internal stabilization of semilinear parabolic systems this work is concerned with the internal stabilization of the steady state solutions to semilinear parabolic systems via finite dimensional feedback controllers the internal controller is active on a nonempty open subset and in one equation only

maximum principle of state constrained optimal control governed by fluid dynamic systems this work deals with maximum principle of optimal control governed by some fluid dynamic systems which include three dimensional navier stokes equations some type of state constraint is involved

optimal control of damped klein gordon equations with state constraints abstract in this paper we study the maximum principles for optimal control problems governed by the damped klein gordon equations with state constraints and we prove the existence of the optimal parameter and deduce the necessary conditions on the optimal parameter

what s next an interactive next best view approach shape from silhouettes algorithms use either a surface or a volumetric approach a problem with the volumetric approach is that in general we know neither the accuracy of the reconstruction nor where to locate new viewpoints for improving the accuracy in this paper we present a general approach to interactive object specific volumetric algorithms based on a necessary condition for the best possible reconstruction to have been performed the outlined approach can be applied to any class of objects as an example of this approach an interactive algorithm has been implemented for convex polyhedra

optimal controls of 3 dimensional navier stokes equations with state constraints this work is concerned with the maximum principles for optimal control problems governed by 3 dimensional navier stokes equations some types of state constraints time variables are considered

the effect of a sparse grad div stabilization on control of stationary navier stokes equations abstract this study presents a reduced sparsity grad div stabilization for the optimal control of an incompressible stationary flow problem the effect of the proposed stabilization is analyzed in terms of stability and velocity a priori error the main difference between this method and the usual grad div stabilization can be observed in numerical computations since the proposed method produces block upper triangular matrices an advantage can be seen in terms of implementation over the common grad div stabilization which produces fully coupled block matrices the stability and the convergence results are given for both the state and the adjoint state variables once the optimality conditions by using the lagrange approach are stated in numerical experiments solutions of the optimal control problem without any stabilization and the proposed method are presented in order to compare the effectiveness of the method the numerical convergence study is also presented

iterative methods for a class of robust control problems in fluid mechanics in this article we consider a class of iterative methods for the numerical solutions of some robust control problems recently studied in t r bewley r temam and m ziane phys d 138 2000 pp 360 392 these methods are based on repeated computations of the state and the adjoint equations using the properties of the control operator we justify these methods and obtain estimates of their convergence rate numerical solutions of a robust control problem related to data assimilation in oceanography using these algorithms are also presented

the visual hull of smooth curved objects the visual hull is a geometric entity that relates the shape of an object to its silhouettes or shadows this paper develops the theory of the visual hull of generic smooth objects we show that the visual hull can be constructed using surfaces which partition the viewpoint space of the aspect graph of the object the surfaces are those generated by the visual events tangent crossing and triple point an analysis based on the shape of the object at the tangency points of these surfaces allows pruning away many surfaces and patches not relevant to the construction an algorithm for computing the visual hull is outlined

the scale space aspect graph currently the aspect graph is computed from the theoretical standpoint of perfect resolution in object shape the viewpoint and the projected image this means that the aspect graph may include details that an observer could never see in practice introducing the notion of scale into the aspect graph framework provides a mechanism for selecting a level of detail that is large enough to merit explicit representation this effectively allows control over the number of nodes retained in the aspect graph this paper introduces the concept of the scale space aspect graph defines three different interpretations of the scale dimension and presents a detailed example for a simple class of objects with scale defined in terms of the spatial extent of features in the image

spike adding in parabolic bursters the role of folded saddle canards abstract the present work develops a new approach to studying parabolic bursting and also proposes a novel four dimensional canonical and polynomial based parabolic burster in addition to this new polynomial system we also consider the conductance based model of the aplysia r15 neuron known as the plant model and a reduction of this prototypical biophysical parabolic burster to three variables including one phase variable namely the baer rinzel carillo brc phase model revisiting these models from the perspective of slow fast dynamics reveals that the number of spikes per burst may vary upon parameter changes however the spike adding process occurs in an explosive fashion that involves special solutions called canards this spike adding canard explosion phenomenon is analysed by using tools from geometric singular perturbation theory in tandem with numerical bifurcation techniques we find that the bifurcation structure persists across all considered systems that is spikes within the burst are incremented via the crossing of an excitability threshold given by a particular type of canard orbit namely the true canard of a folded saddle singularity however there can be a difference in the spike adding transitions in parameter space from one case to another according to whether the process is continuous or discontinuous which depends upon the geometry of the folded saddle canard using these findings we construct a new polynomial approximation of the plant model which retains all the key elements for parabolic bursting including the spike adding transitions mediated by folded saddle canards finally we briefly investigate the presence of spike adding via canards in planar phase models of parabolic bursting namely the theta model by ermentrout and kopell

optimal control of the primitive equations of the ocean with state constraints abstract we investigate in this article pontryagin s maximum principle for a class of control problems associated with the primitive equations pes of the ocean these optimal problems involve a state constraint similar to that considered in wang 2002 7 for the three dimensional navier stokes ns equations the main difference between this work and wang 2002 7 is that the nonlinearity in the pes is stronger than in the three dimensional ns systems

