicable to multidimensional convolution operators also sparse representations of shift operators in orthonormal bases of compactly supported wavelets are discussed and a fast algorithm requiring o n log n operations for computing the wavelet coefficients of all n circulant shifts of a vector of the length n 2 n is constructed as an example of an application of this algorithm it is shown that the storage requirements of the fast algorithm for applying the standard form of a pseudodifferential operator to a vector see g beylkin r r coifman and v rokhlin comm pure appl math 44 1991 pp 141 183 may be reduced from o n to o log 2 n significant entries

the structure of nonlinear control systems possessing symmetries a concept of symmetry is defined for general nonlinear control systems it is shown under various technical conditions that nonlinear control systems with symmetries admit local and or global decompositions in terms of lower dimensional subsystems and feedback loops the structure of the individual subsystems is dependent on the structure of the symmetry group for example if the symmetry group is abelian one of the subsystems is a quadrature an additional feature of the decomposition is that the state space dimensions of the subsystems sum to the state space dimension of the original system

estimation of parameters in carbon sequestration models from net ecosystem exchange data the use of net ecosystem exchange nee data to estimate carbon transfer coefficients is investigated in the context of a deterministic compartmental carbon sequestration system sensitivity and approximation properties are investigated for the underlying model initial value problems joint probability distributions are obtained by including nee data along with corresponding synthetic nee values generated from the model and are compared with a priori distributions these distributions are used to estimate individual transfer parameters and to predict future carbon states results are compared with those obtained using only a priori information without the benefit of data shannon information content is introduced to measure the dependence of results on the lengths of observational intervals and provide an additional indicator of the value added by the inclusion of nee data

output regulation of nonlinear systems with nonhyperbolic zero dynamics previous solvability conditions for the output relation of nonlinear systems are applicable only to those with hyperbolic zero dynamics it is shown in this note that output regulation of nonlinear systems with nonhyperbolic zero dynamics is also possible by a reduction of the plant dynamics and an augmentation of the exosystem

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

noncommutative rational functions invariant under the action of a finite solvable group abstract this paper describes the structure of invariant skew fields for linear actions of finite solvable groups on free skew fields in d generators these invariant skew fields are always finitely generated which contrasts with the free algebra case for abelian groups or solvable groups g with a well behaved representation theory it is shown that the invariant skew fields are free on g d 1 1 generators finally positivity certificates for invariant rational functions in terms of sums of squares of invariants are presented

symmetry reduction contact geometry and partial feedback linearization let pfaffian system omega define an intrinsically nonlinear control system which is invariant under a lie group of symmetries g using the contact geometry of brunovsky normal forms and symmetry reduction this paper solves the problem of constructing subsystems alpha subset omega such that alpha defines a static feedback linearizable control system a method for representing the trajectories of omega from those of alpha using reduction by a distinguished class g of lie symmetries is described a control system will often have a number of inequivalent linearizable subsystems depending upon the subgroup structure of g this can be used to obtain a variety of representations of the system trajectories in particular if g is solvable the construction of trajectories can be reduced to quadrature it is shown that the identification of linearizable subsystems in any given problem can be carried out algorithmically once the explicit lie algebra of g is known all the const

conservation of generalized momentum maps in mechanical optimal control problems with symmetry summary in this paper a structure preserving direct method for the optimal control of mechanical systems is developed the new method accommodates a large class of one step integrators for the underlying state equations the state equations under consideration govern the motion of affine hamiltonian control systems if the optimal control problem has symmetry associated generalized momentum maps are conserved along an optimal path this is in accordance with an extension of noether s theorem to the realm of optimal control problems in the present work we focus on optimal control problems with rotational symmetries the newly proposed direct approach is capable of exactly conserving generalized momentum maps associated with rotational symmetries of the optimal control problem this is true for a variety of one step integrators used for the discretization of the state equations examples are the one step theta method a partitioned variant of the theta method and energy momentum em consistent integrators numerical investigations confirm the theoretical findings copyright 2016 john wiley sons ltd

