containment control for partial differential multi agent systems abstract this paper investigates the containment control problem for a class of partial differential multi agent systems which are governed by the parabolic equations heat equations or the second order hyperbolic equations wave equations the distributed containment based feedback control laws are obtained by constructing an appropriate lyapunov functional and under the action of the feedback control laws the containment errors between the followers states and the convex hull spanned by the leaders states on an appropriate sobolev space can converge to zero as time tends to infinity simulation examples are finally used to show the effectiveness of the theoretical analysis

sharp inequalities that generalize the divergence theorem an extension of the notion of quasi convexity subject to suitable boundary conditions being imposed sharp inequalities are obtained on integrals over a region of certain special quadratic functions f e where e x derives from a potential u

modified curvature motion for image smoothing and enhancement we formulate a general modified mean curvature based equation for image smoothing and enhancement the key idea is to consider the image as a graph in some r sup 72 and apply a mean curvature type motion to the graph we consider some special cases relevant to grey scale and color images

disturbance estimator based output feedback exponential stabilization for euler bernoulli beam equation with boundary control in this paper we are concerned with the output feedback exponential stabilization problem for a system plant described by a one dimensional euler bernoulli beam equation the measurements are only the displacement and the angular velocity at the right end an infinite dimensional estimator is designed to estimate the disturbance with the estimated disturbance we propose a state observer that is exponentially convergent to the original system then design two different kinds of stabilizing controllers one is based on the velocity feedback the other is based on the angular velocity feedback in both cases by adopting the riesz basis approach the exponential stability of the closed loop systems is built with guaranteeing that all internal systems are uniformly bounded the numerical experiments are carried out to illustrate the theoretical results

young measure solutions of a class of forward backward diffusion equations abstract this paper is devoted to young measure solutions of a class of forward backward diffusion equations inspired by the idea from a recent work of demoulini we first discuss the regular case by introducing the young measure solutions and prove the existence for such solutions and then approximate the extreme case by the approach of regularization and establish the existence of young measure solutions in the class of functions with bounded variation

fuzzy output tracking control of semi linear first order hyperbolic pde systems with matched perturbations abstract this paper considers the design problem of a fuzzy output tracking controller via a finite number of actuators for a class of nonlinear distributed parameter systems with unknown matched perturbations described by semi linear first order hyperbolic partial differential equations pdes firstly a t s fuzzy hyperbolic pde model is assumed to be used to accurately represent the semi linear first order hyperbolic pde system subsequently based on the t s fuzzy pde model the classic variable structure control technique is adopted to develop a fuzzy output tracking controller such that the output of the semi linear pde system exponentially tracks a desired reference and the state of the system is uniformly bounded in the filippov sense by constructing a strict lyapunov function the sufficient condition on the existence of the fuzzy output tracking controller is derived and presented in terms of algebraic linear matrix inequalities lmis in space with an equality constraint it has been shown that when these algebraic lmis with an equality constraint are feasible fuzzy tracking control design can be obtained via the existing convex optimization techniques finally the developed design methodology is successfully applied to the control of a semi linear lotka volterra pde system and the achieved results illustrate its effectiveness

a necessary and sufficient condition for lower semicontinuity abstract it is well known that w 1 p quasiconvexity is a necessary condition for sequential weak lower semicontinuity of the variational integral i u f u x d x on the sobolev space w 1 p and that it is sufficient too provided that the integrand f satisfies suitable growth conditions related to the exponent p we show that for extended real valued integrands a closely related convexity condition defined in terms of gradient young measures is both necessary and sufficient for lower semicontinuity in the more general and flexible setting of compensated compactness our main results identify the relaxation lower semicontinuous envelope in two related situations

stability preserving maps for finite time convergence super twisting sliding mode algorithm the super twisting algorithm sta has become the prototype of second order sliding mode algorithm it achieves finite time convergence by means of a continuous action without using information about derivatives of the sliding constraint thus chattering associated to traditional sliding mode observers and controllers is reduced the stability and finite time convergence analysis have been jointly addressed from different points of view most of them based on the use of scaling symmetries homogeneity or non smooth lyapunov functions departing from these approaches in this contribution we decouple the stability analysis problem from that of finite time convergence a nonlinear change of coordinates and a time scaling are used in the new coordinates and time space the transformed system is stabilized using any appropriate standard design method conditions under which the combination of the nonlinear coordinates transformation and the time scaling is a stability preserving map are given provided convergence in the transformed space is faster than o 1 t where t is the transformed time convergence of the original system takes place in finite time the method is illustrated by designing a generalized super twisting observer able to cope with a broad class of perturbations

