fake algebraic riccati techniques and stability conditions sufficient and necessary for monotonic behavior of the solutions of the riccati differential equation and riccati difference equation are derived for the optimal filtering respectively control equation these results are derived without the usual requirement of detectability respectively stabilizability the monotonic behavior allows proof of stabilizing properties of the solutions subject only to requirements on the initial conditions

maximal versus strong solution to algebraic riccati equations arising in infinite markov jump linear systems abstract we deal with a perturbed algebraic riccati equation in an infinite dimensional banach space which appears for instance in the optimal control problem for infinite markov jump linear systems from now on imjls infinite or finite here has to do with the state space of the markov chain being infinite countable or finite see e g m d fragoso j baczynski optimal control for continuous time lq problems with infinite markov jump parameters siam j control optim 40 1 2001 270 297 by using a certain concept of stochastic stability a sort of l 2 stability we have proved in j baczynski m d fragoso maximal solution to algebraic riccati equations linked to infinite markov jump linear systems internal report lncc no 6 2006 existence and uniqueness of maximal solution for this class of equations as it is noticed in this paper unlike the finite case including the linear case we cannot guarantee anymore that maximal solution is a strong solution in this setting via a discussion on the main mathematical hindrance behind this issue we devise some mild conditions for this implication to hold specifically our main result here is that under stochastic stability along with a condition related with convergence in the infinite dimensional scenario and another one related to spectrum weaker than spectral continuity we ensure the maximal solution to be also a strong solution these conditions hold trivially in the finite case allowing us to recover the result of strong solution of c e de souza m d fragoso on the existence of maximal solution for generalized algebraic riccati equations arising in stochastic control systems control lett 14 1990 233 239 set for mjls the issue of whether the convergence condition is restrictive or not is brought to light and together with some counterexamples unveil further differences between the finite and the infinite countable case

analysis of continuous time kalman filtering under incorrect noise covariances abstract the behavior of the continuous time kalman filter under incorrect noise covariances is analyzed the filter performance is quantified by the actual state error covariance through this quantity the characteristic of the filter is examined convergence and divergence analyses of the actual state error covariance are given the significance of the results presented in the paper is that they help one to understand and be able to predict certain behavior of the kalman filter when inexact values of noise covariances are used

convergence properties of the riccati difference equation in optimal filtering of nonstabilizable systems this paper studies the convergence and properties of the solutions of the riccati difference equation special emphasis is given to systems which are not necessarily stabilizable in the filtering sense particularly those having uncontrollable roots on the unit circle besides generalizing and unifying previous work the results have application to a number of important problems including filtering and control of systems with purely deterministic disturbances such as sinusoids and drift components

criterion for the convergence of the solution of the riccati differential equation the optimal control problem for a linear system with a quadratic cost function leads to the matrix riccati differential equation the convergence of the solution of this equation for increasing time interval is investigated as a function of the final state penalty matrix a necessary and sufficient condition for convergence is derived for stabilizable systems even if the output in the cost function is not detectable an algorithm is developed to determine the limiting value of the solution which is one of the symmetric positive semidefinite solutions of the algebraic riccati equation examples for convergence and nonconvergence are given a discussion is also included of the convergence properties of the solution of the riccati differential equation to any real symmetric not necessarily positive semidefinite solution of the algebraic riccati equation

an optimization approach for minimum norm and robust partial quadratic eigenvalue assignment problems for vibrating structures the partial quadratic eigenvalue assignment problem pqevap concerns the reassignment of a small number of undesirable eigenvalues of a quadratic matrix pencil while leaving the remaining large number of eigenvalues and the corresponding eigenvectors unchanged the problem arises in controlling undesirable resonance in vibrating structures and in stabilizing control systems the solution of this problem requires computations of a pair of feedback matrices for practical effectiveness these feedback matrices must be computed in such a way that their norms and the condition number of the closed loop eigenvector matrix are as small as possible these considerations give rise to the minimum norm partial quadratic eigenvalue assignment problem mnpqevap and the robust partial quadratic eigenvalue assignment problem rpqevap respectively in this paper we propose new optimization based algorithms for solving these problems the problems are solved directly in a second order setting without resorting to a standard first order formulation so as to avoid the inversion of a possibly ill conditioned matrix and the loss of exploitable structures of the original model the algorithms require the knowledge of only the open loop eigenvalues to be replaced and their corresponding eigenvectors the remaining open loop eigenvalues and their corresponding eigenvectors are kept unchanged the invariance of the large number of eigenvalues and eigenvectors under feedback is guaranteed by a proven mathematical result furthermore the gradient formulas needed to solve the problems by using the quasi newton optimization technique employed are computed in terms of the known quantities only above all the proposed methods do not require the reduction of the model order or the order of the controller even when the underlying finite element model has a very large degree of freedom these attractive features coupled with minimal computational requirements such as solutions of small diagonal sylvester equations make the proposed algorithms ideally suited for application to large real life structures numerical results show significant improvement in feedback norms and in the condition number of the closed loop system also the closed loop eigenvalues have acceptable accuracy