analysis synthesis techniques for subband image coding analysis synthesis systems designed for low bit rate image coding their impact on overall system quality and their computational complexity are discussed the investigation focuses on the design of analysis synthesis systems for image coding and the perceptual impact of these systems at low bit rates two objectives are emphasized in developing these systems confining the total size of the subband images to be equal to the original image size and designing the filters so that perceptual distortion is not introduced by the analysis synthesis system methods based on circular convolution and symmetric extensions are developed and discussed in detail the theory design and implementation of both recursive and nonrecursive filtering systems are discussed methods are introduced which display advantages over conventional quadrature mirror filter based approaches

on controlled invariance in nonlinear systems abstract the notion of generalized controlled invariance gci is introduced to allow for the loss of degrees of freedom in control that may be the necessary price for achieving a desired invariance it is shown that subject to some technical rank restrictions controlled invariance implies gci a sequential procedure that definitively establishes for a given system pair whether is a gci of is introduced and through it a verdict o the solvability of the controlled invariance problem cip is reached

symmetric failures in symmetric control systems abstract this paper discusses the fault tolerance of symmetric systems with respect to controllability which is a fundamental characteristic of control systems in particular we reveal the underlying mathematical mechanism of the loss of controllability for symmetric systems induced by failures based on the decomposition of the symmetric systems into subsystems under the symmetry the controllability of the entire system can be discussed by checking that of each subsystem the analysis of the fault tolerance in this paper is an extension of this idea with the aid of the chain adapted transformation matrix for the decomposition the result is shown as a necessary condition for symmetric systems to retain the controllability despite some symmetric failures we also discuss sufficient conditions

regular wavelets a discrete time approach regularity is a new filter property brought by wavelet theory for perfect reconstruction octave band filter banks tools for investigating its role in coding applications are provided first discrete time interpretations and optimal estimates of regularity are reviewed then a simple design procedure for paraunitary fir filter banks with optimal trade off between frequency selectivity and regularity is given finally the obtained filters are used to measure the effect of regularity versus frequency selectivity in a still image compression scheme with optimized rate distortion in this case regularity is shown to be more relevant than frequency selectivity especially for short filters

symmetry preserving observers this paper presents the theory of invariant observers i e symmetry preserving observers we consider an observer to consist of a copy of the system and a correction term and we propose a constructive method based on the cartan moving frame method to find all the symmetry preserving correction terms the construction relies on an invariant frame a classical notion and on an invariant output error a less standard notion precisely defined here using the theory we build three non linear observers for three examples of engineering interest a non holonomic car a chemical reactor and an inertial navigation system for each example the design is based on physical symmetries and the convergence analysis relies on the use of invariant state errors a symmetry preserving way to define the estimation error

modeling and inversion of net ecological exchange data using an ito stochastic differential equation approach a system of stochastic differential equations is studied describing a compartmental carbon transfer model that includes uncertainties arising in the model from environmental and photosynthetic effects as well as initial conditions justification is given for the modeling of observed times series as weiner processes the solution of the resulting system is obtained as a stochastic process a formulation is given appropriate for obtaining continuity and differentiability with respect to model transfer coefficients and numerical approximation results are given estimation results of coefficients from nee data are obtained using quasi monte carlo techniques the error resulting in nee stochastic models is observed to be approximately gaussian this result is used to construct a joint probability density defined on a sample space of transfer coefficients finally the joint probability density function is used with quasi monte carlo to obtain information on transfer coefficients and predicted carbon pools this information is compared with a priori results obtained without the benefit of nee data

disturbance decoupling by observation feedback for hamiltonian systems in this note we show that if disturbance decoupling by dynamic observation feedback for a linear hamiltonian system is possible it is also possible using a hamiltonian compensator this gives an example of a theory in which we look for solutions of control problems which remain in the same class of systems