lower semicontinuity of multiple integrals and the biting lemma weak lower semicontinuity theorems in the sense of chacon s biting lemma are proved for multiple integrals of the calculus of variations a general weak lower semicontinuity result is deduced for integrands which are acomposition of convex and quasiconvex functions the biting weak limit of the corresponding integrands is characterised via the young measure and related to the weak limit in the sense of measures finally an example is given which shows that the young measure corresponding to a general sequence of gradients may not have an integral representation of the type valid in the periodic case

on homogeneous finite time control for linear evolution equation in hilbert space based on the notion of generalized homogeneity a new algorithm of feedback control design is developed for a plant modeled by a linear evolution equation in a hilbert space with a possibly unbounded operator the designed control law steers any solution of the closed loop system to zero in a finite time a method of homogeneous extension is presented in order to make the developed control design principles to be applicable for evolution systems with nonhomogeneous operators the design scheme is demonstrated for the heat equation with the control input distributed on the segment 0 1

sliding mode control of schrodinger equation ode in the presence of unmatched disturbances abstract in this paper we consider boundary stabilization for a cascade of schrodinger equation ode system with both matched and unmatched disturbances the backstepping method is first applied to transform the system into an equivalent target system where the target system is input to state stable to reject the matched disturbance the sliding mode control smc law is designed for the target system the well posedness of the closed loop system is proved and the reachability of the sliding manifold in finite time is justified by infinite dimensional system theory it is shown that the resulting closed loop system is input to state stable a numerical example illustrates the efficiency of the sliding mode design that reduces the ultimate bound of the closed loop system by rejecting the matched disturbance

a general framework for low level vision we introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented we consider intensity images as surfaces in the x i space the image is thereby a two dimensional 2 d surface in three dimensional 3 d space for gray level images and 2 d surfaces in five dimensions for color images the new formulation unifies many classical schemes and algorithms via a simple scaling of the intensity contrast and results in new and efficient schemes extensions to multidimensional signals become natural and lead to powerful denoising and scale space algorithms

semicontinuity problems in the calculus of variations soit f r 3 r une fonction deux fois continument differentiable et pour u w 1 1 a b f u a b a b f x u x u x dx si f r n r m r nm r satisfait 1 f est mesurable en x continue en cs et 2 0 f x s a x c s p p ou p 1 a est une fonction localement sommable non negative et c une constante non negative alors la fonctionnelle f u a b est sequentiellement faiblement semi continue inferieurement sur w 1 p r m si et seulement si f x s est quasi convexe pour chaque s et presque chaque x

quasiconvexity and relaxation of nonconvex problems in the calculus of variations keywords quasiconvexity relaxation reference caa article 1982 002doi 10 1016 0022 1236 82 90046 5view record in web of science record created on 2008 11 25 modified on 2017 05 12

stabilisation of a thermo elastic system under nonuniformly bounded disturbances in the boundary input abstractwe consider the exponential stabilisation for a thermo elastic system of type ii with nonuniformly bounded external disturbances in the boundary control we begin with finding feedback controls for the system without disturbances by lyapunov function approach then based on the resulting feedback control we give new dynamic feedback control laws that make the system exponentially stable by tracking disturbances exponentially through a time varying high gain observer we apply the linear operator semi group theory to prove the well posedness of the resulting closed system finally we prove that the solution of the closed loop system can approach zero polynomially or exponentially by the lyapunov function approach

retinal vessel centerline extraction using multiscale matched filters confidence and edge measures motivated by the goals of improving detection of low contrast and narrow vessels and eliminating false detections at nonvascular structures a new technique is presented for extracting vessels in retinal images the core of the technique is a new likelihood ratio test that combines matched filter responses confidence measures and vessel boundary measures matched filter responses are derived in scale space to extract vessels of widely varying widths a vessel confidence measure is defined as a projection of a vector formed from a normalized pixel neighborhood onto a normalized ideal vessel profile vessel boundary measures and associated confidences are computed at potential vessel boundaries combined these responses form a six dimensional measurement vector at each pixel a training technique is used to develop a mapping of this vector to a likelihood ratio that measures the vesselness at each pixel results comparing this vesselness measure to matched filters alone and to measures based on the hessian of intensities show substantial improvements both qualitatively and quantitatively the hessian can be used in place of the matched filter to obtain similar but less substantial improvements or to steer the matched filter by preselecting kernel orientations finally the new vesselness likelihood ratio is embedded into a vessel tracing framework resulting in an efficient and effective vessel centerline extraction algorithm