minimum norm partial eigenvalue assignment of high order linear system with no spill over abstract in this paper we consider the partial eigenvalue assignment problem peap of high order linear system by state feedback to prevent spill over phenomenon we establish the new orthogonality relations for the eigenvectors of matrix polynomial such that the unwanted eigenvalues are moved to prescribed values and the wanted eigenvalues remain unchanged based on the orthogonality relations the solvability conditions for peap are presented and the parametric expression of feedback matrices is derived in terms of the known quantities only finally an optimization based algorithm is proposed to find the minimum norm solution two numerical examples are given to show the application of the proposed method

shape topology optimization for navier stokes problem using variational level set method we consider the shape topology optimization of the navier stokes problem a new algorithm is proposed based on the variational level set method by this algorithm a relatively smooth evolution can be maintained without re initialization and drastic topology change can be handled easily finally the promising features of the proposed method are illustrated by two benchmark examples

solution and asymptotic behavior of coupled riccati equations in jump linear systems a new necessary and sufficient condition for the existence of a positive semidefinite solution of coupled riccati equations occurring in jump linear systems is derived by verifying a riccati inequality it is shown that such a solution exists in addition two numerical algorithms are given to compute it an example is given to illustrate the proposed method

convergence of the dre solution to the are strong solution in this paper we use the boundary solutions to a linear matrix inequality lmi associated with kalman filtering to investigate the convergence of the solution of a differential riccati equation dre to the so called strong solution of an algebraic riccati equation are we furthermore extend our results to kalman filtering with indefinite input noise covariances

nested and self adaptive bezier parameterizations for shape optimization this article is a sequel of j a desideri hierarchical optimum shape algorithms using embedded bezier parameterizations in y kuznetsov et al ed numerical methods for scientific computing variational problems and applications cimne barcelona 2003 in which we defined formally a hierarchical shape optimization method based on a multi level shape representation by nested bezier parameterizations famosa and j a desideri a janka multi level shape parameterization for aerodynamic optimization application to drag and noise reduction of transonic supersonic business jet in e heikkola et al ed european congress on computational methods in applied sciences and engineering eccomas 2004 jyvaskyla 24 28 july 2004 where we conducted some preliminary numerical experiments of shape optimization in aerodynamics here we are testing the full multi level optimum shape algorithm analogous in logical structure to the classical full multigrid method second we propose a technique for parameterization self adaptivity both methodological enhancements are assessed by novel numerical experiments on an inverse shape model problem confirming both are very effective

orthogonality and partial pole assignment for the symmetric definite quadratic pencil abstract the eigenvectors of a symmetric matrix can be chosen to form an orthogonal set with respect to the identity and to the matrix itself similarly the eigenvectors of a symmetric definite linear pencil can be chosen to be orthogonal with respect to the pair this paper presents the three sets of matrix weights with respect to which the eigenvectors of the symmetric definite quadratic pencil are orthogonal one of these is used to derive an explicit solution of the partial pole assignment problem by state feedback control for a control system modeled by a system of second order differential equations the solution may be of particular interest in the stabilization and control of flexible large space structures where only a small part of the spectrum is to be reassigned and the rest of the spectrum is required to remain unchanged

optimal and robust noncausal filter formulations the paper describes an optimal minimum variance noncausal filter or fixed interval smoother the optimal solution involves a cascade of a kalman predictor and an adjoint kalman predictor a robust smoother involving h sub spl infin predictors is also described filter asymptotes are developed for output estimation and input estimation problems which yield bounds on the spectrum of the estimation error these bounds lead to a priori estimates for the scalar spl gamma in the h sub spl infin filter and smoother design the results of simulation studies are presented which demonstrate that optimal robust and extended kalman smoothers can provide performance benefits

a necessary and sufficient condition for solvability of the linear quadratic control problem without stabilty in this short paper a necessary and sufficient condition is given for the existence of a minimizing control for the regular non negative definite linear quadratic control problem without stability

state space newton s method for topology optimization abstract we introduce a new algorithm for solving certain classes of topology optimization problems which enjoys fast local convergence normally achieved by the full space methods while working in a smaller reduced space the computational complexity of newton s direction finding subproblem in the algorithm is comparable with that of finding the steepest descent direction in the traditional first order nested reduced space algorithms for topology optimization that is the space reduction is computationally inexpensive and more importantly it does not ruin the sparsity of the full space system of optimality conditions the fast local convergence of the algorithm allows one to efficiently solve a sequence of optimization problems for varying parameters numerical continuation this can be utilized for eliminating the errors introduced by the approximate enforcement of the boundary conditions or 0 1 type constraints on the design field through penalties in many topology optimization approaches we test the algorithm on the benchmark problems of dissipated power minimization for stokes flows and in all cases the algorithm outperforms the traditional first order reduced space nested approaches by a factor varying from two to almost twenty in terms of the number of iterations while attaining an almost unprecedented accuracy in solving the discretized topology optimization problem finally we present a few extensions to the algorithm one involving computations on adaptively refined meshes and another related to solving topology optimization problems for non newtonian fluids