reduction of sufficient conditions for optimal control problems with subgroup symmetry in this paper we apply symmetry reduction techniques from geometric mechanics to sufficient conditions for local optimality in optimal control problems after reinterpreting some previous results for left invariant problems on lie groups we focus on optimal control problems with subgroup symmetry for these problems the necessary conditions for optimality can be simplified by exploiting symmetries so as to reduce the number of variables needed to describe trajectories of the system we show that sufficient conditions for optimality based on the non existence of conjugate points can be simplified in an analogous way to the necessary conditions we demonstrate these simplifications by analyzing an optimal control problem that models a spinning top in a gravitational field and we give particular attention to the example of an axisymmetric sleeping top the results we derive in this paper allow us to determine which trajectories of a sleeping top are locally optimal solutions of the optimal control problem which is a new result that has not appeared in previous literature

design of iir digital allpass filters based on eigenvalue problem a new method is proposed for designing iir digital allpass filters with an equiripple phase response that can be proven to be optimal in the chebyshev sense the proposed procedure is based on the formulation of an eigenvalue problem by using the remez exchange algorithm since there exists more than one eigenvalue in the general eigenvalue problem we introduce a new and very simple selection rule for the eigenvalue to be searched for where the rational interpolation is performed if and only if the real maximum eigenvalue is chosen therefore the solution of the rational interpolation problem can be gotten by computing only one eigenvector corresponding to the real maximum eigenvalue and the optimal filter coefficients are easily obtained through a few iterations without any initial guess of the solution the design algorithm proposed not only retains the speed inherent in the remez exchange algorithm but also simplifies the interpolation step because it has been reduced to the computation of the real maximum eigenvalue two examples are designed to demonstrate the effectiveness of this method

reduction and non linear controllability of symmetric distributed systems this paper considers the reduction problem for distributed control systems in particular we consider controllability of systems containing multiple instances of diffeomorphic components where the overall system dynamics is invariant with respect to a discrete group action a subclass of such systems are systems with a set of identical components where the overall system dynamics are invariant with respect to physically interchanging these components the main result is a proposition which shows that for an equivalence class of symmetric systems of this type controllability of the entire class of systems can be determined by analysing the member of the equivalence class with the smallest state space the reduction methods developed are illustrated by considering the controllability of a team of mobile robots and a platoon of underwater vehicles

image coding using wavelet transform a scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed this method involves two steps first a wavelet transform used in order to obtain a set of biorthogonal subclasses of images the original image is decomposed at different scales using a pyramidal algorithm architecture the decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image second according to shannon s rate distortion theory the wavelet coefficients are vector quantized using a multiresolution codebook to encode the wavelet coefficients a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed in order to allow the receiver to recognize a picture as quickly as possible at minimum cost a progressive transmission scheme is presented it is shown that the wavelet transform is particularly well adapted to progressive transmission

a new class of biorthogonal wavelet systems for image transform coding we construct general biorthogonal coifman wavelet systems a new class of compactly supported biorthogonal wavelet systems with vanishing moments equally distributed for a scaling function and wavelet pair a time domain design method is employed and closed form expressions for the impulse responses and the frequency responses of the corresponding dual filters are derived the resulting filter coefficients are all dyadic fractions which is an attractive feature in the realization of multiplication free discrete wavelet transform even ordered systems in this family are symmetric which correspond to linear phase dual filters in particular three filterbanks fbs in this family are systematically verified to have competitive compression potential to the 9 7 tap biorthogonal wavelet fb by cohen et al 1992 which is currently the most widely used one in the field of wavelet transform coding in addition the proposed fb s have much smaller computational complexity in terms of floating point operations required in transformation and therefore indicate a better tradeoff between compression performance and computational complexity

wavelets and recursive filter banks it is shown that infinite impulse response iir filters lead to more general wavelets of infinite support than finite impulse response fir filters a complete constructive method that yields all orthogonal two channel filter banks where the filters have rational transfer functions is given and it is shown how these can be used to generate orthonormal wavelet bases a family of orthonormal wavelets that have a maximum number of disappearing moments is shown to be generated by the halfband butterworth filters when there is an odd number of zeros at pi it is shown that closed forms for the filters are available without need for factorization a still larger class of orthonormal wavelet bases having the same moment properties and containing the daubechies and butterworth filters as the limiting cases is presented it is shown that it is possible to have both linear phase and orthogonality in the infinite impulse response case and a constructive method is given it is also shown how compactly supported bases may be orthogonalized and bases for the spline function spaces are constructed

