the role of the unitary interactor matrix in the explicit solution of the singular lq output feedback control problem abstract this paper is concerned with the unitary interactor matrix and its role in the explicit solution of the minimum variance and singular lq output feedback control problems the unitary interactor matrix an all pass factor that factors the infinite zeros while keeping the spectrum of the underlying system unchanged is also extended to include the weighted unitary interactor matrix with the weighted unitary interactor matrix the multivariate minimum variance control law as proposed by goodwin and sin 1984 is shown to be pairinginvariant and identical to the singular lq output feedback control law

a semi implicit level set method for structural shape and topology optimization this paper proposes a new level set method for structural shape and topology optimization using a semi implicit scheme structural boundary is represented implicitly as the zero level set of a higher dimensional scalar function and an appropriate time marching scheme is included to enable the discrete level set processing in the present study the hamilton jacobi partial differential equation pde is solved numerically using a semi implicit additive operator splitting aos scheme rather than explicit schemes in conventional level set methods the main feature of the present method is it does not suffer from any time step size restriction as all terms relevant to stability are discretized in an implicit manner the semi implicit scheme with additive operator splitting treats all coordinate axes equally in arbitrary dimensions with good rotational invariance hence the present scheme for the level set equations is stable for any practical time steps and numerically easy to implement with high efficiency resultantly it allows enhanced relaxation on the time step size originally limited by the courant friedrichs lewy cfl condition of the explicit schemes the stability and computational efficiency can therefore be greatly improved in advancing the level set evolvements furthermore the present method avoids additional cost to globally reinitialize the level set function for regularization purpose it is noted that the periodically applied reinitializations are time consuming procedures in particular the proposed method is capable of creating new holes freely inside the design domain via boundary incorporating splitting and merging processes which makes the final design independent of initial guess and helps reduce the probability of converging to a local minimum the availability of the present method is demonstrated with two widely studied examples in the framework of the structural stiffness designs

explicit level set based topology optimization using an exact heaviside function and consistent sensitivity analysis summary this paper presents a level set based topology optimization method based on numerically consistent sensitivity analysis the proposed method uses a direct steepest descent update of the design variables in a level set method the level set nodal values an exact heaviside formulation is used to relate the level set function to element densities the level set function is not required to be a signed distance function and reinitialization is not necessary using this approach level set based topology optimization problems can be solved consistently and multiple constraints treated simultaneously the proposed method leads to more insight in the nature of level set based topology optimization problems the level set based design parametrization can describe gray areas and numerical hinges consistency causes results to contain these numerical artifacts we demonstrate that alternative parameterizations level set based or density based regularization can be used to avoid artifacts in the final results the effectiveness of the proposed method is demonstrated using several benchmark problems the capability to treat multiple constraints shows the potential of the method furthermore due to the consistency the optimizer can run into local minima a fundamental difficulty of level set based topology optimization more advanced optimization strategies and more efficient optimizers may increase the performance in the future copyright 2012 john wiley sons ltd

conditions for a symmetrized decomposable tensor to be zero let x1ast xm be a decomposable symmetrized tensor corresponding to the symmetric group sm and an irreducible character a necessary and sufficient condition on the vectors x1 xm is given for x1 xm to be zero

explicit solution to the singular lq regulation problem an explicit solution to the multivariable discrete linear quadratic lq regulation problem is obtained in the limiting singular case where the input weighting matrix tends to zero such a solution follows from a suitable spectral factorization of the input spectrum density matrix under the assumption that the system is stabilizable and detectable and that its transfer function matrix is of full rank the suitable spectral factor is shown to be the product of the system s minimum phase image and its unitary interactor matrix the unitary interactor matrix defined is a special case of the nilpotent interactor matrix defined by m w rogozinski et al 1987

a level set based parameterization method for structural shape and topology optimization this paper presents an effective parametric approach by extending the conventional level set method to structural shape and topology optimization using the compactly supported radial basis functions rbfs and the optimality criteria oc method the structural design boundary is first represented implicitly by embedding into a higher dimensional level set function as its zero level set and the rbfs of a favorable smoothness are then applied to interpolate the level set function the original initial value problem is thus converted to a parametric optimization with the expansion coefficients of the interplant posed as the design variables the oc method is then applied to advance the structure boundary in terms of the velocity field derived from the parametric optimization hence the structural shape and topology optimization is now transformed into a process of iteratively finding coefficients to update the level set function to achieve an optimal configuration the numerical considerations of the conventional level set method including upwind schemes velocity extension and reinitialization are eliminated the proposed scheme is capable of addressing structural shape fidelity and topology change simultaneously and of keeping the boundary smooth during the optimization process furthermore numerical convergence is expected to be improved a widely investigated example in the framework of structural stiffness designs is applied to demonstrate the efficiency and accuracy of the proposed approach copyright 2007 john wiley sons ltd

