optimum sensitivity derivatives of objective functions in nonlinear programming the feasibility of eliminating second derivatives from the input of optimum sensitivity analyses of optimization problems is demonstrated this elimination restricts the sensitivity analysis to the first order sensitivity derivatives of the objective function it is also shown that when a complete first order sensitivity analysis is performed second order sensitivity derivatives of the objective function are available at little additional cost an expression is derived whose application to linear programming is presented

on the syntactic transformation semigroup of a language generated by a finite biprefix code abstract let p be a finite biprefix code and let x q s be the syntactic transformation semigroup ts of p we show that if e s is an idempotent then the ts x e qe eqe consists of partial one to one maps we also show that any ts of partial one to one maps divides a ts of partial one to one maps which is the syntactic ts of a finite biprefix code

improving the efficiency of aerodynamic shape optimization the computational efficiency of an aerodynamic shape optimization procedure that is based on discrete sensitivity analysis is increased through the implementation of two improvements the first improvement involves replacing a grid point based approach for surface representation with a bezier bernstein polynomial parameterization of the surface explicit analytical expressions for the grid sensitivity terms are developed for both approaches the second improvement proposes the use of newton s method in lieu of an alternating direction implicit methodology to calculate the highly converged flow solutions that are required to compute the sensitivity coefficients

on locally reversible languages there exist several works that study the class of reversible languages defined as the union closure of 0 reversible languages their properties and suitable representations in this work we define and study the class of locally reversible languages defined as the union closure of k reversible languages we characterize the class and prove that it is a local positive variety of formal languages we also extend the definition of quasi reversible automata to deal with locally reversible languages and propose a polynomial algorithm to obtain for any given locally k reversible language a quasi k reversible automaton

geometric programming for aircraft design optimization formulating conceptual stage aircraft design problems as geometric programs which are a specific type of convex optimization problem is proposed recent advances in convex optimization offer sign

stabilization of positive switched linear systems and its application in consensus of multiagent systems in this note we study the stabilization problem of positive switched linear system psls with disturbance by introducing a class of weak common linear copositive lyapunov functions we design time dependent switching rules under which the system is asymptotically stable both continuous time and discrete time psls are taken into consideration and the obtained results are also extended to nonpositive switched systems finally the theoretical results are applied to consensus problem of multiagent systems with switching topologies and disturbance

aerodynamic design optimization using sensitivity analysis and computational fluid dynamics a new and efficient method is presented for aerodynamic design optimization which is based on a computational fluid dynamics cfd sensitivity analysis algorithm the method is applied to design a simplified scramjet afterbody configuration for an optimized axial thrust the euler equations are solved for the inviscid analysis of the flow which provides the objective function and the constraints of the optimization problem the cfd analysis is then coupled with the optimization procedure that used a constrained minimization method the sensitivity coefficients i e gradients of the objective function and the constraints needed for the optimization are obtained using a quasi analytic al method rather than the traditional finite difference approximations during the one dimensional search of the optimization procedure an approximate flow analysis predicted flow based on a first order taylor series expansion is used to reduce the computational cost finally the sensitivity of the optimum objective function to various flowfield problem parameters such as the mach number which are kept constant during the optimization is computed to predict new optimum solutions the flow analysis of the demonstrative example are compared with the experimental data it is shown that the method is more efficient than the traditional methods

two dimensional transonic aerodynamic design method this paper demonstrates the capabilities of a new transonic two dimensional design method based on the simultaneous solution of multiple streamtubes coupled through the position of and pressure at the streamline interfaces this allows the specification of either the airfoil shape direct analysis mode or the airfoil surface pressure distribution inverse design mode the nonlinear system of equations is formulated in a conservative manner which guarantees the correct treatment of shocks and is solved by a rapid newton solution method viscous effects can also be included through a coupled integral boundary layer analysis the first set of results shows the effect of different far field treatments demonstrating the improvement in accuracy obtained by including the second order doublet terms in addition to the usual first order vortex term the results are also compared to those obtained by specifying straight far field streamlines corresponding to solid wall wind tunnel experiments or constant far field pressure corresponding to freejet experiments to show the sensitivity to the farfield distance in the second set of results the design method is used to design a transonic airfoil with c 1 000 at a oo 0 70 it is shown that the off design performance is improved by specifying a surface pressure distribution with a very weak shock