on decomposition of nonlinear control systems in this paper the problem is studied when the system x i k 1 u t g t x x 0 x 0 defined on an n dimensional analytic manifold can be decomposed into either independent subsystems or a cascade of subsystems necessary and sufficient conditions for the existence of such local decompositions are given in terms of lie algebras generated by the system

representing a nonlinear state space system as a set of higher order differential equations in the inputs and outputs an algorithm is presented for transforming a nonlinear state space system into a threefold set of equations the first subset describing the dynamics of the unobservable part of the system the second subset representing the remaining state variables as functions of inputs and outputs and their derivatives and the last subset defining the external behaviour of the system

synchronisation of complex dynamical networks with different dynamics of nodes via decentralised dynamical compensation controllers this paper investigates the synchronisation of nonlinear coupled complex dynamical networks with different nonlinear nodes and different orders by using decentralised dynamical compensation controllers we propose a dynamical network mathematical model with similar nonlinear nodes whose dimensions are different for this kind of network model the decentralised dynamical compensation controllers are designed for the state synchronisation of the coupled nodes in addition the synchronisation manifold is defined as an invariant manifold which is regarded as the generalised case of dynamical networks with the same nodes dynamics furthermore some stability criteria for the synchronisation are derived by means of rigorous theoretical analysis finally numerical examples are presented to verify the effectiveness of the obtained theoretical results

conservation laws in hamiitonian control systems under unmodelled dynamics utilisation pour la definition des lois de conservation de commande d un concept plus general qui comprend la consideration des quantites a la fois conservees et non conservees etude de l influence des dynamiques lineaires non modelisees sur les lois de conservation

almost disturbance decoupling with global asymptotic stability for nonlinear systems with disturbance affected unstable zero dynamics the problem of global almost disturbance decoupling problem with stability for nonlinear system is revisited and is shown to be solvable for a class of nonlinear systems whose zero dynamics contains a chain of integrators affected by disturbance this result complements some recent work on the topic where unstable zero dynamics is not allowed to be affected by the disturbances

controlled invariance for nonlinear systems necessary and sufficient conditions are derived for a b invariance called here controlled invariance for nonlinear systems dot x f x u the obtained results generalize and elucidate already known results about systems dot x a x sum min i 1 max m u i b i x a new and direct differential geometric interpretation of the concept of controlled invariance and the derived conditions is given

nonlinearizable single input control systems do not admit stationary symmetries the main result of the paper states that almost any analytic single input control system which is truly nonlinear that is not feedback linearizable with controllable linearization at an equilibrium point does not admit any symmetry preserving that point by almost any system we mean that we exclude a small class of odd systems that admit just one nontrivial symmetry conjugated to minus identity the obtained results are based on a recent classification of nonlinear single input systems under formal feedback we also describe symmetries of feedback linearizable systems

abstractions of hamiltonian control systems given a control system and a desired property an abstracted system is a reduced system that preserves the property of interest while ignoring modeling detail in previous work abstractions of linear and nonlinear control systems were considered while preserving reachability properties in this paper we consider the abstraction problem for hamiltonian control systems where in addition to the property of interest we also preserve the hamiltonian structure of the control system we show how the hamiltonian structure of control systems can be exploited to simplify the abstraction process we then focus on local accessibility preserving abstractions and provide conditions under which local accessibility properties of the abstracted hamiltonian system are equivalent to the local accessibility properties of the original hamiltonian control system

linear convergence of comparison based step size adaptive randomized search via stability of markov chains in this paper we consider emph comparison based adaptive stochastic algorithms for solving numerical optimisation problems we consider a specific subclass of algorithms called cprs cb sars where the state variables at a given iteration are a vector of the search space and a positive parameter the step size typically controlling the overall standard deviation of the underlying search distribution we investigate the emph linear convergence of cb sars on emph scaling invariant objective functions scaling invariant functions preserve the ordering of points with respect to their function value when the points are scaled with the same positive parameter the scaling is done w r t a fixed reference point this class of functions includes norms composed with strictly increasing functions as well as many emph non quasi convex and emph non continuous functions on scaling invariant functions we show the existence of a homogeneous markov chain as a consequence of natural invariance properties of cb sars essentially scale invariance and invariance to strictly increasing transformation of the objective function we then derive sufficient conditions for emph global linear convergence of cb sars expressed in terms of different stability conditions of the normalised homogeneous markov chain irreducibility positivity harris recurrence geometric ergodicity and thus define a general methodology for proving global linear convergence of cb sars algorithms on scaling invariant functions as a by product we provide a connexion between emph comparison based adaptive stochastic algorithms and markov chain monte carlo algorithms

