application of sobolev gradient method to poisson boltzmann system the idea of a weighted sobolev gradient introduced and applied to singular differential equations in 1 is extended to a poisson boltzmann system with discontinuous coefficients the technique is demonstrated on fully nonlinear and linear forms of the poisson boltzmann equation in one two and three dimensions in a finite difference setting a comparison between the weighted gradient and fas multigrid is given for large jump size in the coefficient function

on the stability proof of adaptive schemes with static normalizing signals and parameter projection it has been shown previously that robust stability in model reference adaptive control mrac is guaranteed by simply using a static instead of a dynamic normalizing signal together with a parameter projection in the adaptive law it is shown here that the stability proof associated with such modification follows directly from the proof of schemes with dynamic normalization consequently the proofs and stability arguments can be simplified considerably

sobolev preconditioning for the poisson boltzmann equation abstract this paper presents an overview of least squares steepest descent using sobolev gradients for several prototype differential equations in the linear case the method is viewed as a very effective preconditioning strategy for the basic iterative method which arises from steepest descent in particular it acts to smooth the euclidean gradient results are given for the one dimensional possion boltzmann equation from semiconductor device modeling

energy minimization related to the nonlinear schrodinger equation in this the window of the sobolev gradient technique to the problem of minimizing a schrodinger functional associated with a nonlinear schrodinger equation we show that gradients act in a suitably chosen sobolev space sobolev gradients can be used in finite difference and finite element settings in a computationally efficient way to find minimum energy states of schrodinger functionals

robust redesign of adaptive control effects of unmodeled high frequency dynamics on stability and performance of adaptive control schemes are analyzed in the regulation problem global stability properties are no longer guaranteed but a region of attraction exists for exact adaptive regulation the dependence of the region of attraction on unmodeled parasitics is examined first then the general case of model reference adaptive control is considered in which parasitics can destroy stability and boundedness properties a modified adaptive law is proposed guaranteeing the existence of a region of attraction from which all signals converge to a residual set which contains the equilibrium for exact tracking the size of this set depends on design parameters the frequency range of parasitics and the reference input signal characteristics

energy minimization using sobolev gradients application to phase separation and ordering a common problem in physics and engineering is the calculation of the minima of energy functionals the theory of sobolev gradients provides an efficient method for seeking the critical points of such a functional we apply the method to functionals describing coarse grained ginzburg landau models commonly used in pattern formation and ordering processes

on the robustness of output feedback control methods to modeling errors singular perturbation analysis is employed to study the robustness of output feedback control schemes for linear time invariant systems the effect of designing the control strategy using a model that neglects unknown parasitic elements is considered it is shown that such a strategy may in general be destabilizing even when the neglected modes are asymptotically stable special structures that will not permit this situation and will guarantee asymptotic stability are illustrated

sobolev gradient approach for the time evolution related to energy minimization of ginzburg landau functionals the sobolev gradient technique has been discussed previously in this journal as an efficient method for finding energy minima of certain ginzburg landau type functionals s sial j neuberger t lookman a saxena energy minimization using sobolev gradients application to phase separation and ordering j comput phys 189 2003 88 97 in this article a sobolev gradient method for the related time evolution is discussed

approximate solutions to poisson boltzmann systems with sobolev gradients a weighted sobolev gradient approach 1 is presented to a nonlinear pbe 2 with discontinuous coefficient functions a comparison is given between the weighted and unweighted sobolev gradient in the finite element setting in two and three dimensions behavior of the various sobolev gradients is discussed for large jump size in the coefficient a comparison with newton s method is given where the failure of newton s method is demonstrated for a test problem

unmodeled dynamics in adaptive control systems revisited an alternative approach to analyze the robustness of adaptive systems with respect to unmodeled dynamics and external disturbances is presented this approach shows that certain restrictive assumptions needed earlier can in fact be discarded it also shows that an adaptation algorithm based on a time varying factor equivalent to a constant factor together with projection can provide a globally asymptotically stable system with respect to a compact residual set under mild requirements

on adaptive state regulation an indirect adaptive state regulator consisting of an adaptive observer and an asymptotic feedback matrix synthesis is discussed in a rigorous analysis lyapunov stability of the resulting closed loop system without the need for external excitation possible global instabilities as well as global convergence subject to sufficient excitation are shown moreover the behavior of the closed loop system is analyzed for cases in which the true plant differs from the assumed linear time invariant model in that it is of higher order contains slight nonlinearities and time variation effects and is subject to plant and measurement disturbances

some remarks on vanishing theorems for holomorphic vector bundles this theorem generalizes kodaira s vanishing theorem 13 and has found a number of geometric applications 2 19 griffiths proof uses method ii above doing curvature calculations for line bundles then the object of this note is to reduce theorem g directly to the kodaira vanishing theorem answering a question of viehweg during the complex analysis meeting in oberwolfach 1982 thus avoiding any curvature calculation this proof has the further advantage that one obtains better results let us state as a sample