problem formulation for multidisciplinary optimization this paper is about multidisciplinary design optimization or mdo the coupling of two or more analysis disciplines with numerical optimization the paper has three goals first it is an expository introduction to mdo aimed at those who do research on optimization algorithms since the optimization community has much to contribute to this important class of computational engineering problems second this paper presents to the mdo research community a new abstraction for multidisciplinary analysis and design problems as well as new decomposition formulations for these problems third the individual discipline feasible idf approaches introduced here make use of existing specialized analysis codes and they introduce significant opportunities for coarse grained computational parallelism particularly well suited to heterogeneous computing environments the key distinguishing characteristic of the three fundamental approaches to mdo formulation discussed here is the kind of disciplinary feasibility that

sensitivity analysis of the aeroacoustic response of turbomachinery blade rows a method for computing the change or sensitivity of the aeroacoustic response of a cascade to small changes in airfoil and cascade geometry is presented the steady flow is modeled by the full potential equation which is discretized using a variational finite element technique a streamline computational grid is generated as part of the steady solution newton iteration is used to solve for the nonlinear steady flow and grid equations with lower upper lu matrix decomposition plus one forward and one back substitution used to solve the resulting matrix equations similarly the unsteady small disturbance flow about the nonlinear mean flow is modeled by the linearized potential equation together with rapid distortion theory to account for vortical gusts these linearized equations are discretized using finite elements and solved with a single lu decomposition the sensitivities of the steady and unsteady flowfields to small changes in geometry are computed by perturbing the discretized equations about the nominal solutions the resulting linear system of equations can be solved very efficiently because the lu factors of the resulting matrix equations are computed as part of the nominal steady and unsteady solution results are presented in this paper to show the accuracy and efficiency of the method and the implications for aeroacoustic design of turbomachinery blades are discussed

a general stability test for switched positive systems based on a multidimensional system analysis the main goal of this technical note is to present a new sufficient condition for the stability of switched positive linear systems this condition is general in two senses first of all because it applies to switching systems of order composed of subsystems for any and secondly because it applies to both discrete and continuous time systems furthermore it is easy to verify as it amounts to check for the stability of a certain matrix the new condition is derived from a multidimensional system analysis where the relation between the stability of multidimensional and switched systems is investigated a comparison with other existing tests is also presented showing that the one proposed here allows to infer about the stability of a system in cases where other tests fail or do not apply at all

stability of continuous time positive switched linear systems a weak common copositive lyapunov functions approach in this paper we study the problem of asymptotic stability of continuous time positive switched linear systems under both arbitrary and restricted switchings it is well known that asymptotic stability under arbitrary switching can be implied by several classes of strong common copositive lyapunov functions clfs i e functions whose derivative along the nontrivial system trajectories is negative however asymptotically stable positive switched systems may not admit strong common clfs the main contribution of this paper is to study the stability problem by requiring only weak common clfs firstly necessary and sufficient conditions are established for asymptotic stability under arbitrary switching among them an easily verifiable graphical stability criterion based on the connectivity of the digraphs associated with the subsystem matrices is proposed secondly we further relax the obtained graphical condition to derive a relaxed weak excitation condition for asymptotic stability under dwell time switching finally two examples are provided to illustrate the effectiveness of our theoretical results

on the simultaneous diagonal stability of a pair of positive linear systems in this paper we derive a necessary and sufficient condition for the existence of a diagonal common quadratic lyapunov function cqlf for a pair of positive linear time invariant lti systems

