two degrees of freedom dead beat control system with robustness this paper deals with the design of a two degrees of freedom tdf dead beat controller with both optimal robustness and minimum settling time based on the parametrization of all stabilizing tdf controllers optimal robustness and minimum time control are achieved simultaneously the minimum time dead beat control is constructed for arbitrary real rational reference input at the same time optimal robustness is achieved under the constraint that the error between reference input and output asymptotically vanishes for any plant perturbation that does not violate the internal stability it is proved that under the same robustness criterion irrespective of its length of settling time the optimal robustness of the tdf system is always superior to that of the one degree of freedom odf system as long as its settling time is finite and they become identical only when the settling time of the odf system goes to infinity a numerical example is given to illustrate the theoretical results

from time series to linear system part i finite dimensional linear time invariant systems abstract in the first part of this paper the definition of a dynamical system as simply consisting of a family of time series will be developed in this context the notions of linearity time invariance and finite dimensionality will be introduced it will be shown that a given family of time series may be represented by a system of ar equations riw t l rl 1w t l 1 r0w t 0 or equivalently by a finite dimensional linear time invariant system x t 1 ax t bu t y t cx t du t w u y if and only if this family is linear shift invariant and complete or as is equivalent closed in the topology of pointwise convergence this yields a very high level and elegant set of axioms which characterize these familiar objects it is emphasized however that no a priori choice is made as to which components of w are inputs and which are outputs such a separation always exists in any specific linear time invariant model starting from these definitions the structural indices of such systems are introduced and it is shown how an ar representation of a system having a given behaviour can be constructed these results will be used in a modelling context in part ii of the paper

analytic hessian derivation for the quasi one dimensional euler equations the hessian for the quasi one dimensional euler equations is derived a pressure minimization problem and a pressure matching inverse problem are considered the flow sensitivity adjoint sensitivity gradient and hessian are calculated analytically using a direct approach that is specific to the model problems for the pressure minimization problem we find that the hessian exists and it contains elements with significantly larger values around the shock location for the pressure matching inverse problem we find at least one case for which the gradient as well as the hessian do not exist in addition two formulations for calculating the hessian are proposed and implemented for the given problems both methods can be implemented in industrial applications such as large scale aerodynamic optimization

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

maximum likelihood estimators and worst case optimal algorithms for system identification abstract for system identification problems with stochastic noise maximum likelihood estimators are frequently used if noise is deterministic worst case optimal algorithms should be considered in this paper we study the following problem under what circumstances are maximum likelihood estimators optimal in the worst case

from time series to linear system part iii approximate modelling abstract in the third part of this paper the problem of finding a linear time invariant complete system which models an observed time series will be continued however in this part it will be assumed that the model is required to explain the observations only approximately this raises the question of what is meant by an approximate model and how one should judge a model against data which in a strict sense falsify the model the initial sections of this paper introduce the methodology either the maximal admissible complexity is fixed and the best fitting model in the model class is sought or the maximally tolerated misfit is fixed and the least complex model in the model class is sought this is illustrated by means of finite dimensional models where natural complexity and misfit functions suggest themselves subsequently what is meant by the complexity of a linear time invariant complete system is discussed a concrete complexity function is proposed which is defined in terms of the richness of the behaviour on finite time intervals and is in one to one correspondence with the number of inputs the number of states and the observability indices of the underlying minimal i s o system the next definition is that of the misfit between an observed time series and a system a concrete misfit function is proposed which takes into consideration the lag structure of the system and in how far the observations fail to corroborate the ar equations which define the system s behaviour how the misfit may be computed by means of the correlation function of the data is then shown these concepts are subsequently used in order to set up two algorithms for approximate modelling of an observed q dimensional time series the first algorithm fixes the maximal complexity in a sense this comes down to fixing the number and the lags of the required ar equations the second algorithm fixes the tolerated misfit it is adaptive in nature in the sense that the number and the structure of the resulting ar equations will depend on the observations these ideas and algorithms are illustrated by means of two simulated examples

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

optimal sampling schedule for parameter estimation of linear models with unknown but bounded measurement errors the problem of optimal sampling design for parameter estimation when data are generated by linear models is addressed the measurements are assumed to be corrupted by an unknown but bounded additive noise the sampling design assumes that the number of samples is unconstrained and no replication is allowed two main results are shown 1 for particular classes of linear models the optimal number of measurements is equal to the number of parameters as in the statistical context 2 the uncertainty intervals of the parameter estimates are bounded from above by quantities that can be computer a priori knowing only the model and the error structure