a computational framework for the regularization of adjoint analysis in multiscale pde systems this paper examines the regularization opportunities available in the adjoint analysis and optimization of multiscale pde systems regularization may be introduced into such optimization problems by modifying the form of the evolution equation and the forms of the norms and inner products used to frame the adjoint analysis typically l2 brackets are used in the definition of the cost functional the adjoint operator and the cost functional gradient if instead we adopt the more general sobolev brackets the various fields involved in the adjoint analysis may be made smoother and therefore easier to resolve numerically the present paper identifies several relationships which illustrate how the different regularization options fit together to form a general framework the regularization strategies proposed are exemplified using a id kuramoto sivashinsky forecasting problem and computational examples are provided which exhibit their utility a multiscale preconditioning algorithm is also proposed that noticeably accelerates convergence of the optimization procedure application of the proposed regularization strategies to more complex optimization problems of physical and engineering relevance is also discussed

projective visual hulls this article presents a novel method for computing the visual hull of a solid bounded by a smooth surface and observed by a finite set of cameras the visual hull is the intersection of the visual cones formed by back projecting the silhouettes found in the corresponding images we characterize its surface as a generalized polyhedron whose faces are visual cone patches edges are intersection curves between two viewing cones and vertices are frontier points where the intersection of two cones is singular or intersection points where triples of cones meet we use the mathematical framework of oriented projective differential geometry to develop an image based algorithm for computing the visual hull this algorithm works in a weakly calibrated setting that is it only requires projective camera matrices or equivalently fundamental matrices for each pair of cameras the promise of the proposed algorithm is demonstrated with experiments on several challenging data sets and a comparison to another state of the art method

pontryagin s maximum principle for optimal control of the stationary primitive equations of the ocean abstract we study in this article pontryagin s maximum principle for a class of control problems associated with the stationary primitive equations pes of the ocean these optimal problems involve a state constraint similar to that considered in g wang pontryagin s maximum principle for optimal control of the stationary navier stokes equations nonlinear anal 52 2003 1853 1866 in the case of the three dimensional navier stokes ns equations the main difference between this work and the one cited above is that the nonlinearity in pes is stronger than that in the three dimensional ns equations

optimal controls of boussinesq equations with state constraints abstract this work is concerned with the maximum principle for an optimal control problem governed by boussinesq equations some integral type state constraints are considered

computing the generalized aspect graph for objects with moving parts algorithms for computing the aspect graph representation are generalized to include a larger more realistic domain of objects known as articulated assemblies those objects composed of rigid parts with articulated connections allowed between parts the generalization suggests two slightly different representations one that directly summarizes the possible general views of the object and another hierarchical form summarizing the possible general configurations and their respective views algorithms are outlined for computing both representations the generalized aspect graphs of assemblies formed using translational connections are examined

viscosity solutions of dynamic programming equations for the optimal control of the two dimensional navier stokes equations in this paper we study the infinite dimensional hamilton jacobi equation associated with the optimal feedback control of viscous hydrodynamics we resolve the global unique solvability problem of this equation by showing that the value function is the unique viscosity solution

acquiring 3 d models from sequences of contours this paper explores shape from contour for acquiring 3 d graphics models in this method a continuous sequence of images is taken as an object rotates a smooth convex shape can be estimated instantaneously from its contour and by the first derivative of contour movement trace of contour or contour distribution with time we also analyze shapes that do not satisfy the conditions of smoothness and visibility which are indispensable for modeling an object a region that does not expose as contour yields a nonsmoothness in the tracked contour movement we can thus detect such a region by contour distribution filtering and extract its accurate location by computing the left and right derivatives of the distribution this has not been studied previously these unknown regions are obtained for further investigation using other visual cues a general approach for building a geometrical object model using contours is then described the entire process from silhouettes to a 3 d model is based local computation this is promising for producing shapes in real time our direct goal is to establish 3 d graphics models of human faces for the growing needs of visual communications we have obtained some good results

efficiently computing and representing aspect graphs of polyhedral objects an efficient algorithm and a data structure for computing and representing the aspect graph of polyhedral objects under orthographic projection are presented the aspect graph is an approach to representing 3 d objects by a set of 2 d views for the purpose of object recognition in this approach the viewpoint space is partitioned into regions such that in each region the qualitative structure of the line drawing does not change the viewing data of an object is the partition of the viewpoint space together with a representative view in each region the algorithm computes the viewing data for line drawings of polyhedral objects under orthographic projection

adjoint based iterative method for robust control problems in fluid mechanics in this article we study the convergence of an adjoint based iterative method recently proposed in t r bewley r temam and m ziane phys d 138 2000 pp 360 392 for the numerical solution of a class of nonlinear robust control problems in fluid mechanics under weaker assumptions than those of t tachim medjo numer funct anal optim 23 2002 pp 849 873 we prove the convergence of the algorithm and we obtain an estimate of the convergence rate numerical solutions of a robust control problem related to data assimilation in oceanography are presented to illustrate the method