an efficient feasible directions algorithm for design synthesis a nonlinear optimization algorithm is described that combines the best features of the method of feasible directions and the generalized reduced gradient method the algorithm uses the direction finding subproblem from the method of feasible directions to find a search direction that is equivalent to that of the generalized reduced gradient method but without the need to add a large number of slack variables associated with inequality constraints this leads to a core efficient algorithm for the solution of optimization problems with a large number of inequality constraints also during the one dimensional search it is not necessary to separate the design space into dependent and independent variables using the present method the concept of infrequent gradient calculations is introduced as a means of gaining further optimization efficiency finally it is shown that using the basic direction finding algorithm contained in this method the sensitivity of the optimum design with respect to problem parameters can be obtained without the need for second derivatives or lagrange multipliers the optimization algorithm and sensitivity analysis is demonstrated by numerical example

exponential stabilization of switched time varying systems with delays and disturbances abstract this paper deals with exponential stabilization for a class of switched time varying systems by taking time varying delays and nonlinear disturbances into consideration time dependent switching signals have been characterized in terms of metzler matrices such that the resulting system is globally exponentially stable compared with preceding works we introduce a model transformation and an approach without involving the lyapunov krasovskii functional to derive new exponential stability criteria for switched time varying systems under the average dwell time switching numerical examples show that the obtained theoretical results can be applied to some cases not covered by some existing results

hurwitz stability of metzler matrices in this note a simple method is presented that is both necessary and sufficient for determining whether a given metzler matrix a is hurwitz the method is based on the well known fact that a hurwitz metzler matrix is also diagonally stable by using this fact very simple conditions are derived for the hurwitz stability of a metzler matrix the conditions are stated in terms of the signs of the diagonal entries of a sequence of lower dimensional matrices the efficacy of the conditions is demonstrated by applying them to determine stability in several examples

stabilization of discrete time switched positive linear systems via weak switched linear copositive lyapunov function abstract by introducing a class of weak switched linear copositive lyapunov functions this paper designs new time dependent switching signals guaranteeing asymptotic stability of discrete time switched positive linear systems whose subsystems are only marginally stable our results have advantages over some existing ones in the literature moreover the main results have been extended to the general switched linear time varying system with disturbance numerical examples well demonstrate the superiority of the obtained results

deforming grid variational principle for unsteady small disturbance flows in cascades a variational method for computing unsteady subsonic flows in turbomachinery blade rows is presented a variational principle that describes the harmonic small disturbance behavior of the full potential equations about a nonlinear mean flow is developed included in this variational principle is the effect of a deforming computational grid that conforms to the motion of vibrating airfoils bilinear isoparametric finite elements are used to discretize the variational principle and the resulting discretized equations are solved efficiently using lower upper decomposition the use of a deforming computational grid dramatically improves the accuracy of the method since no error producing extrapolation is required to apply the upwash boundary conditions or to evaluate the unsteady pressure on the airfoil surfaces

brief paper on linear co positive lyapunov functions for sets of linear positive systems in this paper we derive necessary and sufficient conditions for the existence of a common linear co positive lyapunov function for a finite set of linear positive systems both the state dependent and arbitrary switching cases are considered our results reveal an interesting characterisation of linear stability for the arbitrary switching case namely the existence of such a linear lyapunov function can be related to the requirement that a number of extreme systems are metzler and hurwitz stable examples are given to illustrate the implications of our results

linearized euler predictions of unsteady aerodynamic loads in cascades a linearized euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and vibratory blade motion is presented using the linearized euler technique one decomposes the flow into a mean or steady flow plus an unsteady harmonically varying small disturbance flow linear variable coefficient equations describe the small disturbance behavior of the flow and are solved using a pseudotime time marching lax wendroff scheme for the blade motion problem a harmonically deforming computational grid that conforms to the motion of vibrating blades eliminates large error producing mean flow gradient terms that would otherwise appear in the unsteady flow tangency boundary condition