control oriented system identification a worst case deterministic approach in h sub infinity the authors formulate and solve two related control oriented system identification problems for stable linear shift invariant distributed parameter plants in each of these problems the assumed a priori information is minimal consisting only of a lower bound on the relative stability of the plant an upper bound on a certain gain associated with the plant and an upper bound on the noise level the first of these problems involves identification of a point sample of the plant frequency response from a noisy finite output time series obtained in response to an applied sinusoidal input with frequency corresponding to the frequency point of interest this problem leads naturally to the second problem which involves identification of the plant transfer function in h sub infinity from a finite number of noisy point samples of the plant frequency response concrete plans for identification algorithms are provided for each of these two problems

relationship between the trace and maximum eigenvalue norms for linear quadratic control design the use of a sum of squares h sub 2 norm is considered for optimal control system design the relative advantages of the linear quadratic gaussian lqg trace norm and the h sub infinity sup norm cost functions are discussed an argument is presented to show that the sum of squares norm ssn problem might be considered alongside the lqg and h sub infinity cost problems when exploring the relationship between the lqg and ssn problems it is found that an lqg controller could be found which correspond to an ssn problem with larger disturbance inputs this suggests that the lqg controller can be computed with the knowledge that it minimizes a well defined ssn problem with worst case uncertainty or disturbances the range of a certain set of eigenvalues is found to provide a measure of the difference between the lqg and ssn problem designs

two dimensional discrete fuzzy numbers and applications in this paper the concept of two dimensional discrete fuzzy numbers is presented based on the idea of representation theorem of one dimensional discrete fuzzy numbers then a sufficient condition is proposed which makes a fuzzy set on r2 become a two dimensional discrete fuzzy number and the representations of joint membership function and the two edge membership functions of two dimensional discrete fuzzy number are given some special two dimensional discrete fuzzy numbers are also defined and then some weak orders in the two dimensional discrete fuzzy number space are set up based on the mass centers and the degree of ambiguities of two dimensional discrete fuzzy numbers and their properties are also investigated at last some practical examples are included to demonstrate the effectiveness and potential of the theoretic results obtained

discrete adjoint of fractional step incompressible navier stokes solver in curvilinear coordinates and application to data assimilation abstract the discrete adjoint of an incompressible navier stokes algorithm in generalized coordinates is derived and applied to estimate the states of saturated and turbulent circular couette flows the forward navier stokes model is based on the fractional step algorithm in curvilinear coordinates on a structured grid 1 which has been widely adopted in direct numerical simulations of transitional and turbulent flows the discrete adjoint equations adopt the same stencil and temporal scheme as the forward discretization and expressions are derived that relate the discrete adjoint variables to their continuous counterpart the key ingredients of the forward algorithm can be retained in the adjoint including the computation of the cell geometry the approximate factorization method and the parallelization strategy the accuracy efficiency and stability of the adjoint solver are also commensurate with the forward model in addition a novel symmetric projector is proposed to guarantee that the the outcome of the adjoint algorithm is divergence free the implementation of the algorithm in double precision satisfies the forward adjoint relation up to eight significant figures and further validation is performed using circular couette flow the forward and adjoint growth rates of instability modes from linear theory are accurately reproduced in addition an adjoint variational data assimilation algorithm 4dvar is adopted to reconstruct the initial condition of circular couette flows from limited measurements obtained from an independent simulation when the flow is comprised of saturated wavy vortices wall measurements are sufficient to reconstruct an initial condition that latches onto the target state after a short time for the more challenging turbulent case coarse grained velocity data are used to estimate the initial condition

exponentially derived switching schemes for inviscid flow abstract a class of exponential schemes used for singular perturbation problems is taken and finite difference schemes for inviscid flow with shocks is derived from them in particular exponential schemes are formulated for steady viscous flow in a variable area duct using both a one equation model with the physical viscous terms and the euler equations with artificial viscosity upon taking the limit as the viscosity coefficient goes to zero exponentially derived switching eds schemes are obtained which switch the direction of finite differencing based upon characteristic directions of the reduced problem for the euler equations some of the eds schemes can be identified as flux vector splitting the split coefficient matrix method and a scheme of huang some aspects of uniqueness of finite difference solutions are discussed

discrete fourier transform and h sub infinity approximation it is shown that uniform rational approximation of nonrational transfer functions can always be obtained by means of the discrete fourier transform dft as long as such approximants exist based on this fact it is permissible to apply the fast fourier transform fft algorithm in carrying out rational approximations without being apprehensive of convergence the dft is used to obtain traditional approximations for transfer functions of infinite dimensional systems justification is provided for using the dft in such approximations it is established that whenever a stable transfer function can be approximated uniformly on the right half plane by a rational function its approximants can always be recognized by means of a dft