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

return map characterizations for a model of bursting with two slow variables various physiological systems display bursting electrical activity bea there exist numerous three variable models to describe this behavior however higher dimensional models with two slow processes have recently been used to explain qualitative features of the bea of some experimentally observed systems t chay and d cook math biosci 90 1988 pp 139 153 p smolen and j keizer j memb biol 127 1992 pp 9 19 r bertram et al biophys j 79 2000 pp 2880 2892 r bertram et al biophys j 68 1995 pp 2323 2332 j keizer and p smolen proc nat acad sci usa 88 1991 pp 3897 3901 in this paper we present a model with two slow and two fast variables for some parameter values the system has stable equilibria while for other values there exist bursting solutions singular perturbation methods are used to define a one dimensional return map wherein fixed points correspond to singular bursting solutions we analytically demonstrate that bursting solutions may exist

sungular hopf bifurcation to relaxation oscillations this paper is a continuation of our study of singular hopf bifurcations to relaxation oscillations siam journal on applied mathematics 46 1986 pp 721 739 in our previous analysis a system of two first order nonlinear equatins is investigated and it is shown how the bifurcation problem can be reduced to a weakly perturbed conservative system of two first order equations in this paper a method based on analyzing nearly conservative quantities was developed to find the bifurcation diagram of the periodic solutions emerging from singular hopf bifurcation points specifically the subcritical hopf bifurcation of the fitzhugh nagumo equations is analyzed the extension from the earlier bifurcation analysis is achieved by performing a perturbation analysis from the first integral of the leading order nonlinear oscillator at a critical value of a parameter the first integral exists up to an additional order in the perturbed equation this condition permits the resolution of features determined by h

analysis and discretization of an optimal control problem for the time periodic mhd equations we consider the mathematical formulation and analysis of an optimal control problem associated with the tracking of the velocity and the magnetic field of a viscous incompressible electrically conducting fluid in a bounded two dimensional domain through the adjustment of distributed controls existence of optimal solutions is proved and first order necessary conditions for optimality are used to derive an optimality system of partial differential equations whose solutions provide optimal states and controls semidiscrete in time approximations are defined and their convergence to the exact optimal solutions is shown

robust control problems in fluid mechanics abstract in this paper we study a class of robust control problems in fluid mechanics recently proposed by bewley et al physica d 138 3 4 2000 360 using a method of shutyaev russ j numer anal math modell 14 2 1999 137 we provide another proof of the existence and the uniqueness of solutions to the robust control problems under weaker assumptions as compared to those of bewley et al physica d 138 3 4 2000 360 from the numerical point of view the method used in this paper is particularly important since it provides a constructive way to approximate the solutions to these nonlinear control problems

a general framework for robust control in fluid mechanics abstract the application of optimal control theory to complex problems in fluid mechanics has proven to be quite effective when complete state information from high resolution numerical simulations is available p moin t r bewley appl mech rev part 2 47 6 1994 s3 s13 t r bewley p moin r temam j fluid mech 1999 submitted for publication in this approach an iterative optimization algorithm based on the repeated computation of an adjoint field is used to optimize the controls for finite horizon nonlinear flow problems f abergel r temam theoret comput fluid dyn 1 1990 303 325 in order to extend this infinite dimensional optimization approach to control externally disturbed flows in which the controls must be determined based on limited noisy flow measurements alone it is necessary that the controls computed be insensitive to both state disturbances and measurement noise for this reason robust control theory a generalization of optimal control theory has been examined as a technique by which effective control algorithms which are insensitive to a broad class of external disturbances may be developed for a wide variety of infinite dimensional linear and nonlinear problems in fluid mechanics an aim of the present paper is to put such algorithms into a rigorous mathematical framework for it cannot be assumed at the outset that a solution to the infinite dimensional robust control problem even exists in this paper conditions on the initial data the parameters in the cost functional and the regularity of the problem are established such that existence and uniqueness of the solution to the robust control problem can be proven both linear and nonlinear problems are treated and the 2d and 3d nonlinear cases are treated separately in order to get the best possible estimates several generalizations are discussed and an appropriate numerical method is proposed

epipolar geometry from profiles under circular motion addresses the problem of motion estimation from profiles apparent contours of an object rotating on a turntable in front of a single camera a practical and accurate technique for solving this problem from profiles alone is developed it is precise enough to reconstruct the shape of the object no correspondences between points or lines are necessary symmetry of the surface of revolution swept out by the rotating object is exploited to obtain the image of the rotation axis and the homography relating epipolar lines in two views robustly and elegantly these together with geometric constraints for images of rotating objects are used to obtain first the image of the horizon which is the projection of the plane that contains the camera centers and then the epipoles thus fully determining the epipolar geometry of the image sequence the estimation of this geometry by this sequential approach avoids many of the problems found in other algorithms the search for the epipoles by far the most critical step is carried out as a simple 1d optimization parameter initialization is trivial and completely automatic at all stages after the estimation of the epipolar geometry the euclidean motion is recovered using the fixed intrinsic parameters of the camera obtained either from a calibration grid or from self calibration techniques finally the spinning object is reconstructed from its profiles using the motion estimated in the previous stage results from real data are presented demonstrating the efficiency and usefulness of the proposed methods

