on the connection between controllability and stabilizability of linear systems with structural uncertain parameters abstract in this paper we investigate the problem of robust stabilization of interval systems by state feedback it is shown under certain conditions that robust stabilizability is equivalent to controllability invariance

variational adaptive correlation method for flow estimation a variational approach is presented to the estimation of turbulent fluid flow from particle image sequences in experimental fluid mechanics the approach comprises two coupled optimizations for adapting size and shape of a gaussian correlation window at each location and for estimating the flow respectively the method copes with a wide range of particle densities and image noise levels without any data specific parameter tuning based on a careful implementation of a multiscale nonlinear optimization technique we demonstrate robustness of the solution over typical experimental scenarios and highest estimation accuracy for an international benchmark data set piv challenge

robust stabilization of linear systems with norm bounded time varying uncertainty abstract in this paper robust stabilization of a class of linear systems with norm bounded time varying uncertainties is considered it is shown that for this class of uncertain systems quadratic stabilizability via linear control is equivalent to the existence of a positive definite symmetric matrix solution to a parameter dependent riccati equation also a construction for the stabilizing feedback law is given in terms of the solution to the riccati equation

bellman inequality for hilbert space operators abstract we establish some operator versions of bellman s inequality in particular we prove that if b h b k is a unital positive linear map a b b h are contractions p 1 and 0 1 then i h a b 1 p i h a 1 p i h b 1 p

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

bayesian and regularization methods for hyperparameter estimation in image restoration in this paper we propose the application of the hierarchical bayesian paradigm to the image restoration problem we derive expressions for the iterative evaluation of the two hyperparameters applying the evidence and maximum a posteriori map analysis within the hierarchical bayesian paradigm we show analytically that the analysis provided by the evidence approach is more realistic and appropriate than the map approach for the image restoration problem we furthermore study the relationship between the evidence and an iterative approach resulting from the set theoretic regularization approach for estimating the two hyperparameters or their ratio defined as the regularization parameter finally the proposed algorithms are tested experimentally

on ultimate boundedness control of uncertain systems in the absence of matching assumptions this paper describes an approach to ultimate boundedness control under hypotheses less stringent than heretofore required instead of imposing the so called matching conditions of previous authors a certain decomposition of the dynamics is performed the resulting decomposed system has two parts a matched portion and a mismatched portion a certain measure of mismatch m is defined and it is shown that effective control is possible as long as m does not exceed some critical mismatch threshold m it is seen that this threshold depends on the choice of feedback hence it becomes possible to investigate the tradeoffs between the size of the mismatch threshold and the sizes of the feedback gains which achieve the desired ultimate boundedness of solutions

refinements of aczel and bellman s inequalities in this paper we establish some new generalizations of aczel s inequality and of bellman s inequality we will conclude by presenting some refinements of these inequalities

quadratic stabilizability of a new class of linear systems with structural independent time varying uncertainty this paper investigates the problem of designing a linear state feedback control to stabilize a new class of single input uncertain linear dynamical systems uncertain parameters in the system matrices are time varying and bounded in given compact sets we first provide a concept called new standard system where some of the entries are required to be negative sign invariant and sign invariant and each entry varies independently in an arbitrarily large range then for a class of new standard systems we derive a necessary and sufficient condition under which a system can be quadratically stabilized by a linear control for all admissible variations of uncertainties the result extends the main result in wei 1990 ieee transactions on automatic control 35 3 268 277

refinements of generalized aczel popoviciu s inequality and bellman s inequality in this paper using the method of diaz barrero et al 2008 j l diaz barrero m grau sanchez p g popescu refinements of aczel popoviciu and bellman s inequalities comput math appl 56 2008 2356 2359 refinements of generalized aczel popoviciu s inequality and generalized bellman s inequalities are established as applications some integral inequalities are given

convex half quadratic criteria and interacting auxiliary variables for image restoration this paper deals with convex half quadratic criteria and associated minimization algorithms for the purpose of image restoration it brings a number of original elements within a unified mathematical presentation based on convex duality firstly the geman and yang 1995 and geman and reynolds 1992 constructions are revisited with a view to establishing the convexity properties of the resulting half quadratic augmented criteria when the original nonquadratic criterion is already convex secondly a family of convex gibbsian energies that incorporate interacting auxiliary variables is revealed as a potentially fruitful extension of the geman and reynolds construction