a simple state space design of an interactor for a non square system via system matrix pencil approach abstract the construction of an interactor cancelling the infinite zeros of a non square proper transfer matrix is discussed in this paper along the line of approach of b r copeland m g safonov int j robust nonlinear control 2 1992 139 in this paper some new properties of the infinite eigenstructure of the system matrix pencil of the transfer matrix are presented a simple state space design of the interactor is proposed by using these properties then some new features about state space relations among the original system the interactor and the compensated system are presented also several conditions about the invariance of the stabilizability or controllability between the state space realizations of the original system and the compensated system are shown furthermore the proposed method of designing the interactor in this paper can be applied to a tall or fat transfer matrix with full normal rank

decomposable critical tensors abstract let 1 t be a partition of m and 1 1 its conjugate partition denote also by the irreducible c character of sm associated with let v be a finite dimensional vector space over c the reach of an element of the symmetry class of tensors v symmetry class of tensors associated with is defined the concept of critical element is introduced as an element whose reach has dimension equal to 1 it is observed that in mv the notions of critical element and decomposable element coincide known results for decomposable elements of mv are extended to critical elements of v in particular for a basis of mv induced by a basis of v generalized plucker polynomials are constructed in a way that the set of their common roots contains the set of the families of components of decomposable critical elements of v

singular filtering via spectral interactor matrix in this paper the notion of spectral interactor matrix sim for a given square transfer matrix is introduced and used in the singular filtering problem a sim is defined as an interactor matrix preserving the spectral properties of the underlying system after studying the class of all spectral interactor matrices associated with a given transfer matrix an algorithm for the computation of a sim is proposed by resorting to the sim it is possible to point out the role played by delays zeros at infinity and nonminimum phase zeros in the solution of the singular filtering problem

an algorithm for the calculation of a nilpotent interactor matrix for linear multivariable systems a new algorithm for the calculation of the delay structure for a linear multivariable system is presented the algorithm evaluates a nilpotent interactor matrix from the matrix of coefficients of the numerator of a right matrix fraction description of the system the resulting nilpotent interactor is a product of first degree nilpotent polynomial matrices

topology optimization of continuum structures with local stress constraints we introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria we first consider relevant stress criteria for porous composite materials initially by studying the stress states of the so called rank 2 layered materials then on the basis of the theoretical study of the rank 2 microstructures we propose an empirical model that extends the power penalized stiffness model also called simp for solid isotropic microstructure with penalization for inter mediate densities in a second part solution aspects of topology problems are considered to deal with the so called singularity phenomenon of stress constraints in topology design an constraint relaxation of the stress constraints is used we describe the mathematical programming approach that is used to solve the numerical optimization problems and show results for a number of example applications 1998 john wiley sons ltd

on the role of the interactor matrix in multiinput multioutput adaptive control recent papers have shown that the system interactor matrix plays an important role in the multiinput multioutput adaptive control in these papers however the impression may have been inadvertently conveyed that the interactor matrix can be taken to be diagonal in almost all cases this note shows that this impression is false and that in general a nondiagonal interactor matrix should be considered

a parameter adaptive control structure for linear multivariable systems this paper presents an adaptive control structure which can be used to assign all poles and zeros of a continuous time linear multivariable system represented by an m times m strictly proper transfer matrix t s provided t s has no right half plane zeros the controller parameters can be directly estimated from input output data the paper also serves to point out the type of a priori information necessary for multivariable adaptive controller design this information is a natural extension of that required in the scalar case

a numerical design of interactors for general descriptor systems in this technical note we develop a numerically reliable method to design an interactor for a general descriptor system relative to a stability region cg and an offending zero set our main result is based on a condensed form this condensed form is independent of the offending zeros and is computed using only orthogonal transformations and hence is numerically backward stable

prior knowledge in model reference adaptive control of multiinput multioutput systems this note shows how the prior knowledge necessary for model reference adaptive control of multiinput multioutput systems can be weakened in particular it is shown that the real variables appearing in the system interactor matrix can be estimated along with the other parameters appearing in the system model this represents a significant reduction in the amount of prior knowledge required relative to previous work which assumed that the full interactor matrix was available a theoretical convergence analysis of the resulting algorithm is presented together with simulation results

equality of immanantal decomposable tensors we state a necessary and sufficient condition for equality of two nonzero decomposable symmetrized tensors when the symmetrizer is associated with an irreducible character of the symmetric group of degree m

topological derivative based topology optimization of structures subject to drucker prager stress constraints abstract an algorithm for topology optimization of elastic structures under plane stress subject to the drucker prager stress constraint is presented the algorithm is based on the use of the topological derivative of the associated objective functional in conjunction with a level set representation of the structure domain in this context a penalty functional is proposed to enforce the point wise stress constraint and a closed formula for its topological derivative is derived the resulting algorithm is of remarkably simple computational implementation it does not require post processing procedures of any kind and features only a minimal number of user defined algorithmic parameters this is in sharp contrast with current procedures for topological structural optimization with local stress constraints the effectiveness and efficiency of the algorithm presented here are demonstrated by means of numerical examples the examples show in particular that it can easily handle structural optimization problems with underlying materials featuring strong asymmetry in their tensile and compressive yield strengths

