determining the optimal parameters for the mhd flow and heat transfer with variable viscosity and hall effect abstract the direct and optimal control solution of the laminar fully developed steady mhd flow of an incompressible electrically conducting fluid in a duct is considered together with the heat transfer the flow is driven by a constant pressure gradient and an external uniform magnetic field the fluid viscosity is temperature dependent varying exponentially and the hall effect viscous and joule dissipations are taken into consideration the control problem is solved by the discretize then optimize approach using mixed finite element method for the mhd and energy equations the control formulations with the hall and viscosity parameters the hartmann and brinkmann number are given to regain the desired velocity and temperature of the mhd flow

control of flow separation over a forward facing step by model reduction abstract design and implementation of reduced order optimal controller for flow separation are investigated the reduced order controller design is based on proper orthogonal decomposition pod and galerkin projection detailed finite element simulations are performed and pod is applied to the resulting data to extract the most energetic eigenmodes these global eigenmodes are then used in conjunction with the galerkin projection to obtain a reduced order low dimensional model reduced order models are not only attractive for real time control computation but also crucial for detailed stability and bifurcation analysis we investigate the design of optimal controller for flow separation in a channel with this model where actuation is performed on a small part of the boundary two different types of surface actuation are considered tangential blowing and suction through a single slot best locations for actuation and adaptive procedure for reduced order model are explored the proposed approaches are evaluated by investigating the control of flow separation over a forward facing step channel our methods are found to be efficient and fast and our methods demonstrate a significant reduction in computational time and feasibility dramatic separation delays are observed on all cases it is found that the tangential blowing is more efficient in mitigating flow separation and reducing wake spread

reduced order optimal control based on approximate inertial manifolds for nonlinear dynamical systems a reduced order method for optimal control problems in infinite dimensions based on approximate inertial manifolds is developed convergence of the cost optimal controls and optimal states of the finite dimensional reduced order optimal control problems to the original optimal control problem is analyzed special attention is given to the particular case when the dynamics are described by the navier stokes equations in dimension two

using fuzzy sets in operational research abstract during the last four decades a large number of mainly mathematical tools have been developed in and for operational research they are primarily devices to find optimal solutions after a problem has been modelled formally hardly any new tools have been developed for proper modelling of problems which are not well structured and which can not easily be cast into classical mathematical models fuzzy set theory as proposed by l zadeh in 1965 promises to bridge part of this gap it is much more adaptable to different problem structures and better suited to model human evaluation and decision making processes than classical mathematics this paper will primarily focus attention on four questions why fuzzy sets in or what are fuzzy sets where can they be used and how are they being used

bi criteria multi facility location problem in fuzzy environment abstract this paper presents a fuzzy goal programming model for locating multiple new facilities on a plane bounded by a convex polygon under the criteria 1 minimize the sum of all the transportation costs and 2 minimize the maximum distances from the facilities to the demand points it has also been proved that the methodology given will always give a nondominated solution recti linear distances have been taken as the scenario may be thought of in an urban setting a numerical example has been given to illustrate the solution methodology

numerical model reduction of 2d steady incompressible laminar flows application on the flow over a backward facing step the numerical solution of most fluid mechanics problems usually needs such a fine mesh that the associated computational times become non negligible parts in any design process in order to couple numerical modelling schemes with inversion or control algorithms the size of such models needs to be highly reduced the identification method is a way to build low order models that fit with the original ones the laminar flow over a backward facing step is used as a test case presented solutions are found to be in good agreement with experimental and numerical results found in the literature