shape optimisation with multiresolution subdivision surfaces and immersed finite elements abstract we develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation similar to wavelets multiresolution surfaces represent the domain boundary using a coarse control mesh and a sequence of detail vectors based on the multiresolution decomposition efficient and fast algorithms are available for reconstructing control meshes of varying fineness during shape optimisation the vertex coordinates of control meshes are updated using the computed shape gradient information by virtue of the multiresolution editing semantics updating the coarse control mesh vertex coordinates leads to large scale geometry changes and conversely updating the fine control mesh coordinates leads to small scale geometry changes in our computations we start by optimising the coarsest control mesh and refine it each time the cost function reaches a minimum this approach effectively prevents the appearance of non physical boundary geometry oscillations and control mesh pathologies like inverted elements independent of the fineness of the control mesh used for optimisation on the immersed finite element grid the domain boundary is always represented with a relatively fine control mesh of fixed resolution with the immersed finite element method there is no need to maintain an analysis suitable domain mesh in some of the presented two and three dimensional elasticity examples the topology derivative is used for introducing new holes inside the domain the merging or removing of holes is not considered

how exciting can a signal really be abstract the rate of parameter convergence in a number of adaptive estimation schemes is related to the smallest eigenvalue of the average information matrix determined by the regression vector using a very simple examples we illustrate that the input signals that maximize this minimum eigenvalue may be quite different from the input signals that optimize more classical input design criteria e g d optimal criterion

a miscellany of results of an equation of count j f riccati a collection of results on the riccati equation is presented the questions addressed are the existence of strong solutions of the algebraic riccati equation and the convergence of solutions of the riccati difference equation to those of the algebraic equation the results derived utilize detestability conditions only

brief monotonicity of the optimal cost in the discrete time regulator problem and schur complements this paper deals with the monotonicity of the optimal rather than the more usual stabilising cost of the discrete time regulator problem the approach relies on a monotonicity result on riccati operators and on a formula for the difference of schur complements

bayesian multiscale modeling of closed curves in point clouds modeling object boundaries based on image or point cloud data is frequently necessary in medical and scientific applications ranging from detecting tumor contours for targeted radiation therapy to the classification of organisms based on their structural information in low contrast images or sparse and noisy point clouds there is often insufficient data to recover local segments of the boundary in isolation thus it becomes critical to model the entire boundary in the form of a closed curve to achieve this we develop a bayesian hierarchical model that expresses highly diverse 2d objects in the form of closed curves the model is based on a novel multiscale deformation process by relating multiple objects through a hierarchical formulation we can successfully recover missing boundaries by borrowing structural information from similar objects at the appropriate scale furthermore the model s latent parameters help interpret the population indicating dimensions of significant structural variability

orthogonal basis selection method for robust partial eigenvalue assignment problem in second order control systems in this paper we study the robust partial eigenvalue assignment problem using state feedback control in second order control systems which means that the feedback control matrices not only assign specific eigenvalues to the second order closed loop system but also that the system is robust or insensitive to perturbations in the coefficient matrices some measures of robustness of the closed loop system are discussed and a numerical method is proposed such that it aims to minimize one measure of the conditioning of the closed loop system numerical examples show that the method is convergent and often leads to better conditioned closed loop system

difference and differential riccati equations a note on the convergence to the strong solution the convergence of the solutions of the differential difference riccati equations to the strong solution of the corresponding algebraic riccati equation are is addressed detectability only is required in the analysis and no assumption is made on the eigenvalues on the real imaginary axis on the unit circle in the discrete time case in particular from the results it follows that under the sole assumption of detectability a positive definite initial condition guarantees convergence to the strong solution even in the presence of unreachable eigenvalues on the imaginary axis or on the unit circle

mean square stabilizing solutions for discrete time coupled algebraic riccati equations in this paper we present new sufficient conditions for the existence of a mean square stabilizing solution for a set of coupled algebraic riccati equations which arises from the study of quadratic optimal control of discrete time linear systems with markov switching parameters the conditions are derived under the assumptions of mean square stabilizability and on the unobservable modes of the system and compared with existing results

monotonicity of maximal solutions of algebraic riccati equations abstract a monotonicity result for the maximal solution of the equation xbb x a x xa q 0 q q a b stabilizable is proved