sliding mode control of the orr sommerfeld equation cascaded by both the squire equation and ode in the presence of boundary disturbances the sliding mode control smc approach is proposed in this paper for the orr sommerfeld equation cascaded by both the squire equation and ode in which orr sommerfeld and squire equations are su

the active disturbance rejection control to stabilization for multi dimensional wave equation with boundary control matched disturbance in this paper we consider boundary stabilization for a multi dimensional wave equation with boundary control matched disturbance that depends on both time and spatial variables the active disturbance rejection control adrc approach is adopted in investigation an extended state observer is designed to estimate the disturbance based on an infinite number of ordinary differential equations obtained from the original multi dimensional system by infinitely many test functions the disturbance is canceled in the feedback loop together with a collocated stabilizing controller all subsystems in the closed loop are shown to be asymptotically stable in particular the time varying high gain is first time applied to a system described by the partial differential equation for complete disturbance rejection purpose and the peaking value reduction caused by the constant high gain in literature the overall picture of the adrc in dealing with the disturbance for multi dimensional partial differential equation is presented through this system the numerical experiments are carried out to illustrate the convergence and effect of peaking value reduction

w1 p quasiconvexity and variational problems for multiple integrals abstract variational problems for the multiple integral i u g u x dx where r m and u r n are studied a new condition on g called w1 p quasiconvexity is introduced which generalizes in a natural way the quasiconvexity condition of c b morrey it being shown in particular to be necessary for sequential weak lower semicontinuity of i in w 1 p r n and for the existence of minimizers for certain related integrals counterexamples are given concerning the weak continuity properties of jacobians in w 1 p r n p n m an existence theorem for nonlinear elastostatics is proved under optimal growth hypotheses

sliding order and sliding accuracy in sliding mode control the synthesis of a control algorithm that stirs a nonlinear system to a given manifold and keeps it within this constraint is considered usually what is called sliding mode is employed in such synthesis this sliding mode is characterized in practice by a high frequency switching of the control it turns out that the deviation of the system from its prescribed constraints sliding accuracy is proportional to the switching time delay a new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced these algorithms feature a bounded control continuously depending on time with discontinuities only in the control derivative it is also shown that the sliding accuracy is proportional to the square of the switching time delay

discontinuous unit feedback control of uncertain infinite dimensional systems control systems driven by a discontinuous unit feedback in a hilbert space are studied the equation which describes a system motion taking place in the discontinuity manifold and further referred to as a sliding mode is derived by means of a special regularization technique based on the sliding mode equation the procedure of synthesis of a discontinuous unit control signal is developed restricted to a class of infinite dimensional systems with finite dimensional unstable part this procedure generates the control law which ensures desired dynamic properties as well as robustness of the closed loop system with respect to matched disturbances as an illustration of the capabilities of the procedure proposed a scalar unit controller of an uncertain exponentially minimum phase dynamic system is constructed and applied to heat processes and distributed mechanical oscillators

lyapunov approach to output feedback stabilization for the euler bernoulli beam equation with boundary input disturbance we propose a boundary output feedback control law for a one dimensional euler bernoulli beam equation with general external disturbance entering the control end a galerkin approximation scheme is constructed to show the existence of solution to the closed loop system the exponential stability of the closed loop system is obtained by the lyapunov functional method numerical simulations are presented for illustration

interior gradient estimates for mean curvature equations the interior gradient estimate for the prescribed mean curvature equation has been extensively studied see 9 and the references therein for high order mean curvature equations it has also been obtained in 11 18 in most articles such estimates were obtained by carrying out analysis on the graphs of solutions and so the arguments depend on the invariance of the equations under rigid motion from the view point of partial differential equations such estimate should hold for equations with similar structural conditions in 13 6 the gradient estimate was obtained for certain fully nonlinear elliptic equations under various conditions different proofs for the gradient estimate for mean curvature equations have been given in 1 3 in this note we show that for curvature and hessian equations the interior gradient estimate can be obtained very easily our proof which is based on suitable choice of auxiliary functions is elementary and avoids geometric computations on the graph of solutions the technique in this note has actually been widely used in literature see e g 9