sensitivity analysis of unsteady inviscid flow through turbomachinery cascades we present a novel sensitivity analysis for predicting the effect of airfoil shape on the unsteady aerodynamic and aeroacoustic response of turbomachinery blading the nominal steady and unsteady e ow in a cascade of turbomachinery blades is modeled using the steady euler equations and the time linearized euler equations respectively boththesteadyandunsteadyeulerequationsaresolvedusing atwo stepe nite volumelax wendroff discretizationwithmultigrid acceleration wecomputetheunsteady aerodynamicloadsduetoboth incominggusts and plunging motion of the cascade airfoils once the nominal steady and unsteady e ows have been computed a sensitivity analysis is performed using the discrete adjoint equations of the computational e uid dynamics scheme used to discretizetheeulerequations for each objectivefunction e g the amplitude peak of theaeroelastic blade motion theresultingadjointequationsaresolvedusingtheadjointlax wendroffscheme whichisalsoaccelerated using a multigrid technique once the adjoint equations have been solved the computed adjoint variables may be used to compute rapidly the sensitivities of the aeroelastic and aeroacoustic objective functions due to arbitrary changes in geometry the method is computationally efe cient with similar convergence rate histories for both the nominal and the adjoint solutions to demonstrate the utility of the present method we use the sensitivity analysis to redesign the shape of the airfoils of a cascade for increased aeroelastic stability we also redesign the shape of the airfoils of an exit guide vane for reduced downstream radiated noise

stabilization of switched positive system with impulse and marginally stable subsystems a mode dependent dwell time method abstract in this article the problem of stabilization for the switched positive linear system spls with impulse and marginally stable subsystems is studied in which both the continuous time case and the discrete time case are taken into account by the usage of a piecewise weak linear copositive lyapunov function lclf and the mode dependent dwell time mdt time dependent switching control laws are designed to guarantee the asymptotic stability of the system furthermore based on the comparison principal for positive systems the main results are generalized to the time variant spls two examples are worked out to indicate that our results have advantages over some known results in the literature

on linear copositive lyapunov functions and the stability of switched positive linear systems we consider the problem of common linear copositive lyapunov function existence for positive switched linear systems in particular we present a necessary and sufficient condition for the existence of such a function for switched systems with two constituent linear time invariant systems several applications of this result are also given

on easily verifiable conditions for the existence of common linear copositive lyapunov functions this technical note addresses the existence of a common linear copositive lyapunov function clclf for continuous time switched positive linear systems two necessary and sufficient conditions for the existence of a clclf are provided one condition shows that the existence of a clclf for a family of n n dimensional metzler matrices can only be determined by n 1 lower dimensional hurwitz matrices the other condition further shows that the existence of a clclf is also determined by n 1 characteristic constants which gives an easily verifiable computation algorithm without checking a large amount of metzler hurwitz matrices

optimal shape design of a two dimensional asymmetric diffuser in turbulent flow an optimal shape of two dimensional asymmetric diffuser with maximum pressure recovery at the exit is numerically obtained using a mathematical theory based on the variational calculus and gradient algorithm the initial diffuser is taken to be a two dimensional asymmetric diffuser for which much experimental and numerical data are available the reynolds number based on the bulk mean velocity and the channel height at the diffuser entrance is 1 8 10 4 f rom this initial shape optimal diffuser shapes are designed for six different geometric constraints such as the streamwise length and height of the diffuser the optimality condition for maximum pressure recovery is obtained to be zero skin friction along the diffuser wall the turbulent flow inside the diffuser is predicted using the k v2 f model and optimal shapes are obtained through iterative procedures to satisfy the optimality condition with the shape design flow separation that appeared in the initial diffuser is completely removed or significantly reduced for one of the optimal diffuser shapes obtained large eddy simulation is carried out to validate the result of the shape design the wall shear stress wall pressure mean velocity and turbulence quantities obtained from large eddy simulation are in good agreement with those from the simulation using the turbulence model

biprefix codes inverse semigroups and syntactic monoids of injective automata abstract we prove for injective automata an analogue of pin s result 1978 that any finite monoid divides the syntactic monoid of p for some finite prefix code p pin s result for arbitrary automata is strengthened in that we show divides can be replaced by is a subsemigroup of we give some conditions sufficient to guarantee that if a syntactic monoid is inverse then the automaton is injective a direct proof is given of reutenaur s result 1979 1981 that if the language recognized by an injective automaton is a subsemigroup then it is of the form b for some biprefix code b