the analysis of zero dynamics of nonlinear control systems with symmetries zero dynamics of nonlinear control systems with symmetries are studied in this paper it is shown that the zero dynamics of a symmetric system is also symmetric and admits a special form of cascade decomposition a local zero dynamics is always possible to be extended to the semiglobal case the relation between the zero dynamics and the quotient system is also discussed

a design method of multidimensional linear phase paraunitary filter banks with a lattice structure a lattice structure of multidimensional md linear phase paraunitary filter banks lppufbs is proposed which makes it possible to design such systems in a systematic manner our proposed structure can produce md lppufbs whose filters all have the region of support spl nscr m spl xi where m and spl xi are the decimation and positive integer diagonal matrices respectively and spl nscr n denotes the set of integer vectors in the fundamental parallelepiped of a matrix n it is shown that if spl nscr m is reflection invariant with respect to some center then the reflection invariance of spl nscr m spl xi is guaranteed this fact is important in constructing md linear phase filter banks because the reflection invariance is necessary for any linear phase filter since our proposed system structurally restricts both the paraunitary and linear phase properties an unconstrained optimization process can be used to design md lppufbs our proposed structure is developed for both an even and an odd number of channels and includes the conventional 1 d system as a special case it is also shown to be minimal and the no dc leakage condition is presented some design examples show the significance of our proposed structure for both the rectangular and nonrectangular decimation cases

global robust stabilization of minimum phase nonlinear systems with uncertainty the problem of global stabilization via state feedback is studied for a class of minimum phase nonlinear systems with unknown unmodelled time varying parameters or disturbances belonging to a given compact set sufficient conditions are presented for the existence of a robust stabilizing state feedback controller the controller is constructed explicitly by using a lyapunov based recursive design procedure the proposed feedback control law is a smooth function of the state and requires information of bounding functions on the size of uncertainties in the case where the disturbance signals represent only an unknown constant vector parameter and appear linearly in the system an adaptive controller is developed based on similar arguments achieving global stability with state regulation the main results of this paper incorporate and generalize a number of robust and adaptive control schemes for global stabilization of uncertain feedback linearizable systems without zero dynamics

controllability of poisson systems sufficient conditions for the controllability of affine nonlinear control systems on poisson manifolds are given the important special case when the poisson manifold is the reduced space of a symplectic manifold by a free lie group action is studied the controllability of the reduced system is linked to that of the given affine nonlinear system several examples illustrating the theory are also presented

design of almost symmetric orthogonal wavelet filter bank via direct optimization it is a well known fact that compact support dyadic wavelets based on the two channel filter banks fbs cannot be simultaneously orthogonal and symmetric although orthogonal wavelets have the energy preservation property biorthogonal wavelets are preferred in image processing applications because of their symmetric property in this paper a novel method is presented for the design of almost symmetric orthogonal wavelet fb orthogonality is structurally imposed by using the unnormalized lattice structure and this leads to an objective function which is relatively simple to optimize the designed filters have good frequency response flat group delay almost symmetric filter coefficients and symmetric wavelet function

symmetries conservation laws and time reversibility for hamiltonian systems with external forces a system theoretic framework is given for the description of hamiltonian systems with external forces and partial observations of the state it is shown how symmetries and conservation laws can be defined within this framework a generalization of noether s theorem is obtained finally a precise definition of time reversibility is given and its consequences are explored

symmetry reduction of optimal control systems and principal connections this paper explores the role of symmetries and reduction in nonlinear control and optimal control systems the focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to obtain explicit expressions of the reduced system by exploiting the geometry in particular we show how to obtain a principal connection to be used in the reduction for various choices of symmetry groups as opposed to assuming such a principal connection is given or choosing a particular symmetry group to simplify the setting our result synthesizes some previous works on symmetry reduction of nonlinear control and optimal control systems affine and kinematic optimal control systems are of particular interest we explicitly work out the details for such systems and also show a few examples of symmetry reduction of kinematic optimal control problems