disturbance estimator and servomechanism based performance output tracking for a 1 d euler bernoulli beam equation in this paper we consider performance output tracking for a one dimensional euler bernoulli beam equation with boundary moment control and unmatched internal uncertainty and external disturbance for such system the reference feng and guo 2017 firstly studied the active disturbance rejection control adrc problem we design an infinite dimensional disturbance estimator to estimate the total disturbance internal uncertainty and external disturbance and the system state simultaneously a servomechanism generated by the reference signal is designed based on the estimated total disturbance we design an output feedback control law such that the performance output signal tracks the reference signal and all the signals of closed loop system are bounded some illustrative simulations are presented

non parametric mean curvature evolution with boundary conditions soit un domaine borne de r n n 2 de frontiere lisse et soit a l operateur de surface minimale donne par a d i a i p a i p i 1 p 2 1 2 on considere des surfaces dont la vitesse en direction de leur normale unite est egale a la courbure moyenne on etudie l equation d evolution qui en resulte u 1 du 2 1 2 au 0 dans 0 t

stabilization of ode with hyperbolic equation actuator subject to boundary control matched disturbance in this paper we consider stabilisation for a cascade of ode and first order hyperbolic equation with external disturbance flowing to the control end the active disturbance rejection control adr

quasiconvexity at the boundary positivity of the second variation and elastic stability for one dimensional problems of the calculus of variations there is a well developed theory relating the positivity of the second variation at a critical point i e linearized stability to strong relative minima these results largely due to weierstrass are usually proved by the method of fields of extremals as is described in bolza 1904 and morrey 1966 or by an argument involving a careful use of taylor series as in hestenes 1966 chapter 3 14

gradient estimates for solutions of parabolic equations and systems 1 statement of the problem let 52 c r n 2 be a bounded domain with smooth boundary r 2 in this note we study scalar quasilinear parabolic differential equations u div y g ivul vu f u 0 1 u a u f u o 2 and systems u da u f u 0 3 on q x 0 co with initial conditions u 0 u0 resp u 0 u0 and homogeneous dirichlet boundary conditions u i x o co o for 1 and 2 resp 4 u1r x 0 00 0 for 3 5

robust distributed control of quasilinear reaction diffusion equations via infinite dimensional sliding modes abstract this paper investigates the problem of robust tracking control for quasilinear reaction diffusion partial differential equations subject to external unknown perturbations the considered class of equations is quite general and includes classical equations such as the heat equation or the fisher kpp equation as special cases global practical stabilization of the tracking error system is established under mild conditions on the disturbance term using a regularized infinite dimensional sliding mode controller extensive simulations support and validate the theoretical results

self similar entropy solutions of a singular diffusion equation in arbitrary spatial dimension abstract in this paper we consider a singular diffusion equation arising in phase transition and investigate its self similar entropy solutions with jump hypersurfaces the existence nonexistence and uniqueness theorems of such solutions are established we also discuss some properties of this kind of solutions including monotonicity and asymptotic behavior

tracking control of the uncertain heat and wave equation via power fractional and sliding mode techniques in the present paper preliminary results towards the generalization to the infinite dimensional setting of some well known robust finite dimensional control algorithms are illustrated more specifically we deal with the tracking problem for some classes of linear uncertain infinite dimensional systems evolving in hilbert spaces we design distributed variable structure stabilizers that are shown to be effective in the presence of external disturbances the main focus of the present paper is on the rejection of nonvanishing external disturbances the generalization to the infinite dimensional setting of the well known finite dimensional controllers namely the power fractional controller s p bhat and d s bernstein siam j control optim 38 2000 pp 751 766 and two second order sliding mode control algorithms the twisting and supertwisting algorithms l fridman and a levant higher order sliding modes as a natural phenomenon in control theory in robust control via variable structure and lyapunov techniques springer verlag berlin 1996 pp 107 133 a levant internat j control 58 1993 pp 1247 1263 is the main contribution of the present investigation first the distributed twisting control algorithm is developed to address the asymptotic state tracking of the perturbed wave equation next the finite time state tracking of the unperturbed heat equation is provided by means of a distributed power fractional controller finally the distributed supertwisting controller is suggested to address the asymptotic state tracking of the heat equation in spite of the presence of persistent disturbances constructive proofs of stability are developed via the lyapunov functional technique which leads to simple tuning rules for the controller parameters simulation results are discussed to verify the effectiveness of the proposed schemes