algorithm developments for discrete adjoint methods this paper presents a number of algorithm developments for adjoint methods using the discrete approach in which the discretisation of the non linear equations is linearised and the resulting matrix is then transposed with a new iterative procedure for solving the adjoint equations exact numerical equivalence is maintained between the linear and adjoint discretisations the incorporation of strong boundary conditions within the discrete approach is discussed as well as a new application of adjoint methods to linear unsteady flow in turbomachinery

stability analysis of positive switched linear systems with delays this technical note addresses the stability problem of delayed positive switched linear systems whose subsystems are all positive both discrete time systems and continuous time systems are studied in our analysis the delays in systems can be unbounded under certain conditions several stability results are established by constructing a sequence of functions that are positive monotonically decreasing and convergent to zero as time tends to infinity additionally continuous for continuous time systems it turns out that these functions can serve as an upper bound of the systems trajectories starting from a particular region finally a numerical example is presented to illustrate the obtained results

efficient aerodynamic design method using a tightly coupled algorithm an efe cient aerodynamic design optimization method for the compressible euler equations is presented a gradient based optimization method is used to e nd the optimal design in conjunction with a continuous adjoint sensitivity analysis method to improve the efe ciency of the design method a tightly coupled algorithm based on a step size estimation isproposed the efe ciency of thepresentmethod is demonstrated through drag minimizations of a wing and an airfoil the result shows that the cost of the present method is signie cantly lower than that of the loosely coupled algorithm nomenclature ci e ux jacobian matrix in the computational domain d design variables vector fi e ux vector in the computational domain fi e ux vector in the physical domain g gradient vector of the object function i object function q conservative e ow variables vector r residual vector in the computational domain s searching direction step size along the searching direction s a lagrangian multiplier vector subscript face value at cell face superscript t transpose of vector or matrix

continuous adjoint sensitivities for optimization with general cost functionals on unstructured meshes a continuous adjoint approach is developed to obtain the sensitivity derivatives for the euler equations the completederivationofthecostateequations andtheirtransversality boundary conditionsarepresented both the state and the costate equations are second order e nite volume discretized for unstructured meshes and they are coupled with a constrained optimization algorithm also integrated into the overall methodology are a geometry parameterization method for the shape optimization and a dynamic unstructured mesh method for the shape evolution and the consequent volume mesh adaptations for the proof of concept three transonic airfoil optimization problems are presented this method accepts general cost functionals which are not necessarily functions of pressure only it is also shown that a switch to the natural coordinate system in conjunction with the reduction of the governing state equation to the control surface results in sensitivity integrals that are only a function of the tangential derivativesof the state variables thisapproach eliminates the need fornormal derivativecomputations that can be erroneous

a numerical approach for shape optimization of fluid flow domains abstract a numerical method for the shape optimization of fluid flow domains is presented and analyzed the procedure is based on a flow solver a mathematical optimization tool and a technique for shape variation which are combined into an integrated procedure the flow solver relies on the discretization of the incompressible navier stokes equations by means of the finite volume method for block structured boundary fitted grids with multi grid acceleration the optimization tool is an implementation of a trust region based derivative free method it is designed to minimize smooth functions whose evaluations are considered expensive and whose derivatives are not available or not desirable to approximate the shape variation is obtained by deforming the computational grid employed by the flow solver for this purpose displacement fields scaled by the design variables are added to the initial grid the displacement vectors are computed once before starting the optimization cycle by using a free form deformation technique applications illustrating the functionality and the properties of the method are presented for some examples of engineering interest such as the minimization of a pressure drop the maximization of a lift force and the optimization of a wall temperature

copositive lyapunov functions for switched systems over cones abstract we answer two open questions on copositive lyapunov functions which were recently posed by m k camlibel and j m schumacher in the book unsolved problems in mathematical systems and control theory edited by v d blondel and a megretski m k camlibel j m schumacher copositive lyapunov functions in v d blondel a megretski eds unsolved problems in mathematical systems and control theory princeton university press 2004 pp 189 193 available online at http press princeton edu math blondel these questions are what are necessary and sufficient conditions for the existence of a lyapunov function for a linear system which is defined over a cone how can this be extended to switched linear systems where the system matrix varies over time we present conditions answering these questions our conditions amount to checking feasibility or infeasibility of a system of linear inequalities