domain decomposition methods for advection dominated linear quadratic elliptic optimal control problems abstract we present an optimization level domain decomposition dd preconditioner for the solution of advection dominated elliptic linear quadratic optimal control problems which arise in many science and engineering applications the dd preconditioner is based on a decomposition of the optimality conditions for the elliptic linear quadratic optimal control problem into smaller subdomain optimality conditions with dirichlet boundary conditions for the states and the adjoints on the subdomain interfaces these subdomain optimality conditions are coupled through robin transmission conditions for the states and the adjoints the parameters in the robin transmission condition depend on the advection this decomposition leads to a schur complement system in which the unknowns are the state and adjoint variables on the subdomain interfaces the schur complement operator is the sum of subdomain schur complement operators the application of which is shown to correspond to the solution of subdomain optimal control problems which are essentially smaller copies of the original optimal control problem we show that under suitable conditions the application of the inverse of the subdomain schur complement operators requires the solution of a subdomain elliptic linear quadratic optimal control problem with robin boundary conditions for the state numerical tests for problems with distributed and with boundary control show that the dependence of the preconditioners on mesh size and subdomain size is comparable to its counterpart applied to a single advection dominated equation these tests also show that the preconditioners are insensitive to the size of the control regularization parameter

a geometric averaging procedure for constructing supertransitive approximation to binary comparison matrices abstract the usefulness of encoding the fuzzy evaluations of alternatives and the importance weights of criteria in a multiple objective decision problem through binary comparison matrices or pairwise judgment matrices is receiving considerable attention the methodology for identifying the best alternative in a given decision problem involves the computation of the principal eigenvectors of the binary comparison matrices the eigenvectors transform the fuzzy evaluations of the importance of the criteria and the ratings of the alternatives into a ratio scale a difficulty that is often experienced in using this approach in practice is the inconsistency of the binary evaluations this paper proposes a simple averaging procedure to construct a supertransitive approximation to a binary comparison matrix where inconsistency is a problem it is further suggested that such an adjustment might be necessary to more closely reflect the inherent fuzziness of the evaluations contained in a binary comparison matrix the procedure is illustrated by means of examples

second order methods for optimal control of time dependent fluid flow second order methods for open loop optimal control problems governed by the two dimensional instationary navier stokes equations are investigated optimality systems based on a lagrangian formulation and adjoint equations are derived the newton and quasi newton methods as well as various variants of sqp methods are developed for applications to optimal flow control and their complexity in terms of system solves is discussed local convergence and rate of convergence are proved a numerical example illustrates the feasibility of solving optimal control problems for two dimensional instationary navier stokes equations by second order numerical methods in a standard workstation environment

existence of optimal controls for viscous flow problems a class of optimal control problems in viscous flow is studied main result is the existence theorem for optimal control three typical flow control problems are formulated within this general class

characterizations of the canonical phase observable in this paper we investigate various properties of phase observables which could serve to determine the canonical phase observable among the family of all phase observables we also show that any contractive weighted shift operator defines a unique phase observable and we characterize phase observables that give the most accurate phase distribution in coherent states in the classical limit

adaptive reduced order controllers for a thermal flow system using proper orthogonal decomposition an adaptive reduced order controller design is presented for flow control using proper orthogonal decomposition pod in reduced order controller design the idea is to start with an ensemble of data obtained from numerical simulation of the underlying partial differential equations pdes pod is then used to obtain a reduced set of basis functions which is then used to derive a reduced order model of the pdes via galerkin projection this reduced order model allows us to derive a reduced order controller however it is not clear a priori what is the best way to obtain an ensemble of data that would give basis functions that represent the influence of the control action on the system in this paper we explore an adaptive procedure for reduced order controller design that improves the reduced order model by successively updating the ensemble of data during the optimization iterations we illustrate this method on a control problem in thermal flow system modeled by a thermally coupled navier stokes equations numerical results are presented for a vorticity regulation problem in fluid flows using boundary temperature as control mechanism through our numerical experiments we demonstrate the feasibility and applicability of the adaptive reduced order controllers

optimal boundary feedback flow stabilization by model reduction abstract in this paper we consider the optimal boundary feedback stabilization of fluid flows governed by navier stokes equations using model reduction the model reduction is carried out using a combination of proper orthogonal decomposition pod and galerkin projection the resulting reduced order model is employed in the optimal linear quadratic regulator lqr design to derive a feedback control the feedback control is then used in the nonlinear navier stokes equation to stabilize the system sufficient conditions are derived for the linear control to stabilize the nonlinear system feasibility of the proposed boundary feedback stabilization design is numerically demonstrated on the problem of stabilizing the flow past an airfoil the control is effected through unsteady blowing on the airfoil surface the computational results show that the closed loop system amplitudes converge to the desired equilibrium state showing the stability predicted by the theory in addition they show that downstream directed blowing on the upper surface of the airfoil near the leading edge is more efficient in stabilizing the state