performance output tracking for multidimensional heat equation subject to unmatched disturbance and noncollocated control this paper investigates performance output tracking for a boundary controlled multidimensional heat equation it is assumed that the so called total disturbance which is composed of internal possibly nonlinear uncertainty and external disturbance the equation is subject to is on one part of the boundary and that the control is applied on the rest of the boundary using only partial boundary measurement we first propose an extended state observer to estimate both system state and the total disturbance this allows us to design a servomechanism and then an output feedback controller under the condition that both the reference signal and the disturbance vanish or belong to spaces h 1 0 infty l 1 gamma 1 and l 2 0 infty l 2 gamma 0 respectively we show that the over all control strategy achieves three objectives on the system performance first exponentially output tracking for arbitrary given reference signal second uniformly boundedness of all internal signals and third the internal asymptotic stability of the closed loop system in addition the control strategy turns out to be robust to the measurement noise we provide numerical experiments to illustrate the effectiveness of the proposed control strategy

similar entropy solutions of a singular diffusion equation in this paper we study the similar entropy solutions of the singular diffusion equation u t x j u x with j s s 1 s 2 these kinds of solutions have nonvertical jump lines we establish the existence and uniqueness and also discuss some properties of these kinds of solutions

detection of blood vessels in retinal images using two dimensional matched filters blood vessels usually have poor local contrast and the application of existing edge detection algorithms yield results which are not satisfactory an operator for feature extraction based on the optical and spatial properties of objects to be recognized is introduced the gray level profile of the cross section of a blood vessel is approximated by a gaussian shaped curve the concept of matched filter detection of signals is used to detect piecewise linear segments of blood vessels in these images twelve different templates that are used to search for vessel segments along all possible directions are constructed various issues related to the implementation of these matched filters are discussed the results are compared to those obtained with other methods

exponential stabilization of conservation systems with interior disturbance abstract in this paper we consider the stabilization problem of the conservation systems with interior disturbance employing the idea of sliding mode control we design a nonlinear distributed feedback controller we prove the solvability of the resulted closed loop system by the maximal monotone operator theory further we prove the exponential stability of the closed loop system in particular we prove that the requirement of a classical solution in the lyapunov approach is unnecessary

performance output tracking for a wave equation subject to unmatched general boundary harmonic disturbance in this paper we consider performance output reference tracking for a wave equation with general harmonic disturbance at one end and the control at the other end we first design a state reference system determined completely by the measured output and the reference signal where the parameter update law is presented an adaptive servomechanism output feedback control is then designed it is shown that the closed loop system is well posed three control objectives are achieved a the performance output is tracking the reference signal b all the internal loops are bounded c when the disturbance and reference are disconnected the closed loop is exponentially stable finally the state of system is shown to be tracking the reference state and the updated parameters are convergent to their true values

boundary control of coupled reaction diffusion processes with constant parameters the problem of boundary stabilization is considered for some classes of coupled parabolic linear pdes of the reaction diffusion type with reference to n coupled equations each one equipped with a scalar boundary control input a state feedback law is designed with actuation at only one end of the domain and exponential stability of the closed loop system is proven the treatment is addressed separately for the case in which all processes have the same diffusivity and for the more challenging scenario where each process has its own diffusivity and a different solution approach has to be taken the backstepping method is used for controller design and particularly the kernel matrix of the transformation is derived in explicit form of series of bessel like matrix functions by using the method of successive approximations to solve the corresponding pde thus the proposed control laws become available in explicit form additionally the stabilization of an underactuated system of two coupled reaction diffusion processes is tackled under the restriction that only a scalar boundary input is available capabilities of the proposed synthesis and its effectiveness are supported by numerical studies made for three coupled systems with distinct diffusivity parameters and for underactuated linearized dimensionless temperature concentration dynamics of a tubular chemical reactor controlled through a boundary at low fluid superficial velocities when convection terms become negligible

the active disturbance rejection control approach to stabilisation of coupled heat and ode system subject to boundary control matched disturbance we consider stabilisation for a linear ordinary differential equation system with input dynamics governed by a heat equation subject to boundary control matched disturbance the active disturbance rejection control approach is applied to estimate in real time the disturbance with both constant high gain and time varying high gain the disturbance is cancelled in the feedback loop the closed loop systems with constant high gain and time varying high gain are shown respectively to be practically stable and asymptotically stable