aerodynamic shape optimization using preconditioned conjugate gradient methods in an effort to further improve upon the latest advancements made in aerodynamic shape optimization procedures a systematic study is performed to examine several current solution methodologies as applied to various aspects of the optimization procedure it is demonstrated that preconditioned conjugate gradient like methodologies dramatically decrease the computational efforts required for such procedures the design problem investigated is the shape optimization of the upper and lower surfaces of an initially symmetric naca 0012 airfoil in inviscid transonic flow and at zero degrees angle of attack the complete surface shape is represented using a bezier bernstein polynomial

infeasible path optimal design methods with applications to aerodynamic shape optimization we consider optimal design of physical systems described by a nonlinear boundary value problem we propose a sequential quadratic programming method specifically tailored to the solution of this class of design problems a particular representation of the null space of the constraint jacobian that exploits its specific structure is employed the resulting method avoids resolution of nonlinear behavior at the optimization iterations while keeping the size of the problem as small as that of conventional approaches three variants of the method are developed and discussed these entail the solution of either two or three linear systems involving the jacobian matrix of the discretized form of the boundary value problem the method is used to solve aerodynamic design problems involving nonlinear transonic flow no special provisions are made for treating discontinuities and therefore the present implementation of the method is limited to problems with no shocks problems with up to 90 shape design variables are solved numerical results demonstrate a substantial performance improvement over conventional methods

multigrid and upwind viscous flow solver on three dimensional overlapped and embedded grids a computationally efficient method is presented for solving the three dimensional governing equations of the viscous compressible flows about complex configurations with geometrically nonsimilar components the physical domain is decomposed into regions for which the grid generation is relatively simple and virtually without significant restrictions the navier stokes equations are solved by an implicit upwind finite volume scheme the convergence is accelerated by a multigrid algorithm despite the holes created in the computational domain by the overlapped grids which are completely or partially embedded within one another the block inversions and the diagonalized scalar inversions of the coefficient matrices are modified to allow the existence of such holes the method is tested through two demonstrative csises the solution for a supersonic flow past a blunt nose cylinder at a high angle of attack is obtained using a c o grid embedded in a global cartesian grid this solution is successfully compared with the one obtained using a single c o grid and the experimental data then supersonic interference flows past an ogive nose cylinder in the close proximity of a flat plate are solved using overlapped and topologically nonsimilar but simple grids

sensitivity analysis of unsteady aerodynamic loads in cascades a method for computing the effect perturbations in the shape of airfoils in a cascade have on the steady and unsteady flow through the cascade is presented first the full potential equation is used to describe the behavior of the nonlinear steady flow and the small disturbance unsteady flow through the cascade the steady flow and small disturbance unsteady flow versions of the full potential equation are then discretized on a computational grid of quadrilateral cells using a variational finite element technique the resulting discretized equations describing the nonlinear steady flow are solved using newton iteration with lower upper decomposition at each iteration similarly the discretized unsteady small disturbance equations which are linear are solved using a single lower upper decomposition next a sensitivity analysis is performed to determine the effect small changes in cascade and airfoil geometry have on the steady and unsteady flowfields the sensitivity analysis makes use of the nominal steady and unsteady flow lower upper decompositions so that no additional matrices need to be factored hence the present method is computationally very efficient

sensitivity analysis of discrete structural systems methods for calculating sensitivity derivatives for discrete structural systems are surveyed primarily covering literature published during the past two decades methods are described for calculating derivatives of static displacements and stresses eigenvalues and eigenvectors transient structural response and derivatives of optimum structural designs with respect to problem parameters the survey is focused on publications developed in nonstructural fields such as electronics controls and physical chemistry which are directly applicable to structural problems most notable among the nonstructural based methods are the adjoint variable technique from control theory and the green s function and fast methods from physical chemistry