properties of a bursting model with two slow inhibitory variables models for certain excitable cells such as the pancreatic beta cell must reproduce bursting oscillations of the membrane potential this has previously been done using one slow variable to drive bursts the dynamics of such models have been analyzed however new models for the beta cell often include additional slow variables and therefore the previous analysis is extended to two slow variables using a simplified version of a beta cell model some unusual time courses of this model motivated a geometric singular perturbation analysis and the application of averaging to reduce the dynamics to the slow variable phase plane a geometric understanding of the solutionstructure and of transitions between various modes of behavior was then developed a novel use of the bifurcation code auto finds nullclines for the slow variables when the fast variables are periodic by averaging over the fast oscillations in contrast with the parabolic neuronal burster this model requires bistability in th

how far 3d shapes can be understood from 2d silhouettes each 2d silhouette of a 3d unknown object o constrains o inside the volume obtained by back projecting the silhouette from the corresponding viewpoint a set of silhouettes specifies a boundary volume r obtained by intersecting the volumes due to each silhouette r more or less closely approximates o depending on the viewpoints and the object itself this approach to the reconstruction of 3d objects is usually referred to as volume intersection this correspondence addresses the problem of inferring the shape of the unknown object o from the reconstructed object r for doing this the author divides the points of the surface of r into hard points which belong to the surface of any possible object originating r and soft points which may or may not belong to o the author considers two cases in the first case r is the closest approximation of o which can be obtained from its silhouettes i e its visual hull in the second case r is a generic reconstructed object in both cases the author supplies necessary and sufficient conditions for a point to be hard and gives rules for computing the hard surfaces

state constrained optimal control of the three dimensional stationary navier stokes equations abstract in this paper an optimal control problem for the stationary navier stokes equations in the presence of state constraints is investigated existence of optimal solutions is proved and first order necessary conditions are derived the regularity of the adjoint state and the state constraint multiplier is also studied lipschitz stability of the optimal control state and adjoint variables with respect to perturbations is proved and a second order sufficient optimality condition for the case of pointwise state constraints is stated

continuous dependence of optimal control to controlled domain of actuator for heat equation abstract in this paper we consider continuous dependence of the optimal control with respect to the actuator domain which is varying as open subset in the spatial domain for a multi dimensional heat equation both time optimal control and norm optimal control problems are considered the reason behind combining these two problems together is that these two problems are actually equivalent the energy to be used to drive the system to target set in minimal time interval is actually the minimal energy of driving the system to target set in this minimal time interval and visa versa it is shown that both optimal control and optimal cost are continuous with respect to open controlled actuator domain under the lebesgue measure

an analysis of a phase field model of a free boundary a mathematical analysis of a new approach to solidification problems is presented a free boundary arising from a phase transition is assumed to have finite thickness the physics leads to a system of nonlinear parabolic differential equations existence and regularity of solutions are proved invariant regions of the solution space lead to physical interpretations of the interface a rigorous asymptotic analysis leads to the gibbs thompson condition which relates the temperature at the interface to the surface tension and curvature

analysis of a multistate control problem related to food technology this paper is concerned with an optimal control problem related to the determination of an optimal profile for the steam temperature into the autoclave along the processing of canned foods the problem studies a system coupling the evolution navier stokes equations with the heat transfer equation by natural convection the so called boussinesq equations and with the microorganisms removal equation the essential difficulties in the study of this multistate control problem arise from the lack of uniqueness for the solution of the state system here we obtain after a careful analysis of the problem mathematical formulation the uniqueness of part of the state and the existence of optimal solutions

semi discrete a priori error analysis for the optimal control of the unsteady navier stokes equations with variational multiscale stabilization in this work the optimal control problems of the unsteady navier stokes equations with variational multiscale stabilization vms are considered at first the first order continuous optimality conditions are obtained since the adjoint equation of the navier stokes problem is a convection diffusion type system then the same stabilization is applied to it semi discrete a priori error estimates are obtained for the state adjoint state and control variables crank nicholson time discretization is used to get the fully discrete scheme numerical examples verify the theoretical findings and show the efficiency of the stabilization for higher reynolds number

computing exact aspect graphs of curved objects algebraic surfaces this article presents an algorithm for computing the exact aspect graph of an opaque solid bounded by a smooth algebraic surface orthographic projection is assumed the algorithm is based on a catalog of visual events available from singularity theory it uses curve tracing cell decomposition homotopy continuation and ray tracing to construct the regions of the view sphere delineated by visual event curves the algorithm has been fully implemented and examples are presented

h control theory of fluid dynamics robust or h control theory has been an expanding subject in recent years because of its wide applications and its close connection to operator theory on hardy spaces we develop an hcontrol theor