dense estimation of fluid flows in this paper we address the problem of estimating and analyzing the motion of fluids in image sequences due to the great deal of spatial and temporal distortions that intensity patterns exhibit in images of fluids the standard techniques from computer vision originally designed for quasi rigid motions with stable salient features are not well adapted in this context we thus investigate a dedicated minimization based motion estimator the cost function to be minimized includes a novel data term relying on an integrated version of the continuity equation of fluid mechanics which is compatible with large displacements this term is associated with an original second order div curl regularization which prevents the washing out of the salient vorticity and divergence structures the performance of the resulting fluid flow estimator is demonstrated on meteorological satellite images in addition we show how the sequences of dense motion fields we estimate can be reliably used to reconstruct trajectories and to extract the regions of high vorticity and divergence

quadratic stabilizability of multi input linear systems with structural independent time varying uncertainties this paper investigates the problem of designing a linear state feedback control to stabilize a class of multi input linear dynamical systems we first show that to ensure a stabilizable system some entries of the system matrices must be sign invariant we then derive a sufficient condition under which a system can he quadratically stabilized by a linear control

constrained restoration and the recovery of discontinuities the linear image restoration problem is to recover an original brightness distribution x sup 0 given the blurred and noisy observations y kx sup 0 b where k and b represent the point spread function and measurement error respectively this problem is typical of ill conditioned inverse problems that frequently arise in low level computer vision a conventional method to stabilize the problem is to introduce a priori constraints on x sup 0 and design a cost functional h x over images x which is a weighted average of the prior constraints regularization term and posterior constraints data term the reconstruction is then the image x which minimizes h a prominent weakness in this approach especially with quadratic type stabilizers is the difficulty in recovering discontinuities the authors therefore examine prior smoothness constraints of a different form which permit the recovery of discontinuities without introducing auxiliary variables for marking the location of jumps and suspending the constraints in their vicinity in this sense discontinuities are addressed implicitly rather than explicitly

quadratic stabilizability of linear systems with structural independent time varying uncertainties the author investigates the problem of designing a linear state feedback control to stabilize a class of single input uncertain linear dynamical systems the systems under consideration contain time varying uncertain parameters whose values are unknown but bounded in given compact sets the method used to establish asymptotical stability of the closed loop system obtained when the feedback control is applied involves the use of a quadratic lyapunov function the author first shows that to ensure a stabilizable system some entries of the system matrices must be sign invariant he then derives necessary and sufficient conditions under which a system can be quadratically stabilized by a linear control for all admissible variations of uncertainties the conditions show that all uncertainties can only enter the system matrices in such a way as to form a particular geometrical pattern called an antisymmetric stepwise configuration for the systems satisfying the stabilizability conditions a computational control design procedure is also provided and illustrated via an example

video extrapolation method based on time varying energy optimization and cip video extrapolation prediction methods are often used to synthesize new videos from images for fluid like images and dynamic textures as well as moving rigid objects most state of the art video extrapolation methods use non physics based models that learn orthogonal bases from a number of images but at high computation cost unfortunately data truncation can cause image degradation i e blur artifact and insufficient motion changes to extrapolate videos that more strictly follow physical rules this paper proposes a physics based method that needs only a few images and is truncation free we utilize physics based equations with image intensity and velocity optical flow navier stokes continuity and advection equations these allow us to use partial difference equations to deal with the local image feature changes image degradation during extrapolation is minimized by updating model parameters where a novel time varying energy balancer model that uses energy based image features i e texture velocity and edge moreover the advection equation is discretized by high order constrained interpolation profile for lower quantization error than can be achieved by the previous finite difference method in long term videos experiments show that the proposed energy based video extrapolation method outperforms the state of the art video extrapolation methods in terms of image quality and computation cost