aerodynamic optimization algorithm with integrated geometry parameterization and mesh movement an efficient gradient based algorithm for aerodynamic shape optimization is presented the algorithm consists of several components including a novel integrated geometry parameterization and mesh movement a parallel newton krylov flow solver and an adjoint based gradient evaluation to integrate geometry parameterization and mesh movement generalized b spline volumes are used to parameterize both the surface and volume mesh the volume mesh of b spline control points mimics a coarse mesh a linear elasticity mesh movement algorithm is applied directly to this coarse mesh and the fine mesh is regenerated algebraically using this approach mesh movement time is reduced by two to three orders of magnitude relative to a node based movement the mesh adjoint system also becomes smaller and is thus amenable to complex step derivative approximations when solving the flow adjoint equations using restarted krylov subspace methods a nested subspace strategy is shown to be more robust than truncating the entire subspace optimization is accomplished using a sequential quadratic programming algorithm the effectiveness of the complete algorithm is demonstrated using a lift constrained induced drag minimization that involves large changes in geometry

feedback minimax sensitivity and optimal robustness in this paper we look for feedbacks that minimize the sensitivity function of a linear single variable feedback system represented by its frequency responses sensitivity to disturbances and robustness under plant perturbations are measured in a weighted h infty norm in an earlier paper zames proposed an approach to feedback design involving the measurement of sensitivity by multiplicative seminorms which have certain advantages over the widely used quadratic norm in problems where there is plant uncertainty or where signal power spectra are not fixed but belong to sets the problem was studied in a general setting and some h infty examples were solved here a detailed study of the single variable case is undertaken the results are extended to unstable plants and explicit formulas for the general situation of a finite number of right half plane rhp plant zeros or poles are provided the q or approximate inverse parametrization of feedbacks that maintain closed loop stability is extended to the ease of unstable plants the h infty and wiener hopf approaches are compared

trapezoidal approximation and aggregation trapezoidal approximation of fuzzy numbers is discussed in relation to data aggregation an important problem whether it is better to simplify initial data before using an aggregation operator or conversely to aggregate original fuzzy values and then to simplify the output is addressed

robust identification and interpolation in h abstract we consider system identification in h in the framework proposed by helmicki jacobson and nett an algorithm using the jackson polynomials is proposed that achieves an exponential convergence rate for exponentially stable systems it is shown that this and similar identification algorithms can be successfully combined with a model reduction procedure to produce low order models connections with the nevanlinna pick interpolation problem are explored and an algorithm is given in which the identified model interpolates the given noisy data some numerical results are provided for illustration finally the case of unbounded random noise is discussed and it is shown that one can still obtain convergence with probability 1 under natural assumptions

discrete shape sensitivity equations for aerodynamic problems intensive research and development in computational fluid dynamics cfd has recently produced many powerful cfd codes to simulate complex aerodynamic phenomena however in order to enhance the usefulness of these cfd codes for design practice development of design sensitivity equations compatible to these codes becomes very important this paper represents a part of such an effort to develop a sensitivity analysts methodology that enables the sensitivity equations to be implemented into existing cfd codes with minimal code modification the methodology is based upon a pre elimination procedure which accounts for consistently linearized boundary conditions formulations of both the direct differentiation and the adjoint variable methods will be presented in the paper

on identification of stable systems and optimal approximation abstract approximative modelling of stable continuous time possibly infinite dimensional systems is studied based on an optimal approximation approach both approximation of analytical system representations system approximation as well as approximation of input output data based system estimates system identification are considered while special emphasis is given to approximative modelling in the h and hankel norms the l1 and l2 norm cases are also discussed the model sets considered here are finite dimensional systems and time shifted systems simple delay systems the theory of approximation numbers is shown to provide a convenient tool to study problems of identification of stable continuous time systems in a deterministic framework with close connections to complexity considerations laguerre fourier series methods and hankel operator techniques can be utilized to develop fully practical identification methods for continuous time possibly infinite dimensional systems

a class of algorithms for identification in h abs traet in this paper a class of algorithms for the problem of system identification in are investigated these algorithms are characterized by a two stage structure and involve a class of window functions some conditions in terms of properties of the window functions are derived which guarantee robust convergence of the algorithms identification errors are analyzed for several common window functions this leads to some insights into the trade off between the error induced by approximation and that due to noise

model reference predictive lqg optimal control law for simo systems the design of linear quadratic gaussian lqg controllers for single input multiple output simo systems is considered this includes the class of multiloop control problems which are often solved using a classical nested loop structure many simplifications can be achieved over the more general multivariate problem which is important in self tuning control applications for example the tracking problem allows a model following capability to be introduced a predictive control feature is also available which enables the future values of the set point to be taken into account as in preprogrammed robot control