h boundary control with state feedback the hyperbolic case we solve the h control problem with state feedback for infinite dimensional boundary control systems of hyperbolic type with distributed disturbances

real time object recognition in sparse range images using error surface embedding a novel object recognition algorithm is introduced to identify objects and recover their pose from sparse range data the method is based upon comparing the 7 d error surfaces of objects in various poses which result from the registration error function between two convolved surfaces the objects and their pose values are encoded by a small set of feature vectors extracted from the minima of the error surfaces the problem of object recognition is thus reduced to comparing these feature vectors to find the corresponding error surfaces between the runtime data and a preprocessed database the algorithm called potential well space embedding pwse has been implemented and tested on both simulated and real data the experimental results show the technique to be both effective and efficient executing at 122 frames per second on standard hardware and with recognition rates exceeding 97 for a database of 60 objects the performance of pwse on the large size database was also evaluated on the princeton shape benchmark containing 1 814 objects in addition it functions well with very sparse data possibly comprising only hundreds of points per image and is shown to be robust to measurement error and outliers with some small modifications we applied pwse to the problem of object class recognition in experiments with the princeton shape benchmark pwse is able to provides better classification rates than the previous methods in terms of nearest neighbour classification

pontryagin maximum principle for semilinear and quasilinearparabolic equations with pointwise state constraints this paper studies the first order necessary conditions for the optimal controls of semilinear and quasilinear parabolic partial differential equations with pointwise state constraints a pontryagin type maximum principle is obtained

the time optimal control of navier stokes equations the maximum principle for the time optimal control of the navier stokes equations in 2 d is established

state constrained optimal control problems governed by coupled nonlinear wave equations with memory this work considers the optimal control problems governed by coupled nonlinear wave equations with memory where the state constraint is a type of integral first we investigate the existence of the optimal solution for the optimal control problem and then we deduce the maximum principle for the optimal solution with state constraint moreover we give a concrete example which is covered by the main result

optimal control of semilinear parabolic equations with k approximate periodic solutions in this paper we study some optimal control problems governed by certain semilinear parabolic equations with mathcal k approximate periodic solutions we first prove the existence and uniqueness theorems for mathcal k approximate periodic solutions of the equations we then use these results to establish the qualified pontryagin maximum principle the existence for such optimal controls is also investigated in the paper

weak solutions of the time fractional navier stokes equations and optimal control abstract in this paper we deal with the navier stokes equations with the time fractional derivative of order 0 1 which can be used to simulate anomalous diffusion in fractal media we firstly give the concept of the weak solutions and establish the existence criterion of weak solutions by means of galerkin approximations in the case that the dimension n 4 moreover a complete proof of the uniqueness is given when n 2 at last we give a sufficient condition of optimal control pairs

optimal control of fluid dynamic systems with state constraint of pointwise type abstract the aim of this work is to obtain the maximum principle by spike perturbation for the optimal control problem with pointwise type state constraint governed by 3 dimensional fluid dynamic systems

optimal control of evolutionary quasi newtonian fluids we are interested in the necessary optimality conditions for optimal control problems of systems describing the unsteady flow of incompressible shear thickening fluids to overcome the difficulties related to the differentiability of the control to state mapping consequence of the lack of regularity of the state variable we first establish some intermediate optimality conditions and then pass to the limit

necessary optimality conditions for infinite dimensional state constrained control problems abstract this paper is concerned with first order necessary optimality conditions for state constrained control problems in separable banach spaces assuming inward pointing conditions on the constraint we give a simple proof of pontryagin maximum principle relying on infinite dimensional neighboring feasible trajectories theorems proved in 20 further we provide sufficient conditions guaranteeing normality of the maximum principle we work in the abstract semigroup setting but nevertheless we apply our results to several concrete models involving controlled pdes pointwise state constraints as positivity of the solutions are allowed

optimal control of the stationary navier stokes equations with mixed control state constraints in this paper we consider the distributed optimal control of the navier stokes equations in the presence of pointwise mixed control state constraints after deriving a first order necessary condition the regularity of the mixed constraint multiplier is investigated second order sufficient optimality conditions are studied as well in the last part of the paper a semismooth newton method is applied for the numerical solution of the control problem the convergence of the method is proved and numerical experiments are carried out

regularized state constrained boundary optimal control of the navier stokes equations abstract the numerical solution of the dirichlet boundary optimal control problem of the navier stokes equations in presence of pointwise state constraints is investigated two different regularization techniques are considered first a moreau yosida regularization of the problem is studied optimality conditions are derived and the convergence of the regularized solutions towards the original one is proved a source representation of the control combined with a lavrentiev type regularization strategy is also presented the analysis concerning optimality conditions and convergence of the regularized solutions is carried out in the last part of the paper numerical experiments are presented for the numerical solution of each regularized problem a semi smooth newton method is applied

