ellipsoidal parameter or state estimation under model uncertainty ellipsoidal outer bounding of the set of all feasible state vectors under model uncertainty is a natural extension of state estimation for deterministic models with unknown but bounded state perturbations and measurement noise the technique described in this paper applies to linear discrete time dynamic systems it can also be applied to weakly non linear systems if non linearity is replaced by uncertainty many difficulties arise because of the non convexity of feasible sets combined quadratic constraints on model uncertainty and additive disturbances are considered in order to simplify the analysis analytical optimal or suboptimal solutions of the basic problems involved in parameter or state estimation are presented which are counterparts in this context of uncertain models to classical approximations of the sum and intersection of ellipsoids the results obtained for combined quadratic constraints are extended to other types of model uncertainty

robustness in the presence of mixed parametric uncertainty and unmodeled dynamics continuing the development of the structured singular value approach to robust control design the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty the problem is shown to be equivalent to a smooth constrained finite dimensional optimization problem in view of the fact that the functional to be maximized may have several local extrema an upper bound on mu whose computation is numerically tractable is established this leads to a sufficient condition of robust stability and performance a historical perspective on the development of the mu theory is included

minimizing euclidian state estimation error for linear uncertain dynamic systems based on multisensor and multi algorithm fusion in this paper a multisensor linear dynamic system with model uncertainty and bounded noises is considered based on previously developed set valued estimation methods in terms of convex optimization we propose several efficient algorithms of centralized sensor fusion distributed sensor fusion and multi algorithm fusion to minimize the euclidian estimation error of the state vector obviously an ellipsoid box with a larger size cannot be in general guaranteed to contain another ellipsoid box with a smaller size since centers and shapes of the two ellipsoids boxes may be different from each other this fact and the complementary advantages of multiple sensors and multiple algorithms motivate us to construct multiple estimation ellipsoids boxes squashed along each entry of the state vector as much as possible respectively by using the technique of multiple differently weighted objectives then intersection fusion of these estimation ellipsoids boxes yields a final euclidian error minimized state estimate numerical examples show that the new method with multi algorithm at both the sensors and the fusion center can significantly reduce the euclidian estimation error of the state

finite element methods principles for their selection abstract principles for the selection of a finite element method for a particular problem are discussed these principles are stated in terms of the notion of approximability optimality and stability several examples are discussed in detail as illustrations conclusions regarding the selection of finite element methods are summarized in the final section of the paper

optimal linear estimation fusion i unified fusion rules this paper deals with data or information fusion for the purpose of estimation three estimation fusion architectures are considered centralized distributed and hybrid a unified linear model and a general framework for these three architectures are established optimal fusion rules based on the best linear unbiased estimation blue the weighted least squares wls and their generalized versions are presented for cases with complete incomplete or no prior information these rules are more general and flexible and have wider applicability than previous results for example they are in a unified form that is optimal for all of the three fusion architectures with arbitrary correlation of local estimates or observation errors across sensors or across time they are also in explicit forms convenient for implementation the optimal fusion rules presented are not limited to linear data models illustrative numerical results are provided to verify the fusion rules and demonstrate how these fusion rules can be used in cases with complete incomplete or no prior information

a game theory approach to robust discrete time h sub spl infin estimation the deterministic robust estimation problem is formulated in the discrete time case as a zero sum two person difference game in which a statistician plays against nature the statistician tries to estimate a linear combination of the states of an uncertain linear system which is driven by nature saddle point strategies for the statistician in the above game are difficult to find a suboptimal strategy is therefore considered which guarantees an h sub spl infin performance bound on the estimation error different patterns of the information that is available to the statistician are treated and the corresponding fixed point fixed lag and fixed interval smoothing strategies are derived

on the value of information in system identification bounded noise case assuming instantaneous bounds on the noise system parameter identification is formulated as membership set estimation problem sequential algorithms are constructed to estimate the membership sets of the parameters which are consistent with the measurements and the noise constraints the important new feature of the proposed algorithms is their ability to ignore redundant data the efficient data extraction property of the new algorithms is achieved with small computational effort and with improved performance when compared to the least square algorithm the convergence properties and the notion of identifiability in the set theoretic context are also studied