triangular norms on partially ordered sets in this paper several methods to construct triangular norms on partially ordered sets are proposed these methods include 1 constructing triangular norms on the poset of closed intervals of a given bounded poset 2 constructing triangular norms via galois connections between bounded posets based on a categorical analysis of the construction of triangular norms on closed intervals via monotone functions and their pseudo inverses 3 constructing triangular norms on function spaces between partially ordered sets

least squares methods for h sub infinity control oriented system identification a series of system identification algorithms that yield identified models which are compatible with current robust controller design methodologies is presented these algorithms are applicable to a broad class of stable distributed linear shift invariant plants the a priori information necessary for their application consists of a lower bound on the relative stability of the unknown plant an upper bound on a certain gain associated with the unknown plant and an upper bound on the noise level the a posteriori data information consists of a finite number of corrugated point frequency response estimates of the unknown plant the extent to which certain standard hilbert space or least squares method are applicable to the h sub infinity system identification problem considered is examined results are established that connect the h sub 2 error of the least squares methods to the h sub infinity error needed for control oriented system identification

dual consistency and functional accuracy consider the discretization of a partial differential equation pde and an integral functional that depends on the pde solution the discretization is dual consistent if it leads to a discrete dual problem that is a consistent approximation of the corresponding continuous dual problem consequently a dual consistent discretization is a synthesis of the so called discrete adjoint and continuous adjoint approaches we highlight the impact of dual consistency on summation by parts sbp finite difference discretizations of steady state pdes specifically superconvergent functionals and accurate functional error estimates in the case of functional superconvergence the discrete adjoint variables do not need to be computed since dual consistency on its own is sufficient numerical examples demonstrate that dual consistent schemes significantly outperform dual inconsistent schemes in terms of functional accuracy and error estimate effectiveness the dual consistent and dual inconsistent discretizations have similar computational costs so dual consistency leads to improved efficiency to illustrate the dual consistency analysis of sbp schemes we thoroughly examine a discretization of the euler equations of gas dynamics including the treatment of the boundary conditions numerical dissipation interface penalties and quadrature by sbp norms

a pde sensitivity equation method for optimal aerodynamic design the use of gradient based optimization algorithms in inverse design is well established as a practical approach to aerodynamic design a typical procedure uses a simulation scheme to evaluate the objective function from the approximate states and its gradient then passes this information to an optimization algorithm once the simulation scheme cfd flow solver has been selected and used to provide approximate function evaluations there are several possible approaches to the problem of computing gradients one popular method is to differentiate the simulation scheme and compute design sensitivities that are then used to obtain gradients although this black box approach has many advantages in shape optimization problems one must compute mesh sensitivities in order to compute the design sensitivity in this paper we present an alternative approach using the pde sensitivity equation to develop algorithms for computing gradients this approach has the advantage that mesh sensitivities need not be computed moreover when it is possible to use the cfd scheme for both the forward problem and the sensitivity equation then there are computational advantages an apparent disadvantage of this approach is that it does not always produce consistent derivatives however for a proper combination of discretization schemes one can showasymptotic consistencyunder mesh refinement which is often sufficient to guarantee convergence of the optimal design algorithm in particular we show that when asymptotically consistent schemes are combined with a trust region optimization algorithm the resulting optimal design method converges we denote this approach as thesensitivity equation method the sensitivity equation method is presented convergence results are given and the approach is illustrated on two optimal design problems involving shocks

a comparison of optimization based approaches for a model computational aerodynamics design problem abstract the objective of this paper is to compare three optimization based methods for solving aerodynamic design problems we use the euler equations for one dimensional duct flow as a model problem the optimization methods are i the black box method with finite difference gradients ii a modification where gradients are found by an algorithm based on the implicit function theorem and iii an all atonce method where the flow and design variables are simultaneously altered the three methods are applied to the model problem and compared for efficiency robustness and implementation difficulty we also show that the black box implicit gradient method is equivalent to applying the variational or optimal control approach to design optimization directly to the discretized analysis problem rather than to the continuous problem as is usually done the black box method with implicit gradients seems to provide a good compromise of features and can be retrofitted to most existing analysis codes to turn them into design codes although the all at once method was found to be less robust than the black box methods when it succeeded it was considerably more efficient

a general theory for the wiener hopf design of multivariable control systems multivariable control system design in a quadratic cost setting is treated for a completely general configuration the class of all controllers is determined for which the general configuration is internally asymptotically stable and a quadratic cost functional is finite this controller class is parameterized in terms of an arbitrary real rational strictly proper matrix z s which is analytic in the closed right hand side of the s plane the choice z identical to 0 gives the controller which minimizes the quadratic cost functional

h2 optimal control for generalized discrete time systems abstract for a generalized discrete time system whose transfer function matrix may be improper or polynomial we give realization based formulas for the h 2 optimal output feedback controller the formulas bear essentially the same elegant simplicity of the proper case