the slow passage through a hopf bifurcation delay memory effects and resonance this paper explores analytically and numerically in the context of the fitzhugh nagumo model of nerve membrane excitability an interesting phenomenon that has been described as a delay or memory effect it can occur when a parameter passes slowly through a hopf bifurcation point and the system s response changes from a slowly varying steady state to slowly varying oscillations on quantitative observation it is found that the transition is realized when the parameter is considerably beyond the value predicted from a straightforward bifurcation analysis which neglects the dynamic aspect of the parameter variation this delay and its dependence on the speed of the parameter variation are described the model involves several parameters and particular singular limits are investigated one in particular is the slow passage through a low frequency hopf bifurcation where the system s response changes from a slowly varying steady state to slowly varying relaxation oscillations we find in this case the onset o

imperfect bifurcation with a slowly varying control parameter we consider a general class of imperfect bifurcation problems described by the following first order nonlinear differential equation y i ky p lambda t y delta where k 1 or 1 and p 2 or 3 are fixed quantities the solution depends on the values of the imperfection parameter delta 0 delta ll 1 and the time dependent control parameter lambda t lambda 0 varepsilon t and 0 varepsilon ll 1 if delta varepsilon 0 this equation admits at lambda 0 a bifurcation from the basic state y 0 to nonzero steady states in the first part of the paper we analyze the perturbation of the bifurcation solutions produced both by the small imperfection delta ne 0 and the slow variation of lambda varepsilon ne 0 we show that lambda 0 does not correspond to the transition between the two branches of slowly varying steady states this transition appears at a larger value of lambda lambda 1 provided that delta is sufficiently

dynamical systems analysis of the maasch saltzman model for glacial cycles abstract this article is concerned with the internal dynamics of a conceptual model proposed by maasch and saltzman 1990 to explain central features of the glacial cycles observed in the climate record of the pleistocene epoch it is shown that in most parameter regimes the long term system dynamics occur on certain intrinsic two dimensional invariant manifolds in the three dimensional state space these invariant manifolds are slow manifolds when the characteristic time scales for the total global ice mass and the volume of the north atlantic deep water are well separated and they are center manifolds when these characteristic time scales are comparable in both cases the reduced dynamics on these manifolds are governed by bogdanov takens singularities and the bifurcation curves associated to these singularities organize the parameter regions in which the model exhibits glacial cycles in addition knowledge of the reduced systems and their bifurcations is useful for understanding the effects of slowly varying parameters which cause passage through hopf bifurcations and of orbital milankovitch forcing both are central to the mechanism proposed by maasch and saltzman for the mid pleistocene transition in their model

sensitivity of inverse advection diffusion reaction to sensor and control a low computational cost tool a two dimensional 2d concentration field may be reconstructed using inverse advection diffusion reaction based on pointwise sensor outputs the studied reconstruction process consists in defining fictitious boundaries and identifying the optimal concentrations on these boundaries that minimize the data misfit the minimization is performed by means of the adjoint method the reconstruction process is observed to fail for some sets of sensor placements therefore in this paper we aim to develop a low computational cost framework that can be used to identify badly placed sensors and to reveal potentially optimal sensor placement from this framework we have derived a sensitivity tool that can predict for a given set of sensors which boundary concentrations are easy or difficult to identify using the inverse method this tool only requires the resolution of an adjoint problem it is compared with the sensitivity to observation method in a 2d water pipe junction with 2000 reynolds number and 1000 peclet number the compared methods do produce similar quantitative and qualitative results

on recognizing and positioning curved 3 d objects from image contours an approach for explicitly relating the shape of image contours to models of curved three dimensional objects is presented this relationship is used for object recognition and positioning object models consist of collections of parametric surface patches and their intersection curves this includes nearly all representations used in computer aided geometric design and computer vision the image contours considered are the projections of surface discontinuities and occluding contours elimination theory provides a method for constructing the implicit equation of these contours for an object observed under orthographic or perspective projection this equation is parameterized by the object s position and orientation with respect to the observer determining these parameters is reduced to a fitting problem between the theoretical contour and the observed data points the proposed approach readily extends to parameterized models it has been implemented for a simple world composed of various surfaces of revolution and tested on several real images

necessary and sufficient conditions for optimal controls in viscous flow problems a class of optimal control problems in viscous flow is studied main results are the pontryagin maximum principle and the verification theorem for the hamilton jacobi bellman equation characterising the feedback problem the maximum principle is established by two quite different methods

optimal boundary control for the evolutionary navier stokes system the three dimensional case optimal boundary control problems for the three dimensional evolutionary navier stokes equations in the exterior of a bounded domain are studied control is effected through the dirichlet boundary condition and is sought in a subset of the trace space of velocity fields with almost minimal possible regularity the control objective is to minimize the drag functional the existence of an optimal solution is proved a strong form of an optimality system of equations is derived on the basis of regularity results established in this work for the adjoint oseen equations with regular initial data which do not satisfy the compatibility conditions