numerical approximation of optimal flow control problems by a penalty method error estimates and numerical results the purpose of this paper is to present numerically convenient approaches to solve optimal dirichlet control problems governed by the steady navier stokes equations we will examine a penalized neumann control approach for solving dirichlet control problems from numerical and computational points of view the control is affected by the suction or injection of fluid through the boundary or by boundary surface movements in the tangential direction the control objective is to minimize the vorticity in the flow or to drive the velocity field to a desired one we develop sequential quadratic programming methods to solve these optimal control problems the effectiveness of the optimal control techniques in flow controls and the feasibility of the proposed penalized neumann control approaches for flow control problems are demonstrated by numerical experiments for a viscous incompressible fluid flow in a two dimensional channel and in a cavity geometry

analysis and finite element approximation of optimal control problems for the stationary navier stokes equations with distributed and neumann controls we examine certain analytic and numerical aspects of optimal control problems for the stationary navier stokes equations the controls considered may be of either the distributed or neumann type the functionals minimized are either the viscous dissipation or the l4 distance of candidate flows to some desired flow we show the existence of optimal solutions and justify the use of lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced we study the regularity of solutions of this system then we consider the approximation by finite element methods of solutions of the optimality system and derive optimal error estimates

an optimal control problem in exterior hydrodynamics in this paper we consider the problem of accelerating an obstacle in an incompressible viscous fluid from rest to a given speed in a given time with minimum energy expenditure an existence theorem for the speed trajectory which corresponds to the absolute minimum is provided the results are valid for arbitrary reynolds numbers

analysis of optimal control problems for the 2 d stationary boussinesq equations this paper deals with optimal control problems associated with the 2 d boussinesq equations the controls considered may be of either the distributed or the neumann type these problems are first put into an appropriate mathematical formulation then the existence of optimal solutions is proved the use of lagrange multiplier techniques is justified and an optimality system of equations is derived

analysis of neumann boundary optimal control problems for the stationary boussinesq equations including solid media this article deals with neumann boundary optimal control problems associated with the boussinesq equations including solid media these problems are first put into an appropriate mathematical formulation then the existence of optimal solutions is proved the use of lagrange multiplier techniques is justified and an optimality system of equations is derived

the use of parametric programming in fuzzy linear programming in this paper the possibility of the identification of a complete fuzzy decision not only the maximizing alternative in fuzzy linear programming by use of the parametric programming technique is presented also it is shown that this fact can be useful in the zimmermann approach to multiple objective linear programming the presented remarks are illustrated by some numerical examples

facility location allocation problem in random fuzzy environment using α β cost minimization model under the hurewicz criterion facility location allocation fla which has been proved to be a valuable method in siting service facility is widely used in real life such as emergency service systems telecommunication net works public services etc many researchers have studied the fla problem in a deterministic stochastic or fuzzy environment however those models cannot satisfy various customers demands in some cases thus this paper considers the fla problem under random fuzzy environment using a b cost minimization model under the hurwicz criterion it will be proved that this model can deal with various fla problems in random fuzzy and random fuzzy environments by varying the value l it can balance the optimistic level of the decision makers for solving the random fuzzy model efficiently the simplex algorithm random fuzzy simulation and genetic algorithm are integrated to produce a hybrid intelligent algorithm finally a numerical example is presented for illustration

linear programming under randomness and fuzziness this paper is concerned with the use of fuzzy sets theory well suited for nuanced human behavior to extend the applicability of linear programming in a way to let both randomness and fuzziness uncertainties be taken into account a fuzzy stochastic linear programming problem is considered and ways to handle it suggested the basic idea behind our approaches is to translate the original problem in deterministic terms via tools provided by fuzzy sets theory to get a classical one some conditions for the resulting problems to be solved without extra computational effort are stressed and illustrative examples given