two level free form and axial deformation for exploratory aerodynamic shape optimization an intuitive shape parameterization and control technique suitable for high fidelity aerodynamic shape optimization is presented it relies on the principles of free form and axial deformation enabling thorough exploration of the design space while keeping the number of design variables manageable surface sensitivities to the design variables are readily available their inclusion in a highly efficient and robust adjoint based optimization methodology involving linearly elastic volume mesh deformation and a newton krylov solver for the euler equations is described the flexibility of the proposed approach is demonstrated through the exploratory shape optimization of a three pronged feathered winglet leading to a span efficiency of 1 19 under a height to span ratio constraint of 0 1 and an optimization of a regional jet wing at transonic speed where a winglet is allowed to develop starting from a planar wingtip extension leading to an 18 8 reduction in drag

a kalman filtering approach to short time fourier analysis the problem of estimating time varying harmonic components of a signal measured in noise is considered the approach used is via state estimation two methods are proposed one involving pole placement of a state observer the other using quadratic optimization techniques the result is the development of a new class of filters akin to recursive frequency sampling filters for inclusion in a parallel bank to produce sliding harmonic estimates kalman filtering theory is applied to effect the good performance in noise and the class of filters is parameterized by the design tradeoff between noise rejection and convergence rate these filters can be seen as generalizing the dft

two dimensional shape optimization using partial control and finite element method for compressible flows abstract the objective of this study is to determine the two dimensional shape of a body located in a compressible viscous flow where the applied fluid force is minimized the formulation to obtain the optimal shape is based on an optimal control theory an optimal state is defined as a state in which the performance function defined as the integration of the square sum of the applied fluid forces is minimized due to a reduction in the applied fluid forces compressible navier stokes equations are treated as constraint equations in other words the body is considered to have a shape that minimizes the fluid forces under the constraint of the navier stokes equations the gradient of the performance function is computed using the adjoint variables a weighted gradient method is used as the minimization algorithm the volume of the body is assumed to be the same as that of the initial body in the case of the algorithm used in this study both the creation of a structured mesh around the surface of the body and the smoothing procedure are employed for the computation of gradient in this study a remeshing technique based on the structured mesh around the body changing its configuration in the iteration cycle is employed for the correction to keep the volume constant the surface coordinates are moved along the radial direction for the discretization of both the state and adjoint equations the efficient bubble function interpolation presented previously by the authors 18 is employed the algorithm which is known as the partial control algorithm is applied to the numerical procedure to determine the movement of the coordinates in the case of the gradient method in order to avoid the convergence of the final shape to the local minimum shape the new algorithm which is called the partial control algorithm is presented in this study in numerical studies the shape determination of a body in a uniform flow field is carried out in 2d domains the initial shape of the body is assumed to be an elliptical cylinder the shape is modified by minimizing the applied fluid forces finally the desired shape of a body whose performance function is reduced and converged to a constant value is obtained by carrying out a procedure that involves the use of the partial control algorithm the desired shape of a body whose performance function is reduced further is obtained stable shape determination of a body in a compressible viscous flow is carried out by using the presented method it is indicated that the optimal shape can be obtained by using the partial control algorithm

robust partial eigenvalue assignment problem for the second order system in this paper we study the partial eigenvalue assignment problem for the second order system where only a small part of eigenvalues of the open loop system is to be reassigned and the rest are required to remain unchanged it is desirable that the feedback controller not only assigns specific eigenvalues to the second order closed loop system but also that the system is robust or insensitive to perturbations we propose a numerical method such that the condition number of the matrix of the eigenvectors of the closed loop system is minimized in the method we only need the knowledge of the eigenvalues to be altered and the corresponding eigenvectors while we do not need the knowledge of the eigenstructures that are required to remain unchanged and are often unknown numerical examples show that the present method often leads to better conditioned closed loop system

monotonicity and stabilizability properties of solutions of the riccati difference equation propositions lemmas theorems fallacious conjectures and counterexamples abstract the problem considered is that of selecting an initial covariance matrix for the kalman filter to ensure that the closed loop filter at every subsequent time instant is exponentially asymptotically stable as a time invariant filter sufficient conditions are derived based on monotonicity properties of the solution of the riccati difference equation the results have application in observer design and the cases of filtering for nonstabilizable systems and systems with singular system matrices are included

pole assignment in vibratory systems by multi input control the problem of reassigning some poles of a vibratory system while keeping the other poles unchanged is considered the problem may be solved uniquely by single input state feedback control a family of solutions to the partial pole assignment problem may be obtained by applying multi input control forces an algorithm for determining a multi input control which is small in some sense is presented the non iterative algorithm proposed defines a closed form solution to the partial pole assignment problem in its natural second order form and no first order realization is used the reduction in the control effort achieved by the proposed method is demonstrated by numerical examples