a new linguistic computational model based on discrete fuzzy numbers for computing with words in recent years several different linguistic computational models for dealing with linguistic information in processes of computing with words have been proposed however until now all of them rely on the special semantics of the linguistic terms usually fuzzy numbers in the unit interval and the linguistic aggregation operators are based on aggregation operators in 0 1 in this paper a linguistic computational model based on discrete fuzzy numbers whose support is a subset of consecutive natural numbers is presented ensuring the accuracy and consistency of the model in this framework no underlying membership functions are needed and several aggregation operators defined on the set of all discrete fuzzy numbers are presented these aggregation operators are constructed from aggregation operators defined on a finite chain in accordance with the granularity of the linguistic term set finally an example of a multi expert decision making problem in a hierarchical multi granular linguistic context is given to illustrate the applicability of the proposed method and its advantages

laguerre series approximation of infinite dimensional systems laguerre fourier approximations of stable systems are shown to exhibit many desirable properties for various classes of infinite dimensional systems specifically time domain supremum and l1 norm convergence results and frequency domain h norm convergence results are given for laguerre fourier approximations it is also shown that the theory of laguerre polynomials solves explicitly the problem of determining laguerre fourier approximations for a large class of delay systems furthermore it is believed that these results are important for the study of orthonormal series identification as a general technique for identification of infinite dimensional systems

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

convergence of upwind schemes for a stationary shock a nonlinear first order boundary value problem with discontinuous solutions is considered it arises in the study of gasflow through a duct and allows in general for multiple solutions new convergence results for three difference schemes are presented and the sharpness of numerical layers is established for the eo scheme stability of a physically correct solution with respect to time evolution is shown

aggregation of subjective evaluations based on discrete fuzzy numbers in this paper aggregation functions defined on the set of all discrete fuzzy numbers whose support is a subset of consecutive natural numbers are introduced and the particular cases of uninorms and nullnorms are studied in detail these aggregation functions are constructed from discrete aggregation functions defined on a finite chain and they are applied to the aggregation of subjective evaluations

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

evaluating students answerscripts using fuzzy numbers associated with degrees of confidence this paper presents a new approach for evaluating students answerscripts using fuzzy numbers associated with degrees of confidence of the evaluator the satisfaction levels awarded to the questions of students answerscripts are represented by fuzzy numbers associated with degrees of confidence between zero and one the arithmetic operations between the alpha cuts of fuzzy numbers are used to evaluate the total mark of each student where alpha isin 0 1 the proposed method can overcome the drawbacks of the methods presented by biswas 1994 and chen and lee 1999 it can evaluate students answerscripts in a more flexible and more intelligent manner

aggregation functions on the set of discrete fuzzy numbers defined from a pair of discrete aggregations abstract in this paper we propose a method to construct aggregation functions on the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers from a couple of discrete aggregation functions the interest on these discrete fuzzy numbers lies on the fact that they can be interpreted as linguistic expert valuations that increase the flexibility of the elicitation of qualitative information based on linguistic terms finally a linguistic decision making model based on a pair of aggregation functions defined on discrete fuzzy numbers is given

approximation and identification of continuous time systems an approximation approach to the identification of stable continuous time possibly infinite dimensional systems is studied for this purpose concrete exponential leg endre series methods are proposed and analysed here for the l1 and l2 approximations of continuous time systems rate of approximation results are given for the proposed methods for an important class of delay systems the proposed exponential legendre series method for the l2 approximation has a certain optimal rate of approximation property for this class of delay systems these results show that exponential legendre series techniques have promising properties in connection with the l1 and l2 identifications of stable continuous time systems the proposed l1 identification method has a direct application to the robust design of control systems

parameter identification in the presence of non parametric dynamic uncertainty abstract this paper provides identification laws which yield monotonic parameter error reduction in the absence of external noise inputs but in the presence of non parametric dynamic uncertainty unmodelled dynamics this paper considers two non parametric uncertainty sets motivated by robust control the weighted ball in h and the weighted ball in the induced l2 norm the non parametric uncertainty produces signals which corrupt the signals used in identification this paper shows that the corruption is non conservatively bounded in an l2 sense this l2 bound is then compared with the signal energy with the result used to enable disable the parameter adjustment of a gradient least squares adjustment mechanism it is proved that the resulting parameter adjustment yields non increasing parameter errors with strictly decreasing parameter errors whenever the parameter errors are distinguishable from zero given the system input and output histories