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

cascade decomposition of nonlinear systems foliations and ideals of transitive lie algebras abstract we relate the cascade decomposition of nonlinear systems to the joint notions of foliations and ideals of transitive lie algebras

stabilization of nonlinear systems via designed center manifold this paper addresses the problem of local state feedback stabilization of a class of nonlinear systems with nonminimum phase zero dynamics a new technique namely the lyapunov function with homogeneous derivative along solution curves was developed to test the approximate stability of the dynamics on the center manifold a set of convenient sufficient conditions are provided to test the negativity of the homogeneous derivatives using these conditions and assuming the zero dynamics has stable and center linear parts a method is proposed to design controls such that the dynamics on the designed center manifold of the closed loop system is approximately stable it is proved that using this method the first variables in each of the integral chains of the linearized part of the system do not affect the approximation order of the dynamics on the center manifold based on this fact the concept of injection degree is proposed according to different kinds of injection degrees certain sufficient conditions are obtained for the stabilizability of the nonminimum phase zero dynamics corresponding formulas are presented for the design of controls

bounded tracking for non minimum phase nonlinear systems with fast zero dynamics in this paper we derive tracking control laws for non minimum phase nonlinear systems with both fast and slow possibly unstable zero dynamics the fast zero dynamics arise from a perturbation of a nominal system these fast zeros can be problematic in that they may be in the right half plane and may cause large magnitude tracking control inputs in this paper we combine the ideas from some recent work of hunt meyer and su with that of devasia chen and paden on an asymptotic tracking procedure for non minimum phase nonlinear systems we give somewhat subtle conditions under which the tracking control input is bounded as the magnitude of the perturbation of the nominal system becomes zero explicit bounds on the control inputs are calculated for both siso and mimo systems using some interesting non standard singular perturbation techniques the method is applied to a suite of examples including the simplified planar dynamics of vtol and ctol aircraft

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

two dimensional orthogonal filter banks and wavelets with linear phase two dimensional 2 d compactly supported orthogonal wavelets and filter banks having linear phase are presented two cases are discussed wavelets with two fold symmetry centrosymmetric and wavelets with four fold symmetry that are symmetric or anti symmetric about the vertical and horizontal axes we show that imposing the requirement of linear phase in the case of order factorable wavelets imposes a simple constraint on each of its polynomial order 1 factors we thus obtain a simple and complete method of constructing orthogonal order factorable wavelets with linear phase this method is exemplified by design in the case of four band separable sampling an interesting result that is similar to the one well known in the one dimensional 1 d case is obtained orthogonal order factorable wavelets cannot be both continuous and have four fold symmetry

approximation power of biorthogonal wavelet expansions this paper looks at the effect of the number of vanishing moments on the approximation power of wavelet expansions the strang fix conditions imply that the error for an orthogonal wavelet approximation at scale a 2 sup i globally decays as a sup n where n is the order of the transform this is why for a given number of scales higher order wavelet transforms usually result in better signal approximations we prove that this result carries over for the general biorthogonal case and that the rate of decay of the error is determined by the order properties of the synthesis scaling function alone we also derive asymptotic error formulas and show that biorthogonal wavelet transforms are equivalent to their corresponding orthogonal projector as the scale goes to zero these results strengthen sweldens earlier analysis and confirm that the approximation power of biorthogonal and semi orthogonal wavelet expansions is essentially the same finally we compare the asymptotic performance of various wavelet transforms and briefly discuss the advantages of splines we also indicate how the smoothness of the basis functions is beneficial in reducing the approximation error