a dissipative feedback control synthesis for systems arising in fluid dynamics a dissipative feedback control synthesis is constructed to regulate the systems arising in fluid dynamics the feedback law is obtained by utilizing nonlinear dynamic programming techniques the control law is designed for driving the system to a prescribed equilibrium state and enhancing the energy dissipation effects of the dynamical system two dimensional navier stokes equations and burgers equation are used for numerical experiments to illustrate the effects of the feedback synthesis and the theoretical results

the velocity tracking problem for navier stokes flows with boundary control we present some systematic approaches to the mathematical formulation and numerical approximation of the time dependent optimal control problem of tracking the velocity for navier stokes flows in a bounded two dimensional domain with boundary control we study the existence of optimal solutions and derive an optimality system from which optimal solutions may be determined we also define and analyze semidiscrete in time and full space time discrete approximations of the optimality system and a gradient method for the solution of the fully discrete system the results of some computational experiments are provided

necessary conditions for optimal control of distributed parameter systems the ekeland variational principle is used to prove a maximum principle for the optimal controls of a general semilinear evolutionary control system in a banach space with strictly convex dual the boundary constraint is of general type which includes the optimal periodic control problem as a special case

constrained optimal control of navier stokes flow by semismooth newton methods abstract we propose and analyze a semismooth newton type method for the solution of a pointwise constrained optimal control problem governed by the time dependent incompressible navier stokes equations the method is based on a reformulation of the optimality system as an equivalent nonsmooth operator equation we analyze the flow control problem and prove q superlinear convergence of the method in the numerical implementation adjoint techniques are combined with a truncated conjugate gradient method numerical results are presented that support our theoretical results and confirm the viability of the approach

a fundamental limit on the heat flux in the control of incompressible channel flow this paper proves that there are no zero net wall transpiration control strategies that can sustain net heat flux below the laminar level in an incompressible channel flow with constant temperature walls the result represents a fundamental limit on the performance of a controlled nonlinear system as measured by a linear cost function over a broad class of admissible initial conditions and control inputs not a zero sum tradeoff in the frequency domain or time domain both buoyancy effects via the boussinesq approximation and viscous heating effects are accounted for and phenomenological justification for the result is also given the boundedness of solutions of the two way coupled navier stokes energy equations when both buoyancy and viscous heating are accounted for is also discussed and a new proof of existence under an appropriate small data assumption is provided

flow invariance preserving feedback controllers for the navier stokes equation abstract in this paper we develop a concrete procedure for designing feedback controllers to ensure that the resultant dynamics of turbulence will preserve certain prescribed physical constraints examples of such constraints include in particular the level sets of well known invariants of the inviscid flow such as helicity we also bring to light a certain m accretivity property of suitable quantization of the nonlinearity in the navier stokes equation and utilize the theory of nonlinear semigroups to resolve the controlled navier stokes inclusion with a multi valued feedback term

computing the visual hull of solids of revolution abstract the visual hull vh s v of an object s relative to a viewing region v is a geometric entity useful for silhouette based image understanding for instance two objects can be distinguished from their silhouettes only if their visual hulls are different an object can be exactly reconstructed from its silhouettes only if equal to its visual hull the visual hull idea also allows to define a measure of the reconstruction accuracy of an object from its silhouettes there are two main cases of visual hull the internal visual hull if v is only bounded by s and the external visual hull if v is bounded by the convex hull of s this paper addresses the problem of computing both visual hulls of solids of revolution two cases are considered smooth polynomial and piecewise linear generators the algorithm has been implemented for the latter case the surface of the visual hulls when it is not coincident with the surface of s turns out to consist of segments of cones annular rings and hyperboloids of one sheet

matrix free methods for the stability and control of boundary layers this paper presents matrix free methods for the stability analysis and control design of high dimensional systems arising from the discretized linearized navier stokes equations the methods are ap

pontryagin s maximum principle for optimal control of the stationary navier stokes equations this paper deals with pontryagin s maximum principle of the optimal control governed by stationary navier stokes equation some kind of state constraint is involved

pontryagin maximum principle of optimal control governed by fluid dynamic systems with two point boundary state constraint over all y u y mad 0 t u subject to the semilinear equation y t ay t by t du t f t a e t 0 t 1 1 with state constraint y 0 y t s 1 2 the following hypotheses will be e9ective throughout this paper h1 v and h are real hilbert spaces with norms and moreover v h v algebraically and topologically with compact injections where v denotes the dual of

periodic optimal control of the boussinesq equation this paper is concerned with the existence and the maximum principle for the optimal control problem governed by the boussinesq equation the case of internal controllers supported on is examined

optimal control problems with state constraint governed by navier stokes equations abstract this work deals with the existence of optimal solution and the maximum principle for optimal control problem governed by navier stokes equations with state constraint of pointwise type in 3d strong results in 2d are also given

optimal control of parabolic differential equations with two point boundary state constraints this paper deals with the necessary conditions of optimality for some optimal control problems governed by some parabolic differential equations involving monotone graphs the two point boundary time variable state constraints are discussed some analyses on the state equations are given