flow by mean curvature of convex surfaces into spheres the motion of surfaces by their mean curvature has been studied by brakke 1 from the viewpoint of geometric measure theory other authors investigated the corresponding nonparametric problem 2 5 9 a reason for this interest is that evolutionary surfaces of prescribed mean curvature model the behavior of grain boundaries in annealing pure metal in this paper we take a more classical point of view consider a compact uniformly convex w dimensional surface m mo without boundary which is smoothly imbedded in r let mo be represented locally by a diffeomorphism

sliding mode control to stabilization of cascaded heat pde ode systems subject to boundary control matched disturbance in this paper we are concerned with the boundary feedback stabilization of a cascade of heat pde ode system with dirichlet neumann interconnection and with the external disturbance flowing the control end in order to deal with the disturbance the sliding model control smc is integrated with the backstepping approach where the disturbance is supposed to be bounded only the existence and uniqueness of the solution for the closed loop system are proved and the monotonicity of the reaching condition is presented without differentiation of the sliding mode function for which it may not always exist for the weak solution of the closed loop system finally the numerical simulations validate the effectiveness of this method for the system with periodic and normal random disturbances respectively

generalisation of euler lagrange equations to find min max optimal solution of uncertain systems a major problem in optimal control theory is existing uncertainty in initial state cost function or in state equations in this paper a generalised euler lagrange approach to find min max optimal solution of uncertain systems with uncertain or certain cost function using calculus of variation is considered the work is based on an admissible system path or a trajectory which minimises the maximum value of the functional over all uncertainty first of all a new form of euler lagrange conditions for uncertain systems is presented then several cases are indicated where final condition can be specified or free also necessary conditions are introduced to existence of min max optimal solution of the uncertain systems also the method is generalised when the uncertainties are bounded with using pontryagin s minimum principle finally efficiency of the proposed methods is verified through some examples

infinite time blow up of solutions to a nonlinear parabolic problem abstract we investigate the blow up of solutions of nonuniformly parabolic equations it will be shown that the gradient of the solution tends to infinity as time goes to infinity even though thel norm of the solution may remain uniformly bounded this phenomenon is in contrast with a result for semilinear heat equations where it follows from regularity theory that the solution converges to an equilibrium if it is uniformly bounded in thel norm

active disturbance rejection control for rejecting boundary disturbance from multidimensional kirchhoff plate via boundary control in this paper an algorithm is developed to reject time and spatially varying boundary disturbances from a multidimensional kirchhoff plate via boundary control the disturbance and control input are assumed to be matched the active disturbance rejection control approach is adopted for developing the algorithm a state feedback scheme is designed to estimate the disturbance based on an infinite number of ordinary differential equations obtained from the original multidimensional system using infinitely many time dependent test functions the proposed control law cancels the disturbance using its estimated value all subsystems in the closed loop are shown to be asymptotically stable simulation results are presented to validate the theoretical conclusions and to exhibit the reduction in the peaking phenomenon due to the use of time varying gains instead of constant high gains

on various semiconvex relaxations of the squared distance function for the euclidean squared distance function f dist 2 k with k m n n we show that k is convex if and only if f equals either its rank one convex quasiconvex or polyconvex relaxations we also establish that if i k is compact and contractible or ii dim c k k n k is convex if and only if f equals one of the semiconvex relaxations when dist 2 p k is sufficiently large and for case i p m nxn for case ii p e k a k dimensional plane containing c k we also give some estimates of the difference between dist 2 p k and its semiconvex relaxations some possible extensions to more general p distance functions are also considered

null lagrangians weak continuity and variational problems of arbitrary order abstract we consider the problem of minimizing integral functionals of the form i u f x k u x dx where r p u r and k u denotes the set of all partial derivatives of u with orders k the method is based on a characterization of null lagrangians l ku depending only on derivatives of order k applications to elasticity and other theories of mechanics are given

a dynamic compensator for in domain control of burgers equation this paper addresses the problem of output regulation control of a burgers equation under pointwise in domain actuation a dynamic compensator that generates the in domain control is developed for

the active disturbance rejection and sliding mode control approach to the stabilization of the euler bernoulli beam equation with boundary input disturbance in this paper we are concerned with the boundary feedback stabilization of a one dimensional euler bernoulli beam equation with the external disturbance flowing to the control end the active disturbance rejection control adrc and sliding mode control smc are adopted in investigation by the adrc approach the disturbance is estimated through an extended state observer and canceled online by the approximated one in the closed loop it is shown that the external disturbance can be attenuated in the sense that the resulting closed loop system under the extended state feedback tends to any arbitrary given vicinity of zero as the time goes to infinity in the second part we use the smc to reject the disturbance by removing the condition in adrc that the derivative of the disturbance is supposed to be bounded the existence and uniqueness of the solution for the closed loop via smc are proved and the monotonicity of the reaching condition is presented without the differentiation of the sliding mode function for which it may not always exist for the weak solution of the closed loop system the numerical simulations validate the effectiveness of both methods