vanishing theorems for ample vector bundles the main result of this article is a general vanishing theorem for the cohomology of tensorial representations of an ample vector bundle on a smooth complex projective variety in particular we extend classical theorems of griffiths and le potier to the whole dolbeault cohomology prove a variant of an uncorrect conjecture of sommese and answer a question of demailly as an application we prove conjectures of debarre and kim for branched coverings of grassmannians and extend a well known barth lefschetz type theorem for branched covers of projective spaces due to lazarsfeld we also obtain new restriction theorems for certain degeneracy loci

brief paper stability analysis of adaptively controlled systems subject to bounded disturbances an approach for studying stability of adaptively controlled systems subject to bounded disturbances with unknown statistics is given a shorter proof of some results established for minimum phase systems is also given new results are established for nonminimum phase systems in each case the uniform boundedness of all signals is proven under a condition that is discussed examples of adaptive schemes that can be treated with this approach are given

an asymptotic error analysis of identifiers and adaptive observers in the presence of parasitics the behavior of identifiers and adaptive observers in the presence of parasitics is analyzed bounds for the state parameter error are established the adaptive schemes considered are shown to be robust provided the input signal is rich for the dominant modes but does not contain high frequencies in the parasitic range the bounds indicate possibilities for reducing the error by a proper choice of the input signal

numerical solution of burgers equation by the sobolev gradient method abstract burgers equation is solved numerically with sobolev gradient methods a comparison is shown with other numerical schemes presented in this journal such as modified adomian method mam 1 and by a variational method vm which is based on the method of discretization in time 2 it is shown that the sobolev gradient methods are highly efficient while at the same time retaining the simplicity of steepest descent algorithms

optical tomography reconstruction algorithm with the finite element method an optimal approach with regularization tools optical tomography is mathematically treated as a non linear inverse problem where the optical properties of the probed medium are recovered through the minimization of the errors between the experimental measurements and their predictions with a numerical model at the locations of the detectors according to the ill posed behavior of the inverse problem some regularization tools must be performed and the tikhonov penalization type is the most commonly used in optical tomography applications this paper introduces an optimized approach for optical tomography reconstruction with the finite element method an integral form of the cost function is used to take into account the surfaces of the detectors and make the reconstruction compatible with all finite element formulations continuous and discontinuous through a gradient based algorithm where the adjoint method is used to compute the gradient of the cost function an alternative inner product is employed for preconditioning the reconstruction algorithm moreover appropriate re parameterization of the optical properties is performed these regularization strategies are compared with the classical tikhonov penalization one it is shown that both the re parameterization and the use of the sobolev cost function gradient are efficient for solving such an ill posed inverse problem

numerical approximation of time evolution related to ginzburg landau functionals using weighted sobolev gradients sobolev gradients have been discussed in sial et al 2003 as a method for energy minimization related to ginzburg landau functionals in this article a weighted sobolev gradient approach for the time evolution of a ginzburg landau functional is presented for different values of k a comparison is given between the weighted and unweighted sobolev gradients in a finite element setting it is seen that for small values of k the weighted sobolev gradient method becomes more and more efficient compared to using the unweighted sobolev gradient a comparison with newton s method is given where the failure of newton s method is demonstrated for a test problem

paper instability analysis and improvement of robustness of adaptive control the effects of unmodeled high frequency dynamics and bounded disturbances on stability and performance of adaptive control schemes are analyzed five possible types of instability mechanisms parameter drift linear instability fast adaptation instability high frequency instability and throughput instability are analyzed using simple examples a procedure is used to construct lyapunov like functions for a modified adaptive controller applied to a dominant plant of relative degree one in the presence of parasitics and disturbances and obtain sufficient conditions under which none of the five types of instability can occur the modified scheme is robust in the sense that it guarantees the existence of a large region of attraction from which all the trajectories remain bounded and the state errors converge exponentially to a much smaller residual set the size of the region of attraction depends on the speed of parasitics in such a way that as the parasitics become infinitely fast the region of attraction becomes the whole space

stable model reference adaptive control in the presence of bounded disturbances the adaptive control of a linear time invariant plant in the presence of bounded disturbances is considered in addition to the usual assumptions made regarding the plant transfer function it is also assumed that the high frequency gain k p of the plant and an upper bound on the magnitude of the controller parameters are known under these conditions the adaptive controller suggested assures the boundedness of all signals in the overall system

new approach to robust model reference adaptive control for a class of plants motivated by recent advances in designing robust adaptive controllers and in dealing with uncertain dynamical systems a new model reference adaptive control which is robust to a class of unmodelled dynamics and bounded output disturbances in the case of relative degree one is presented the implementation of the controllers includes a switching mechanism which plays a crucially important role in functions of stabilizing as well as tracking it is shown that global stability of the overall system is achieved under no assumption of persistency of excitation and tracking errors will converge to a residual set whose size can be directly related to the size of unmodelled dynamics and of output disturbances explicitly in the ideal case the residual set degenerates to a single null point and convergence can be achieved in finite time without any requirement of persistency of excitation