fuzzy numbers from raw discrete data using linear regression this paper focuses on modelling fuzzy numbers with meaningful membership functions more precisely it proposes a method to construct trapezoidal fuzzy number approximations from raw discrete data in many applications input information is numerical and therefore particular fuzzy sets such as fuzzy numbers hold great interest and relevance in managing data imprecision and vagueness the proposed technique provides an efficient way to obtain trapezoidal numbers using linear regression the technique is simple fast and effective preliminary tests are performed using different types of input data a gaussian function a sigmoidal function three datasets of synthetic discrete data and an histogram obtained from a colour satellite image

the lqg ltr procedure for multivariable feedback control design this paper provides a tutorial overview of the lqg ltr design procedure for linear multivariable feedback systems lqg ltr is interpreted as the solution of a specific weighted h2 tradeoff between transfer functions in the frequency domain properties of this solution are examined for both minimum phase and nonminimum phase systems this leads to a formal weight augmentation procedure for the minimum phase case which permits essentially arbitrary specification of system sensitivity functions in terms of the weights while such arbitrary specifications are not possible for nonminimum phase problems a direct relationship between weights and sensitivities is developed for nonminimum phase siso and certain nonminimum phase mimo cases which guides the weight selection process

h2 output feedback control for descriptor systems this paper solves the h 2 output feedback control problem for continuous time descriptor systems an existence condition of the h 2 optimal controller is derived based on the standard model matching technique and a characterization of the optimal controller is given in terms of the solutions of two generalized algebraic riccati equations it turns out that the optimal controller has an observer based structure well known in the state space case so that the results in this paper are natural extensions of the state space results to the descriptor systems a numerical example is also included to show the applicability of the proposed results

canonical representations of discrete fuzzy numbers in this paper we obtain two canonical representations of discrete fuzzy numbers in particular it is shown that any discrete fuzzy number can be represented by a triangular or a block discrete fuzzy number having the same value ambiguity and fuzziness as the original number

a note on h sub 2 optimal control problems with passivity constraints considers the problem of determining the closest function that has a positive real part on the unit disk to a given function in h sub 2 an explicit characterization of the projection is given remarks on potential applications using this projection result to control synthesis and system identification problems are made

nearest piecewise linear approximation of fuzzy numbers abstract the problem of the nearest approximation of fuzzy numbers by piecewise linear 1 knot fuzzy numbers is discussed by using 1 knot fuzzy numbers one may obtain approximations which are simple enough and flexible to reconstruct the input fuzzy concepts under study they might be also perceived as a generalization of the trapezoidal approximations moreover these approximations possess some desirable properties apart from theoretical considerations approximation algorithms that can be applied in practice are also given

admitting the inadmissible adjoint formulation for incomplete cost functionals in aerodynamic optimization we derive the adjoint equations for problems in aerodynamic optimization which are improperly considered as inadmissible for example a cost functional which depends on the density rather than on the pressure is considered inadmissible for an optimization problem governed by the euler equations we show that for such problems additional terms should be included in the lagrangian functional when deriving the adjoint equations these terms are obtained from the restriction of the interior pde to the control surface demonstrations of the explicit derivation of the adjoint equations for inadmissible cost functionals are given for the potential euler and navier stokes equations

optimality of central and projection algorithms for bounded uncertainty this paper investigates optimality properties of central and projection algorithms for linear problems in the field of system identification in a context in which uncertainty is described in a deterministic rather than statistical way particular attention is devoted to least squares algorithms when the measurement noise is assumed to be unknown but bounded in a hilbert norm a major contribution of this paper consists in proving that least squares algorithms enjoy strong optimality properties on the contrary it is pointed out that these properties do not hold for other frequently used projection algorithms such as least absolute values or minimax algorithms corresponding to a description of the measurement error in h or l norm respectively

adjoint based derivative computations for the optimal control of discontinuous solutions of hyperbolic conservation laws we propose a rigorous procedure to obtain the adjoint based gradient representation of cost functionals for the optimal control of discontinuous solutions of conservation laws hereby it is not necessary to introduce adjoint variables for the shock positions our approach is based on stability properties of the adjoint equation we give a complete analysis for the case of convex scalar conservation laws the adjoint equation is a transport equation with discontinuous coefficients and special reversible solutions must be considered to obtain the correct adjoint based gradient formula reversible solutions of the adjoint transport equation and the required stability properties are analyzed in detail