young measure solutions and instability of the one dimensional perona malik equation we apply a variational approach to the one dimensional version of the widely used perona malik equation in image processing we rephrase the problem into the one related to the quasiconvex hull of a graph in the space of 2 x 2 matrices m 2x2 we then use the solutions of some heat equations as the centre of the mass for the young measure valued solutions to construct the approximate solutions by using simple laminates the approximate solutions can be viewed as solutions of a perturbation problem by w 1 w p or w 1 w infinity functions the sequences of the approximate solutions generates young measure valued solutions our results also show that the solutions of the one dimensional perona malik equation are unstable under small w 1 w infinity perturbations

existence and regularity of extremal solutions for a mean curvature equation we study a class of mean curvature equations mu h up where m denotes the mean curvature operator and for p 1 we show that there exists an extremal parameter such that this equation admits a minimal weak solutions for all 0 while no weak solutions exists for weak solutions will be defined as critical points of a suitable functional in the radially symmetric case we then show that minimal weak solutions are classical solutions for all 0 and that another branch of classical solutions exists in a neighborhood of

unknown input observer design and output feedback stabilization for multi dimensional wave equation with boundary control matched uncertainty abstract in this paper we consider boundary output feedback stabilization for a multi dimensional wave equation with boundary control matched unknown nonlinear internal uncertainty and external disturbance a new unknown input type extended state observer is proposed to recover both state and total disturbance which consists of internal uncertainty and external disturbance a key feature of the proposed observer in this paper is that we do not use the high gain to estimate the disturbance by the active disturbance rejection control adrc strategy the total disturbance is compensated canceled in the feedback loop which together with a collocated stabilizing controller without uncertainty leads to an output feedback stabilizing feedback control it is shown that the resulting closed loop system is well posed and asymptotically stable under weak assumption on internal uncertainty and external disturbance the numerical experiments are carried out to show the effectiveness of the proposed scheme

general retinal vessel segmentation using regularization based multiconcavity modeling detecting blood vessels in retinal images with the presence of bright and dark lesions is a challenging unsolved problem in this paper a novel multiconcavity modeling approach is proposed to handle both healthy and unhealthy retinas simultaneously the differentiable concavity measure is proposed to handle bright lesions in a perceptive space the line shape concavity measure is proposed to remove dark lesions which have an intensity structure different from the line shaped vessels in a retina the locally normalized concavity measure is designed to deal with unevenly distributed noise due to the spherical intensity variation in a retinal image these concavity measures are combined together according to their statistical distributions to detect vessels in general retinal images very encouraging experimental results demonstrate that the proposed method consistently yields the best performance over existing state of the art methods on the abnormal retinas and its accuracy outperforms the human observer which has not been achieved by any of the state of the art benchmark methods most importantly unlike existing methods the proposed method shows very attractive performances not only on healthy retinas but also on a mixture of healthy and pathological retinas

boundary second order sliding mode control of an uncertain heat process with unbounded matched perturbation the primary concern of the present paper is the regulation of an uncertain heat process with collocated boundary sensing and actuation the underlying heat process is governed by an uncertain parabolic partial differential equation pde with neumann boundary conditions it exhibits an unknown constant diffusivity parameter and it is affected by a smooth boundary disturbance which is not available for measurements and which is possibly unbounded in magnitude the proposed robust synthesis is formed by the linear feedback design and by the twisting second order sliding mode control algorithm suitably combined and re worked in the infinite dimensional setting a non standard lyapunov functional is invoked to establish the global asymptotic stability in a sobolev space involving spatial state derivatives of the same order as that of the plant equation the stability proof is accompanied by a set of simple tuning rules for the controller parameters the effectiveness of the developed control scheme is supported by simulation results

boundary regularity and sufficient conditions for strong local minimizers abstract in this paper we present a new proof of the sufficiency theorem for strong local minimizers concerning c 1 extremals at which the second variation is strictly positive the results are presented in the quasiconvex setting in accordance with the original statement by grabovsky and mengesha 31 the strategy that we follow relies on a decomposition theorem that allows to split a sequence of variations into its oscillating and its concentrating parts as well as on a sufficiency result according to which smooth extremals are spatially local minimizers furthermore we prove partial regularity up to the boundary for strong local minimizers in the non homogeneous case and a full regularity result for lipschitz extremals with gradient of vanishing mean oscillation as a consequence we also establish a sufficiency result for this class of extremals the regularity results are established via a blow up argument