numerical treatment of stochastic differential equations we define general runge kutta approximations for the solution of stochastic differential equations sde these approximations are proved to converge in quadratic mean to the solution of an sde with a corrected drift the explicit form of the correction term is given concerning the order of convergence we show that in general it is impossible for the quadratic mean of the one step error to be of an order greater than o h 3 this order is attained e g by the stochastic analogue of heun s method in the n dimensional case the highest order of convergence is in general only o h 2 attained by euler s method the order o h 3 can only be reached if nabla x sigma r sigma s nabla x sigma s sigma r for the diffusion matrix

coiflet systems and zero moments the coifman wavelets created by daubechies 1992 have more zero moments than imposed by specifications this results in systems with approximately equal numbers of zero scaling function and wavelet moments and gives a partitioning of the systems into three well defined classes the nonunique solutions are more complex than for daubechies wavelets

wavelet filter evaluation for image compression choice of filter bank in wavelet compression is a critical issue that affects image quality as well as system design although regularity is sometimes used in filter evaluation its success at predicting compression performance is only partial a more reliable evaluation can be obtained by considering an l level synthesis analysis system as a single input single output linear shift variant system with a response that varies according to the input location module 2 sup l 2 sup l by characterizing a filter bank according to its impulse response and step response in addition to regularity we obtain reliable and relevant for image coding filter evaluation metrics using this approach we have evaluated all possible reasonably short less than 36 taps in the synthesis analysis pair minimum order biorthogonal wavelet filter banks of this group of over 4300 candidate filter banks we have selected and present here the filters best suited to image compression while some of these filters have been published previously others are new and have properties that make them attractive in system design

formulas for orthogonal iir wavelet filters explicit solutions are given for the rational function p z for two classes of iir orthogonal two band wavelet bases for which the scaling filter is maximally flat p z denotes the rational transfer function h z h 1 z where h z is the lowpass scaling filter the first is the class of solutions that are intermediate between the daubechies 1992 and the butterworth wavelets it is found that the daubechies the butterworth and the intermediate solutions are unified by a single formula the second is the class of scaling filters realizable as a parallel sum of two allpass filters a particular case of which yields the class of symmetric iir orthogonal wavelet bases for this class a closed form solution is provided by the solution to an older problem in group delay approximation by digital allpole filters

symmetries and conservation laws for hamiltonian systems with inputs and outputs a generalization of noether s theorem the definition of symmetries and conservation laws for autonomous i e without external cases hamiltonian systems are generalized to hamiltonian systems with inputs and outputs it is shown that a symmetry implies the existence of a conservation law and vice versa thereby generalizing noether s theorem for autonomous hamiltonian systems

symmetric systems structure of the state space it is shown that every module of every finite dimensional associative algebra is associated with the state space of some class of symmetric systems the general structure of symmetric systems is investigated

stabilization of minimum phase nonlinear systems by dynamic output feedback in this paper the stabilization problem of minimum phase nonlinear systems by dynamic output feedback is investigated it is shown that if the zero dynamics of an affine nonlinear system is asymptotically stable according to the kth approximation then the system is stabilizable by dynamic output feedback the proof is constructive which provides a method to design the stabilizer the result is applied to investigating the stabilization problem of the rotating stall in axial flow compressors

large scale dissipative and passive control systems and the role of star and cyclic symmetries in this technical note symmetries in large scale dissipative and passive control systems are considered in the framework of dissipativity and passivity theory stability conditions for large scale systems are derived by categorizing agents into symmetry groups and applying local control laws under limited interconnections with neighbors building upon previous studies on stability of q s r dissipative large scale systems we show that for cyclic and star shaped symmetric systems there exists an upper bound on the number of subsystems that can be added to preserve stability of dissipative systems in cyclic and star shaped symmetric systems the subsystems can be heterogeneous as long as they satisfy the same dissipative inequalities approximate symmetry with respect to interconnections is also considered and the robustness of the results is demonstrated