on the stability of positive linear switched systems under arbitrary switching laws we consider n dimensional positive linear switched systems a necessary condition for stability under arbitrary switching is that every matrix in the convex hull of the matrices defining the subsystems is hurwitz several researchers conjectured that for positive linear switched systems this condition is also sufficient recently gurvits shorten and mason showed that this conjecture is true for the case n 2 but is not true in general their results imply that there exists some minimal integer np such that the conjecture is true for all n np but is not true for n np we show that np 3

reduction of the adjoint gradient formula for aerodynamic shape optimization problems we present a new continuous adjoint method for aerodynamic shape optimization using the euler equations which reduces the computational cost of the gradients by reducing the volume integral part of the adjoint gradient formula to a surface integral the savings are particularly significant for three dimensional aerodynamic shape optimization problems on general unstructured and overset meshes to validate the concept the new gradient equations have been tested for various aerodynamic shape optimization problems including an inverse problem for three dimensional wing configurations and drag minimization problems of a single element airfoil and a three dimensional wing fuselage configuration

linear copositive lyapunov functions for continuous time positive switched systems continuous time positive systems switching among p subsystems are introduced and a complete characterization for the existence of a common linear copositive lyapunov function for all the subsystems is provided when the subsystems are obtained by applying different feedback control laws to the same continuous time single input positive system the above characterization leads to a very easy checking procedure

approximation method for configuration optimization of trusses an efficient method for truss configuration optimization is presented elastic trusses are designed for minimum weight by varying the areas of the members and the location of the joints constraints on member stresses and euler buckling are imposed and multiple loading conditions are considered the method presented here utilizes an approximate structural analysis based on first order taylor series expansions of the member forces the force approximation succeeds in reducing the degree of coupling between the sizing and geometry design variables and thereby increases the accuracy of the approximation a numerical optimizer uses information from the approximate structural analysis as it minimizes the weight of the truss

necessary and sufficient conditions for stabilizability of positive lti systems this paper obtains necessary and sufficient conditions for the stabilization of positive lti systems using a vertex algorithmic approach the results of this paper also encompass positive direct output feedback control the topic of the sequential separation principle and a particularly efficient algorithm for a class of positive systems

methodology for calculating aerodynamic sensitivity derivatives a general procedure is developed for calculating aerodynamic sensitivity coefficients using the full equations of inviscid fluid flow where the focus of the work is the treatment of geometric shape design variables using an upwind cell centered finite volume approximation to represent the euler equations sensitivity derivatives are determined by direct differentiation of the resulting set of coupled nonlinear algebraic equations that model the fluid flow

response surface techniques for diffuser shape optimization the design of incompressible diffusers for maximum pressure recovery is used to demonstrate the utility of response surface approximations for design optimization of eow devices two examples involving two and eve design variables are treated with the diffuser wall shapes described by polynomials and b splines in both cases monotonicity conditions drastically reduce the design space in this irregularly shaped space a pool of designs is selected by a d optimality criterion and analyzed by a e nite volume computational euid dynamics cfd code quadratic polynomial response surfaces are then e tted to the pressure recovery coefe cients to improve the prediction accuracy uncertain regressor terms and possible outlier design points are excluded based on statistical tests a standard optimization algorithm is used to e nd the optimal diffuser design from the response surface approximations the optimum diffusers exhibit minimal e ow separation and yield similar wall shapes for the two parameterizations a main asset of the response surface optimization approach lies in the smoothing of noisy response functions therefore theissueofnumericalnoiseincfd results basedon theuseof two different analysis codes is addressed

on the stability of switched positive linear systems it was recently conjectured that the hurwitz stability of the convex hull of a set of metzler matrices is a necessary and sufficient condition for the asymptotic stability of the associated switched linear system under arbitrary switching in this note we show that 1 this conjecture is true for systems constructed from a pair of second order metzler matrices 2 the conjecture is true for systems constructed from an arbitrary finite number of second order metzler matrices and 3 the conjecture is in general false for higher order systems the implications of our results both for the design of switched positive linear systems and for research directions that arise as a result of our work are discussed toward the end of the note