finite time stability and robust control synthesis of uncertain switched systems stability analysis is developed for uncertain nonlinear switched systems while being asymptotically stable and homogeneous of degree q 0 these systems are shown to approach the equilibrium point in finite time restricted to second order systems this feature is additionally demonstrated to persist regardless of inhomogeneous perturbations based on this fundamental property switched control algorithms are then developed to globally stabilize uncertain minimum phase systems of uniform m vector relative degree 2 2 t the controllers constructed do not rely on the generation of sliding motions while providing robustness features similar to those possessed by their sliding mode counterparts the proposed synthesis procedure is illustrated via application to a friction servo motor

entropy solutions for a fourth order nonlinear degenerate problem for noise removal abstract in this paper we establish the existence and uniqueness of entropy solutions for a fourth order nonlinear degenerate parabolic problem for noise removal in dimension 1 d 4

mountain pass solutions for a double well energy we establish the existence of a mountain pass solution for a variational integral involving a quasiconvex function with a double well structure in the geometrically linear elasticity setting we show that under small dead load perturbations the neumann boundary value problem has at least three solutions a global minimizer a local minimizer and a mountain pass solution we show that our variational integral satisfies a weak palais smale condition wps hence the mountain pass lemma applies

boundary time varying feedbacks for fixed time stabilization of constant parameter reaction diffusion systems in this paper the problem of fixed time stabilization of constant parameter reaction diffusion partial differential equations by means of continuous boundary time varying feedbacks is considered moreover the time of convergence can be prescribed in the design the design of time varying feedbacks is carried out based on the backstepping approach using a suitable target system with a time varying coefficient one can state that the resulting kernel of the backstepping transformation is time varying and rendering the control feedback to be time varying as well explicit representations of the kernel solution in terms of generalized laguerre polynomials and modified bessel functions are derived the fixed time stability property is then proved a simulation example is presented to illustrate the main results

fast detection of facial wrinkles based on gabor features using image morphology and geometric constraints facial wrinkles are important features of aging human skin which can be incorporated in several image based applications related to aging facial wrinkles are 3d features of skin and appear as subtle discontinuities or cracks in surrounding skin texture however facial wrinkles can easily be masked by illumination acquisition conditions in 2d images due to the specific nature of skin surface texture and its reflective properties existing approaches to image based analysis of aging skin are based on the analysis of wrinkles as texture and not as curvilinear discontinuity crack features previously we proposed a stochastic approach based on marked point processes mpp to localize facial wrinkles as curves in this paper we present a fast deterministic algorithm based on gabor filters and image morphology to improve localization results we propose image features based on gabor filter bank to highlight the subtle curvilinear discontinuities in skin texture caused by wrinkles then image morphology is used to incorporate geometric constraints to localize curvilinear shapes of wrinkles at image sites of large gabor filter responses experiments are conducted on two sets of low and high resolution images and results are compared with those of mpp modeling experiments show that the proposed algorithm not only is significantly faster than mpp based approach but also provides visually better results highlightsthe algorithm localizes subtle cracks in skin texture caused by wrinkles the algorithm is computationally fast based on the morphology the algorithm localizes wrinkles as curvilinear objects from the results typical challenges in localization of wrinkles are highlighted

a novel vessel segmentation algorithm for pathological retina images based on the divergence of vector fields in this paper a method is proposed for detecting blood vessels in pathological retina images in the proposed method blood vessel like objects are extracted using the laplacian operator and noisy objects are pruned according to the centerlines which are detected using the normalized gradient vector field the method has been tested with all the pathological retina images in the publicly available stare database experiment results show that the method can avoid detecting false vessels in pathological regions and can produce reliable results for healthy regions

a general approach to lower semicontinuity and lower closure in optimal control theory a self contained approach to lower semicontinuity and lower closure evolves from an extension of relaxed control theory which is based on a central relative weak compactness criterion called tightness and relaxation in all but one variable two lower closure results for outer integral functionals with variable abstract time domain are developed the first of these has a convexity condition for the integrand and generalizes all similar results in the literature the second lower closure result is of a new kind among other things it implies a quite general version of fatou s lemma in several dimensions