spectral tau approximation of the two dimensional stokes problem we analyse the spectral tau method for the approximation of the stokes system on a square with dirichlet boundary conditions we provide an error estimate in the norm of the sobolev spaceh s for the approximation of a divergence free vector field with polynomial divergence free vector fields we apply this result to prove some convergence estimates for the solution of the discrete stokes problem

ellipsoidal bounds for uncertain linear equations and dynamical systems abstract in this paper we discuss semidefinite relaxation techniques for computing minimal size ellipsoids that bound the solution set of a system of uncertain linear equations the proposed technique is based on the combination of a quadratic embedding of the uncertainty and the s procedure this formulation leads to convex optimization problems that can be essentially solved in o n3 n being the size of unknown vector by means of suitable interior point barrier methods as well as to closed form results in some particular cases we further show that the uncertain linear equations paradigm can be directly applied to various state bounding problems for dynamical systems subject to set valued noise and model uncertainty

p version of mixed finite element methods for stokes like problems abstract we investigate various sample extremum saddle point and minimization problems from the point of view of stability of increasing order mixed finite element methods problems discussed include the stokes poisson and linear elasticity problems

fluid flow over a nonlinearly stretching sheet numerical solutions are obtained for a class of nonlinear third order differential equations arising in fluid flows over a nonlinearly stretching sheet using a similarity transformation which is different from that of the linearly stretching sheet problem furthermore using the schauder theory existence of a solution of the third order differential equation over a large but finite interval is established moreover the analytical solutions are obtained and are compared with the corresponding numerical solutions the results obtained for the flow characteristics reveal many interesting behaviors that warrant further study of the effects of nonlinear stretching on the flow characteristics

set valued observers and optimal disturbance rejection a set valued observer also called guaranteed state estimator produces a set of possible states based on output measurements and models of exogenous signals we consider the guaranteed state estimation problem for linear time varying systems with a priori magnitude bounds on exogenous signals we provide an algorithm to propagate the set of possible states based on output measurements and show that the centers of these sets provide optimal estimates in an l sup spl infin induced norm sense we then consider the utility of set valued observers for disturbance rejection with output feedback and derive the following general separation structure an optimal controller can consist of a set valued observer followed by a static nonlinear function on the observed set of possible states a general construction of this function is provided in the scalar control case furthermore in the special case of full control i e the number of control inputs equals the number of states optimal output feedback controllers can take the form of an optimal estimate of the full state feedback controller

viscous flow over a nonlinearly stretching sheet an analysis is carried out to study the flow and heat transfer characteristics in a viscous fluid over a nonlinearly stretching sheet the equations of conservation of momentum mass and energy which govern the flow and heat transfer are partially decoupled using a similarity transformation which is different from that of the linearly stretching sheet problem however the results for the linearly stretching sheet problem can be obtained as a special case the basic nonlinear differential equation for the velocity field f and the differential equation with variable coefficient for the temperature field q are solved numerically by using a fourth order runge kutta integration scheme the numerical results thus obtained for the flow and heat transfer characteristics are presented by a table and graphs furthermore it is shown that the heat flow is always from the stretching sheet to the fluid

robust filtering for discrete time systems with bounded noise and parametric uncertainty this note presents a new approach to finite horizon guaranteed state prediction for discrete time systems affected by bounded noise and unknown but bounded parameter uncertainty our framework handles possibly nonlinear dependence of the state space matrices on the uncertain parameters the main result is that a minimal confidence ellipsoid for the state consistent with the measured output and the uncertainty description may be recursively computed in polynomial time using interior point methods for convex optimization with n states l uncertain parameters appearing linearly in the state space matrices with rank one matrix coefficients the worst case complexity grows as o l n l sup 3 5 with unstructured uncertainty in all system matrices the worst case complexity reduces to o n sup 3 5