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

shape optimization for delay of laminar turbulent transition a method using gradient based optimization is introduced for the design of wing profiles with the aim of natural laminar flow as well as minimum wave drag the euler equations of gasdynamics the laminar boundary layer equations for compressible flows on infinite swept wings and the linear parabolized stability equations pse are solved to analyze the evolution of convectively unstable disturbances laminar turbulent transition is assumed to be delayed by minimizing a measure of the disturbance kinetic energy of a chosen disturbance which is computed using the pse the shape gradients of the disturbance kinetic energy are computed based on the solutions of the adjoints of the state equations just named numerical tests are carried out to optimize the rae 2822 airfoil with the aim to delay simultaneously the transition reduce the pressure drag coefficient and maintain the coefficients of lift and pitch moments constraints are also applied on the geometry results show a reduction of the total amplification of a large number of disturbances which is assumed to represent a delay of the transition in the boundary layer because delay of the transition implies reduction of the viscous drag the present method enables shape optimization to perform viscous drag reduction

steady shock tracking and newton s method applied to one dimensional duct flow abstract a new computational approach combining shock tracking and newton s method is applied to steady one dimensional flow through a variable area duct on a transformed computational grid where the shock is fixed the physical shock location appears explicitly as an unknown in a set of finite difference equations and is coupled to the other unknowns the space time characteristics for the associated time dependent problem are used in formulating the boundary conditions the resulting system is solved by newton s method the computed results agree very well with an exact solution and the newton iterates converge rapidly in comparison to some explicit shock capturing time asymptotic methods

dual criterion stochastic optimal control problem for robustness improvement the solution of the dual criterion linear quadratic stochastic optimal control problem is obtained by following a wiener type of solution procedure a stabilizing solution is guaranteed by parameterizing the controller using the desoer fractional representation approach the dual criterion includes sensitivity and complementary sensitivity weighting terms which provide a means of varying the robustness characteristics of the multivariable system

ℋ2 control of siso fractional order systems abstract in this paper we propose a systematic method to design the optimal 2 output feedback controller for single input single output plants of fractional order based on wiener hopf spectral factorization the plant is allowed to be unstable non minimum phase and incommensurate order using the fractional order youla parameterization the resulting controller satisfies the closed loop internal stability requirement because of the branch point singularities associated with fractional order transfer functions the spectral decompositions are effected via an integral technique an example is provided to demonstrate the design procedure

the law of large numbers and renewal process for t related weighted fuzzy numbers on rp this paper considers the law of large numbers for t related weighted fuzzy variables whose underlying spaces are r p we provide new sufficient conditions that do not depend on the shape of fuzzy numbers and the additive generator of a t norm t for the law of large numbers for t related weighted fuzzy variables the results provide a far reaching generalization of previous findings on the law of large numbers for t related fuzzy numbers in addition we prove t related fuzzy renewal theorems in which the inter arrival time is characterized as weighted fuzzy numbers under t norm based fuzzy operations on r p by using the law of large numbers for weighted fuzzy variables on r p we also investigate the law of large numbers and the renewal process for t related fuzzy numbers on r p with respect to the credibility measure the chance measure and the expected value

a sensitivity and adjoint calculus for discontinuous solutions of hyperbolic conservation laws with source terms we present a sensitivity and adjoint calculus for the control of entropy solutions of scalar conservation laws with controlled initial data and source term the sensitivity analysis is based on shift variations which are the sum of a standard variation and suitable corrections by weighted indicator functions approximating the movement of the shock locations based on a first order approximation by shift variations in l1 we introduce the concept of shift differentiability which is applicable to operators having functions with moving discontinuities as images and implies differentiability for a large class of tracking type functionals in the main part of the paper we show that entropy solutions are generically shift differentiable at almost all times t 0 with respect to the control hereby we admit shift variations for the initial data which allows us to use the shift differentiability result repeatedly over time slabs this is useful for the design of optimization methods with time domain decomposition our analysis especially of the shock sensitivity combines structural results by using generalized characteristics and an adjoint argument our adjoint based shock sensitivity analysis does not require us to restrict the richness of the shock structure a priori and admits shock generation points the analysis is based on stability results for the adjoint transport equation with discontinuous coefficients satisfying a one sided lipschitz condition as a further main result we derive and justify an adjoint representation for the derivative of a large class of tracking type functionals

an approximately factored incremental strategy for calculating consistent discrete aerodynamic sensitivity derivatives in this study involving advanced fluid flow codes an incremental iterative formulation also known as the delta or correction form together with the well known spatially split approximate factorization algorithm is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis for smaller 2d problems a direct method can be applied to solve these linear equations in either the standard or the incremental form in which case the two are equivalent iterative methods are needed for larger 2d and future 3d applications however because direct methods require much more computer memory than is currently available iterative methods for solving these equations in the standard form are generally unsatisfactory due to a lack of diagonal dominance and perhaps ill conditioning of the coefficient matrix this problem can be overcome when these equations are cast in the incremental form these and other benefits are discussed herein the methodology is successfully implemented and tested in 2d using an upwind cell centered finite volume formulation applied to the thin layer navier stokes equations results are presented for two sample airfoil problems 1 subsonic low reynolds number laminar flow and 2 transonic high reynolds number turbulent flow