optimal controls of multidimensional modified swift hohenberg equation in this paper we deal with the optimal control problem governed by multidimensional modified swift hohenberg equation after showing the relationship between the control problem and its approximation we derive the optimality conditions for an optimal control of our original problem by using one of the approximate problems

h_ infty boundary control with state feedback the hyperbolic case necessary and sufficient conditions of existence for the h infty control problem associated with infinite dimensional boundary control systems of hyperbolic type are given

nonexistence and existence results of an optimal control problem governed by a class of multisolution semilinear elliptic equations abstract an optimal control problem governed by a class of multisolution semilinear elliptic equations is studied in this paper it is pointed out that the control domain and cost functional are nonconvex by analyzing the maximum condition for an optimal relaxed control one nonexistence and some existence results of an optimal pair are obtained the idea of using relaxed controls is mainly derived from the paper lou 2007 by lou where a linear and well posed controlled system was considered the present paper is mainly devoted to discussing the case not contained in lou 2007

pontryagin s principle for state constrained boundary control problems of semilinear parabolic equations this paper deals with state constrained optimal control problems governed by semilinear parabolic equations we establish a minimum principle of pontryagin s type to deal with the state constraints we introduce a penalty problem by using ekeland s principle the key tool for the proof is the use of a special kind of spike perturbations distributed in the domain where the controls are defined conditions for normality of optimality conditions are given

the geometry of view space of opaque objects bounded by smooth surfaces abstract a view of a smooth opaque object is a line drawing consisting of contour fragments which form closed loops terminate or form t junctions given a compact object we have a global decomposition of the space of camera positions into cells from which topologically equivalent views are obtained to apply certain image based object recognition techniques based on characteristic views of an object one needs to know this cellular decomposition of view space the boundaries of such cells of stable views are formed by the view bifurcation set from which transitional degenerate views are seen we derive a finite list of geometrical models of the view bifurcation set the view bifurcation set of any particular object is a combination of such model surfaces from this list to match a characteristic view with an image one has to find the visible fragments of the apparent contour in the image and we briefly describe an observation which might lead to an algorithm for finding such contour fragments

the enumerative geometry of projective algebraic surfaces and the complexity of aspect graphs the aspect graph is a popular viewer centered representation that enumerates all the topologically distinct views of an object building the aspect graph requires partitioning viewpoint space in view equivalent cells by a certain number of visual event surfaces if the object is piecewise smooth algebraic then all visual event surfaces are either made of lines having specified contacts with the object or made of lines supporting the points of contacts of planes having specified contacts with the object in this paper we present a general framework for studying the enumerative properties of line and plane systems the context is that of enumerative geometry and intersection theory in particular we give exact results for the degrees of all visual event surfaces coming up in the construction of aspect graphs of piecewise smooth algebraic bodies we conclude by giving a bound on the number of topologically distinet views of such objects

the visual hull concept for silhouette based image understanding many algorithms for both identifying and reconstructing a 3 d object are based on the 2 d silhouettes of the object in general identifying a nonconvex object using a silhouette based approach implies neglecting some features of its surface as identification clues the same features cannot be reconstructed by volume intersection techniques using multiple silhouettes of the object this paper addresses the problem of finding which parts of a nonconvex object are relevant for silhouette based image understanding for this purpose the geometric concept of visual hull of a 3 d object is introduced this is the closest approximation of object s that can be obtained with the volume intersection approach it is the maximal object silhouette equivalent to s i e which can be substituted for s without affecting any silhouette only the parts of the surface of s that also lie on the surface of the visual hull can be reconstructed or identified using silhouette based algorithms the visual hull depends not only on the object but also on the region allowed to the viewpoint two main viewing regions result in the external and internal visual hull in the former case the viewing region is related to the convex hull of s in the latter it is bounded by s the internal visual hull also admits an interpretation not related to silhouettes algorithms for computing visual hulls are presented and their complexity analyzed in general the visual hull of a 3 d planar face object turns out to be bounded by planar and curved patches

stability enhancement by boundary control in 2 d channel flow in this paper we stabilize the parabolic equilibrium profile in a two dimensional 2 d channel flow using actuators and sensors only at the wall the control of channel flow was previously considered by speyer and coworkers and bewley and coworkers who derived feedback laws based on linear optimal control and implemented by wall normal actuation with an objective to achieve global lyapunov stabilization we arrive at a feedback law using tangential actuation using teamed pairs of synthetic jets or rotating disks and only local measurements of wall shear stress allowing to embed the feedback in microelectromechanical systems mems hardware without need for wiring this feedback is shown to guarantee global stability in at least h sup 2 norm which by sobolev s embedding theorem implies continuity in space and time of both the flow field and the control as well as their convergence to the desired steady state the theoretical results are limited to low values of reynolds number however we present simulations that demonstrate the effectiveness of the proposed feedback for values five order of magnitude higher

optimal control of semilinear parabolic systems with state constraint abstract the aim of this work is to obtain the existence of optimal solution and maximum principle for optimal control problem with pointwise type state constraint governed by semilinear parabolic systems with certain polynomial like nonlinearity application to optimal control problems of the phase transition system is given