on computing the pressure by thep version of the finite element method for stokes problem this paper introduces and analyzes two ways of extracting the hydrostatic pressure when solving stokes problem using thep version of the finite element method when one uses a localh 1 projection we show that optimal rates of convergence for the pressure approximation is achieved when the pressure is not inh 1 or the value of the pressure is only needed at a few points one may extract the pressure pointwise using e g a single layer potential recovery negative zero and higher norm estimates for the stokes velocity are derived within the framework of thep version of the f e m

state bounding with ellipsoidal set description of the uncertainty the paper presents recursive algorithms for state bounding using ellipsoidal sets to describe the state uncertainties and to bound the process and observation noises the algorithms optimize each stage of updating according to the minimum volume and minimum trace criteria simulations compare the performance of the bounding algorithms with that of a kalman filter and investigate the influence of noise distribution within the bounds

on a certain boundary value problem arising in shrinking sheet flows abstract this paper presents an analysis of the boundary value problem resulting from the magnetohydrodynamic mhd viscous flow influenced by a shrinking sheet with suction for the cases of two dimensional m 1 and axisymmetric m 2 shrinking the influences of the parameter m as well as the effects of suction parameter s and hartmann number m 2 on similar entrainment velocity f and flow characteristics are studied to this purpose the resulting nonlinear ordinary differential equation is solved numerically using the 4th order runge kutta method in combination with a shooting procedure the obtained results elucidate reliability and efficiency of the technique from which interesting features between the skin friction coefficient f 0 and the entrainment velocity f as function of the mass transfer parameter s can also be obtained

on equivalence of major relaxation methods for minimum ellipsoid covering intersection of ellipsoids abstract this paper investigates the problem on the minimum trace or volume ellipsoid covering intersection of ellipsoids this problem can be solved by three major relaxation methods involving semi definite programming relaxation s procedure relaxation and parameterized bounding ellipsoid relaxation they are proposed from the different ideas or viewpoints so that it is difficult to judge which relaxation method is the most suitable for the different practical implementations to the best of our knowledge the problem of proving the convexity of the optimization problem derived by the third relaxation method remains open by rigorous analysis we reveal the equivalence among the three relaxation methods and address the open problem i e the optimization problem derived by the third relaxation method can be equivalently transformed to a convex optimization problem the computation complexity of these relaxation methods are also discussed and the equivalent result is helpful to set membership filter and multisensor fusion obtaining a tighter ellipsoid to contain the state with lower computation complexity finally the performance of each method is evaluated by several typical numerical examples in information fusion and filtering

viscous flow and heat transfer over a nonlinearly stretching sheet this paper presents a numerical analysis for flow and heat transfer in a viscous fluid over a nonlinear stretching sheet by employing a novel numerical procedure and two cases are studied namely i the sheet with constant surface temperature cst case and ii the sheet with prescribed surface temperature pst case the governing partial differential equations are converted into highly nonlinear ordinary differential equations by a similarity transformation the variations of dimensionless surface temperature dimensionless surface temperature gradient as well as flow and heat transfer characteristics with the governing parameters are graphed and tabulated

exact recursive polyhedral description of the feasible parameter set for bounded error models a method is described which exactly characterizes the set of all the values of the parameter vector of a linear model that are consistent with bounded errors on the measurements it provides a parameterized expression of this set which can be used for robust control design or for optimizing any criterion over the set this approach is based on a new variant of the double description method for determining the edges of a polyhedral cone it can be used in real time and provides a suitable context for implementation on a computer whenever a new measurement modifies the set the characterization is updated the technique is illustrated with a simple example

analysis of some mixed finite element methods related to reduced integration we prove error estimates for the following two mixed finite element methods related to reduced integration a method for stokes problem using rectangular elements with piecewise bilinear approximations for the velocities and piecewise constants for the pressure and one method for a plate problem using bilinear approximations for transversal displacement and rotations and piecewise constants for the shear stress the main idea of the proof in the case of stokes problem is to combine a weak babuska brezzi type stability estimate for the pressure with a superapproximability property for the velocities a similar technique is used in the case of the plate problem