paper parameterization issues in multivariable adaptive control this paper gives both an overview of multivariable adaptive control algorithms which have evolved to date and presents some new approaches to the design of indirect multivariable adaptive control systems all algorithms are presented using a unified pole placement approach furthermore the emphasis is on parameterization issues such as types of control structures necessary for implementation required prior information necessary for implementation and techniques for reducing the size of the resulting parameter estimation problem

a short proof of gamas s theorem abstract if is the irreducible character of s n corresponding to the partition of n then we may symmetrize a tensor v 1 v n by gamas s theorem states that the result is not zero if and only if we can partition the set v i into linearly independent sets whose sizes are the parts of the transpose of we give a short and self contained proof of this fact

structural optimization using sensitivity analysis and a level set method in the context of structural optimization we propose a new numerical method based on a combination of the classical shape derivative and of the level set method for front propagation we implement this method in two and three space dimensions for a model of linear or nonlinear elasticity we consider various objective functions with weight and perimeter constraints the shape derivative is computed by an adjoint method the cost of our numerical algorithm is moderate since the shape is captured on a fixed eulerian mesh although this method is not specifically designed for topology optimization it can easily handle topology changes however the resulting optimal shape is strongly dependent on the initial guess

recursive identification algorithms for right matrix fraction description models multivariable identification algorithms are usually designed only for left matrix fraction description lmfd models in this paper we consider recursive identification algorithms for right matrix fraction description rmfd models with diagonal denominator matrices the algorithms are of prediction error pe and model reference mr type results from simulations illustrate the performance of the algorithms

the covering number of the elements of a matroid and generalized matrix functions abstract let s be a nonempty finite set with cardinality m let m be a matroid on s with no loops the covering number of an element x in s is the smallest positive integer k such that x is a coloop of the union of k copies of m we investigate connections between the structure of m and the values of the covering numbers of elements of s applications to the study of the rank partition and generalized matrix functions are presented

decoupling properties of singular lq regulation problem some properties of a limiting solution derived from a standard lq regulator problem are discussed in the case where the input weighting matrix tends to zero for a discrete time system the explicit limiting solution is given in some literature it is shown that the limiting solution is closely connected with a disturbance decoupling problem moreover it is pointed out that the limiting feedback gain with the help of feedforward gain constructs the decoupled system with the maximum number of blocks

on the equality of families of decomposable symmetrized tensors abstract we give some necessary and equivalent conditions for x 1 x m y 1 y m to hold for all s m in arbitrary symmetry classes of tensors

from singular to nonsingular filtering of periodic systems filling the gap with the spectral interactor matrix with reference to periodic discrete time systems the concept of the periodic spectral interactor matrix operator psimo is introduced such an interactor enables one to transform the singular system into a nonsingular one with identical spectral properties this concept is useful to characterize the family of periodic solutions of the singular periodic riccati equation arising from the singular filtering problem the psimo is also a synthetic tool to represent the invariant zeros structure at infinity delays of periodic systems in an operational fashion

the multilinear algebra of jose dias da silva and the portuguese school of mathematics abstract in portugal multilinear algebra has a strong group of researchers that achieved in the last years some impressive results in this area this paper surveys the results obtained by this group and the current state of knowledge on the different problems

a note on the orthogonal basis of a certain full symmetry class of tensors abstract it is shown that the full symmetry class of tensors associated with the irreducible character 2 1 n 2 of s n does not have an orthogonal basis consisting of decomposable symmetrized tensors

decomposable λ critical tensors abstract let 1 s be a partition of m and let v be a finite dimensional vector space over c we also denote by the irreducible character of s m associated with the partition and by v we denote the symmetry class of tensors associated with and v let j 1 1 and z v the concept of j reach of z is defined using this concept we introduce the concept of critical element of v generalized plucker polynomials are constructed in a way that the set of their common roots contains the set of the families of components of decomposable critical elements of v the concepts and results are generalizations of those defined and proved in 4

a level set approach for topology optimization with local stress constraints summary the purpose of this work is to present a level set based approach for the structural topology optimization problem of mass minimization submitted to local stress constraints the main contributions are threefold first the inclusion of local stress constraints by means of an augmented lagrangian approach within the level set context second the proposition of a constraint procedure that accounts for a continuous activation deactivation of a finite number of local stress constraints during the optimization sequence finally the proposition of a logarithmic scaling of the level set normal velocity as an additional regularization technique in order to improve the minimization sequence a set of benchmark tests in two dimensions achieving successful numerical results assesses the good behavior of the proposed method in these examples it is verified that the algorithm is able to identify stress concentrations and drive the design to a feasible local minimum copyright 2014 john wiley sons ltd