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

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

bisimilar control affine systems the notion of bisimulation plays a very important role in theoretical computer science where it provides several notions of equivalence between models of computation these equivalences are in turn used to simplify verification and synthesis for these models as well as to enable compositional reasoning in systems theory a similar notion is also of interest in order to develop modular verification and design tools for purely continuous or hybrid control systems in this paper we introduce two notions of bisimulation for nonlinear systems we present differential geometric characterizations of these notions and show that bisimilar systems of different dimensions are obtained by factoring out certain invariant distributions furthermore we also show that all bisimilar systems of different dimension are of this form

stabilization of hamiltonian systems 1 hamiltonian systems in this paper we will be concerned with the stabilization by feedback of hamiltonian systems in order to facilitate our discussions especially when applying lyapunov s second method we will restrict ourselves to a particular although natural subclass of hamiltonian systems given in the following way l let q be an n dimensional smooth manifold denoting the configuration space and let t q be the cotangent bundle denoting the phase space or srufe space furthermore there is a smooth m dimensional output manifold y m n and a smooth output map c q y smooth will mean c or ck with k sufficiently big although we shall restrict ourselves in the second part of section 2 to analytic data for simplicity we take c to be submersive so rank dc q m we assume that the system on t q has an internal energy which is the sum of a kinetic energy k and a porentiul energy v this means that there exists a riemannian metric on q in local coordinates q q j for q given by

stabilization via dynamic output feedback for systems with output nonlinearities abstract the problem of asmptotically stabilizing a class of systems by means of continuous output feedback is considered these systems are characterized by nonlinear terms depending only on the ouputs it is shown that for these systems stabilization via continuous state feedback plus stabilization via output injection imply stabilization via continuous dynamic output feedback this generalizes a well knwon result for linear systems

minimum phase properties for input nonaffine nonlinear systems for input nonaffine nonlinear control systems the minimum phase property of the system in general depends on the control law switching or discontinuous controllers may offer advantages in this context in particular there may not exist a continuous control law which would keep the output identically equal to zero and for which the zero output constrained dynamics are locally stable whereas a discontinuous controller which achieves this exists for single input single output input nonaffine nonlinear systems we give sufficient conditions for existence and present a method for the design of discontinuous switching controllers which yield locally stable zero dynamics

on static output feedback stabilization of systems with stable generalized zero dynamics in this note we define generalized zero dynamics introduce a generalized zero dynamics algorithm and give a sufficient condition which ensures stabilizability of linear systems with asymptotically stable generalized zero dynamics by static output feedback

optimal planar turns under acceleration constraints this technical note considers the problem of finding optimal trajectories for a particle moving in a 2 d plane from a given initial position and velocity to a specified terminal heading under a magnitude constraint on the acceleration the cost functional to be minimized is the integral over time of a non negative power of the particle s speed special cases of such a cost functional include travel time and path length unlike previous work on related problems variations in the magnitude of the velocity vector are allowed pontryagin s maximum principle is used to show that the optimal paths possess a special property whereby the vector that divides the velocity and acceleration vectors in a specific ratio which depends on the cost functional is a constant this property is used to characterize the optimal acceleration vector and obtain the parametric equations of the corresponding optimal paths sufficiency conditions for optimality are used to show that trajectories satisfying the necessary conditions are actually optimal if the heading change required is sufficiently small solutions of the time optimal and the length optimal problems are obtained as special cases of the general problem

non linear symmetry preserving observers on lie groups in this technical note we give a geometrical framework for the design of observers on finite dimensional lie groups for systems which possess some specific symmetries the design and the error between true and estimated state equation are explicit and intrinsic we consider also a particular case left invariant systems on lie groups with right equivariant output the theory yields a class of observers such that the error equation is autonomous the observers converge locally around any trajectory and the global behavior is independent from the trajectory which is reminiscent of the linear stationary case

estimation of carbon transfer coefficients using duke forest free air co2 enrichment data a compartmental carbon model is presented in which there are parameters quantifying the transfer between various carbon pools these parameters are estimated using two co 2 data sets elevated and ambient from the duke forest face data set a quadratic objective criterion is used to compare closeness of fit of system output co 2 flux to the observed co 2 flux data adjoint equations are developed based on the system of difference equations approximating the solution of the model equations the data and the criterion parameter estimation algorithms are developed using minimization techniques it is found that the estimated parameters obtained using the two different data sets agree closely