quadratic stability and stabilization of dynamic interval systems this note presents necessary and sufficient conditions for the quadratic stability and stabilization of dynamic interval systems the results are obtained in terms of linear matrix inequalities lmis and extended to the quadratic stability and stabilization of linear systems with uncertain parameters with the powerful lmi toolbox it is very convenient to solve these problems the illustrative examples show that this method is effective and less conservative to check the robust stability and to design the stabilizing controller for dynamic interval systems

refinements of aczel popoviciu and bellman s inequalities in this paper splitting finite sums refinements of the inequalities of aczel popoviciu and bellman are obtained

paper linear ultimate boundedness control of uncertain dynamical systems given a state equation whose description includes uncertain parameters it is often desirable to design a feedback controller which renders all solutions uniformly and ultimately bounded when facing such a problem one often has available or assumes an upper bound for the excursions of the uncertain parameters within this framework the objective is to guarantee no matter how nature selects the uncertainty that the state will eventually end up and remain within some pre specified region when this region is a small neighborhood about the origin the concept of uniform ultimate boundedness is tantamount to practical asymptotic stability the objectives of this paper are twofold first and foremost our goal is to show that a class of ultimate boundedness problems which have been solved to date via nonlinear control can in point of fact be solved via linear control this is the main result and is given in theorem 4 1 secondly we show that some of the so called matching assumptions which have been required in the earlier literature can be weakened somewhat this enables one to design controllers for a larger class of dynamical systems than previously considered

a pole placement design approach for systems with multiple operating conditions the author proposes design procedures based on state space pole placement techniques for systems with multiple operating conditions this is the so called simultaneous pole placement problem first the full state feedback problem is studied in which a nonlinear local pole placement solution is proposed the design condition is formulated in terms of the rank condition of a multimode controllability matrix then the output feedback problem is approached using a multimodel controller design which is an extension of the observer design to multimode systems the design is decomposed into separated global pole placement subproblems and a local pole placement subproblem for a system with some operating conditions having modes on the j omega axis but no modes at the origin in the open right half of the complex plane stabilizability and detectability conditions for the design of an asymptotically stabilizing control are established without any restriction on the number of inputs or outputs relations of this approach to other simultaneous control design approaches are pointed out

divergence free wavelets and high order regularization expanding on a wavelet basis the solution of an inverse problem provides several advantages first of all wavelet bases yield a natural and efficient multiresolution analysis which allows defining clear optimization strategies on nested subspaces of the solution space besides the continuous representation of the solution with wavelets enables analytical calculation of regularization integrals over the spatial domain by choosing differentiable wavelets accurate high order derivative regularizers can be efficiently designed via the basis s mass and stiffness matrices more importantly differential constraints on vector solutions such as the divergence free constraint in physics can be nicely handled with biorthogonal wavelet bases this paper illustrates these advantages in the particular case of fluid flow motion estimation numerical results on synthetic and real images of incompressible turbulence show that divergence free wavelets and high order regularizers are particularly relevant in this context

motion estimation for dynamic texture videos based on locally and globally varying models motion estimation i e optical flow of fluid like and dynamic texture dt images videos is an important challenge particularly for understanding outdoor scene changes created by objects and or natural phenomena most optical flow models use smoothness based constraints using terms such as fluidity from the fluid dynamics framework with constraints typically being incompressibility and low reynolds numbers re such constraints are assumed to impede the clear capture of locally abrupt image intensity and motion changes i e discontinuities and or high re over time this paper exploits novel physics based optical flow models constraints for both smooth and discontinuous changes using a wave generation theory that imposes no constraint on re or compressibility of an image sequence iterated two step optimization between local and global optimization is also used first an objective function with varying multiple sine cosine bases with new local image properties i e orientation and frequency and with a novel transformed dispersion relationship equation are used second the statistical property of image features is used to globally optimize model parameters experiments on synthetic and real dt image sequences with smooth and discontinuous motions demonstrate that the proposed locally and globally varying models outperform the previous optical flow models