optimal control of thermally convected fluid flows we examine the optimal control of stationary thermally convected fluid flows from the theoretical and numerical point of view we use thermal convection as control mechanism that is control is effected through the temperature on part of the boundary control problems are formulated as constrained minimization problems existence of optimal control is given and a first order necessary condition of optimality from which optimal solutions can be obtained is established we develop numerical methods to solve the necessary condition of optimality and present computational results for control of cavity and channel type flows showing the feasibility of the proposed approach

dynamic programming of the navier stokes equations a class of optimal control problems in viscous flow is studied main results are the pontryagin maximum principle and the verification theorem for the hamilton jacobi bellman equation

adjoint based iterative method for robust control problems in fluid mechanics in this article we study the convergence of an adjoint based iterative method recently proposed in t r bewley r temam and m ziane phys d 138 2000 pp 360 392 for the numerical solution of a class of nonlinear robust control problems in fluid mechanics under weaker assumptions than those of t tachim medjo numer funct anal optim 23 2002 pp 849 873 we prove the convergence of the algorithm and we obtain an estimate of the convergence rate numerical solutions of a robust control problem related to data assimilation in oceanography are presented to illustrate the method

on the rayleigh benard marangoni system and a related optimal control problem abstract in this paper we study a boundary control problem associated to the stationary rayleigh benard marangoni rbm system in presence of controls for the velocity and the temperature on parts of the boundary we analyze the existence uniqueness and regularity of weak solutions for the stationary rbm system in polyhedral domains of r 3 and then we prove the existence of the optimal solution by using the theorem of lagrange multipliers we derive an optimality system we also give a second order sufficient optimality condition and we establish a result of uniqueness of the optimal solution

control of the freezing interface motion in two dimensional solidification processes using the adjoint method the aim of this work is to calculate the optimum history of boundary cooling conditions that in two dimensional conduction driven solidification processes results in a desired history of the freezing interface location motion the freezing front velocity and heat flux on the solid side of the front define the obtained solidification microstructure that can be selected such that desired macroscopic mechanical properties and soundness of the final cast product are achieved the so called two dimensional inverse stefan design problem is formulated as an infinite dimensional minimization problem the adjoint method is developed in conjunction with the conjugate gradient method for the solution of this minimization problem

reduced order control based on approximate inertial manifolds a reduced order method based on approximate inertial manifolds is applied to optimal control problems in infinite dimensional state spaces a detailed analysis of the method is given for the linear quadratic regulator problem the method can also be applied to higher order control systems with an appropriate decomposition of the state space in terms of slow and fast exponential decay

numerical solution of a flow control problem vorticity reduction by dynamic boundary action in order to laminarize an unsteady internal flow the vorticity field is minimized in a least squares sense using an optimal control approach the flow model is the navier stokes equation for a viscous incompressible fluid and the flow is controlled by suction and blowing on a part of the boundary a quasi newton method is used for the minimization of a quadratic objective function involving a measure of the vorticity and a regularization term the navier stokes equations are approximated using a finite difference scheme in time and finite element approximations in space accurate expressions for the gradient of the discrete objective function are needed to obtain a satisfactory convergence rate of the minimization algorithm therefore first order necessary conditions for a minimizer of the objective function are derived in the fully discrete case a memory saving device is discussed without which problems of any realistic size especially in three space dimensions would remain computationally intractable the feasibility of the optimal control approach for flow control problems is demonstrated by numerical experiments for a two dimensional flow in a rectangular cavity at a reynolds number high enough for nonlinear effects to be important

linear programming with multiple fuzzy goals abstract this paper describes the use of fuzzy set theory in goal programming gp problems in particular it is demonstrated how fuzzy or imprecise aspirations of the decision maker dm can be quantified through the use of piecewise linear and continuous functions models are then presented for the use of fuzzy goal programming with preemptive priorities with archimedean weights and with the maximization of the membership function corresponding to the minimum goal examples are also provided