optimal control of flow with discontinuities optimal control of the 1 d riemann problem of euler equations is studied with the initial values for pressure and density as control parameters the least squares type cost functional employs either distributed observations in time or observations calculated at the end of the assimilation window existence of solutions for the optimal control problem is proven smooth and nonsmooth optimization methods employ the numerical gradient respectively a subgradient of the cost functional obtained from the adjoint of the discrete forward model the numerical flow obtained with the optimal initial conditions obtained from the nonsmooth minimization matches very well with the observations the algorithm for smooth minimization converges for the shorter time horizon but fails to perform satisfactorily for the longer time horizon except when the observations corresponding to shocks are detected and removed

smoothed sensitivity equation method for fluid dynamic design problems we consider shape optimization problems involving compressible fluid flows which are characterized by non smooth and or noisy objective functions such functions are difficult to optimize using derivative based techniques to overcome such a difficulty we suggest an approach for estimating the sensitivity derivatives based on a suitable smoothing of the sensitivity equations the smoothing affects only the sensitivity derivatives and not the accuracy of the analysis the basic mechanism by which the smoothing process achieves this result is illustrated with the help of an inverse design problem involving an inviscid quasi one dimensional flow having a closed form solution the convergence properties and the computational efficiency of the approach are demonstrated on two inverse design problems involving two dimensional inviscid compressible flows

extension of discrete t norms and t conorms to discrete fuzzy numbers the aim of this paper is to extend a monotone operation defined on a discrete setting to a closed binary operation on the partially ordered set a 1 of discrete fuzzy numbers whose support is a subset of natural numbers moreover we study several properties like the monotonicity commutativity associativity or the boundary condition when the extended operation is a discrete t norm or a discrete t conorm defined on a finite chain l 0 1 n n also we study the frank s equation for t norms and t conorms defined on a special subset of a 1 finally we propose an application to obtain consensus opinion based on discrete fuzzy weighted normed operators

fuzzy approximation relations on fuzzy n cell number space and their applications in classification in this paper the problems of fuzzy binary relations on fuzzy n cell number space and their applications are investigated firstly we have defined some fuzzy approximation relations on fuzzy n cell number space and studied their properties secondly as application we have developed an algorithmic version of classification in an imprecise or uncertain environment by using the fuzzy approximation relations practical examples are provided to show the application and rationality of the proposed techniques

new methods for students evaluation using fuzzy sets in an earlier work biswas 1995 presented two methods for the application of fuzzy sets in students answerscripts evaluation in this paper we extend his work to propose two new methods for evaluating students answerscripts using fuzzy sets the proposed methods can overcome the drawbacks in biswas 1995 due to the fact that they do not need to perform the complicated matching operations and they can evaluate students answerscripts in a more fair manner

estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors linear families of models and estimators the problem of parameter estimation and of the evaluation of related uncertainty intervals is considered in the case that a probabilistic description of noise and errors is not available of suitable but only a bound on them is known in the present paper only linear parametrizations and estimators are considered very simple and computationally feasible algorithms are derived for evaluating two different types of uncertainty intervals estimates uncertainty intervals parameter uncertainty intervals the relationships between the eui s and the pui s are established and the solution to the problem of the minimum uncertainty intervals estimator is given the latter can be obtained by means of a simple linear programming algorithm

feedback properties of multivariable systems the role and use of the return difference matrix for linear time invariant multivariable feedback systems the feedback properties of plant disturbance attenuation sensor noise response stability margins and sensitivity to plant and sensor variation are quantitatively related to the bode magnitude versus frequency plots of the singular values of the return difference matrix i l and of the associated inverse return difference matrix i l 1 implied fundamental limits of feedback performance are quantitatively described and design tradeoffs are discussed the penalty function in the stochastic linear quadratic gaussian lqg optimal control problem is found to be a weighted sum of the singular values with the weights determined by the quadratic cost and noise intensity matrices this enables systematic tuning of lqg cost and noise matrices so that the resulting optimal return difference and inversereturn difference meet inequality constraints derived from design specifications on feedback properties the theory has been used to synthesize a multivariable automatic controller for the longitudinal dynamics of an advanced fighter aircraft

on the wiener hopf approach to optimal feedback design abstract a simple solution is given to the problem of designing a proper feedback which minimizes the h 2 norm of the sensitivity function multiplied by a suitable weighting function

optimal mixed sensitivity for siso distributed plants the authors extend previous results for the single input single output siso mixed sensitivity problem for distributed parameter systems to a more general setting in which the transfer function of the plant to be controlled has both irrational stable and irrational unstable parts these developments were originally motivated by the computation of the infimal h sup spl infin norm of the weighted mixed sensitivity for the irrational transfer function model of a damped flexible beam