stabilization of linear time invariant interval systems via constant state feedback control this paper investigates the stabilization problem of linear uncertain systems via constant state feedback control the systems under consideration contain time invariant uncertain parameters whose values are unknown but bounded in given compact sets and are thus called interval systems the criterion for the asymptotic stability of the closed loop system obtained when a state feedback control is applied is that all the eigenvalues of the resulting system matrix are in the strict left half of the complex plane first the author shows that to insure an interval system stabilizable some entries of the system matrices must be sign invariant more precisely the number of the least required sign invariant entries in system matrices is equal to the system order then the author studies the stabilizability of a set of interval systems called standard systems which contain sufficient numbers of sign invariant entries in proper locations after dividing all standard systems into some subsets by the uncertainty locations the author then derives necessary and sufficient conditions under which every system in a subset is stabilizable regardless of its parameter varying bounds the conditions show that all uncertain entries in system matrices should form a particular geometrical pattern called a generalized antisymmetric stepwise configuration for an interval system satisfying the stabilizability conditions a computational control design procedure is also provided and illustrated via an example the result is further generalized for nonstandard systems via linear transformation

bayesian estimation of turbulent motion based on physical laws describing the multiscale structure of turbulent flows this paper proposes a regularizer for fluid motion estimation from an image sequence regularization is achieved by imposing some scale invariance property between histograms of motion increments computed at different scales by reformulating this problem from a bayesian perspective an algorithm is proposed to jointly estimate motion regularization hyperparameters and to select the most likely physical prior among a set of models hyperparameter and model inference are conducted by posterior maximization obtained by marginalizing out non gaussian motion variables the bayesian estimator is assessed on several image sequences depicting synthetic and real turbulent fluid flows results obtained with the proposed approach exceed the state of the art results in fluid flow estimation

bayesian inference of models and hyperparameters for robust optical flow estimation selecting optimal models and hyperparameters is crucial for accurate optical flow estimation this paper provides a solution to the problem in a generic bayesian framework the method is based on a conditional model linking the image intensity function the unknown velocity field hyperparameters and the prior and likelihood motion models inference is performed on each of the three levels of this so defined hierarchical model by maximization of marginalized a posteriori probability distribution functions in particular the first level is used to achieve motion estimation in a classical a posteriori scheme by marginalizing out the motion variable the second level enables to infer regularization coefficients and hyperparameters of non gaussian m estimators commonly used in robust statistics the last level of the hierarchy is used for selection of the likelihood and prior motion models conditioned to the image data the method is evaluated on image sequences of fluid flows and from the middlebury database experiments prove that applying the proposed inference strategy yields better results than manually tuning smoothing parameters or discontinuity preserving cost functions of the state of the art methods

on stabilization of a new class of linear time invariant interval systems via constant state feedback control the paper is concerned with stabilization problem of a new class of linear time invariant uncertain systems via linear state feedback control we derive a necessary and sufficient condition that extends a previous result in terms of system form

structural stabilization of uncertain systems necessity of the matching condition this paper investigates one aspect of the problem of stabilizing an uncertain linear system that is the systems under consideration contain uncertain parameters which are unknown but bounded the question arises as to whether such a system can be stabilized via feedback control in some of the previous papers in this area the system is assumed to satisfy a so called matching condition this type of assumption is used to assure that the uncertain system can be stabilized it is known however that the matching condition is not a necessary condition for stabilizability this paper introduces a strengthened notion of stabilizability referred to as structural stabilizability via a nominally determined quadratic lyapunov function it is then shown that if a system is to have this stronger property the matching condition must necessarily be satisfied

delay dependent stabilization of stochastic interval delay systems with nonlinear disturbances in this paper a delay dependent approach is developed to deal with the robust stabilization problem for a class of stochastic time delay interval systems with nonlinear disturbances the system matrices are assumed to be uncertain within given intervals the time delays appear in both the system states and the nonlinear disturbances and the stochastic perturbation is in the form of a brownian motion the purpose of the addressed stochastic stabilization problem is to design a memoryless state feedback controller such that for all admissible interval uncertainties and nonlinear disturbances the closed loop system is asymptotically stable in the mean square where the stability criteria are dependent on the length of the time delay and therefore less conservative by using ito s differential formula and the lyapunov stability theory sufficient conditions are first derived for ensuring the stability of the stochastic interval delay systems then the controller gain is characterized in terms of the solution to a delay dependent linear matrix inequality lmi which can be easily solved by using available software packages a numerical example is exploited to demonstrate the effectiveness of the proposed design procedure