chebyshev finite difference method for heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching surface with ohmic heating and viscous dissipation numerical solutions are obtained for the problem which involves both the heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching surface with ohmic heating and viscous dissipation using chebyshev finite difference method chfd a similarity transformation was employed to change the governing momentum angular momentum energy and concentration partial differential equations into ordinary ones numerical calculations have been carried out for various values of magnetic field parameter material parameter prandtl number eckert number schmidt number couple stress at the surface local nusselt number and sherwood number the numerical results indicate that the temperature and the concentration increase while the velocities the nusselt number and the sherwood number decrease with increasing magnetic field parameter in all of the above results the material parameter has the opposite effect of magnetic field parameter the temperature increases with increasing eckert number and decreases with increasing prandtl number an increase in the schmidt number gives an increase in the sherwood number or a decrease in the concentration

worst case input output identification we consider worst case l1 identification of causal linear shift invariant systems from time series many results are given on general aspects of identification algorithm performance existence of optimal algorithms robust convergence and input experiment design the identification methodology studied here is compatible with the modelling requirements of modern robust control design

time varying versus time invariant compensation for rejection of persistent bounded disturbances and robust stabilization it is shown that time varying compensation does not improve the optimal rejection of persistent bounded disturbances this result is obtained by exploiting a key observation that any time varying compensator which yields a given degree of disturbance rejection must do so uniformly over time thereby removing any advantage of time variation this key observation is exploited to show that time varying compensation does not improve the optimal rejection of disturbances regardless of the norm used to measure the disturbances thus absolutely summable finite energy or persistent bounded disturbances may be treated in the same manner it is shown that time varying compensation does not help in the bounded input bounded output robust stabilization of time invariant plants with unstructured uncertainty in doing so it is also shown that the small gain theorem is both necessary and sufficient for the bounded input bounded output stability of certain linear time varying plants subject to unstructured linear time varying perturbations

event triggered global robust output regulation for a class of nonlinear systems this note studies the global robust output regulation problem for a class of nonlinear systems by an output based event triggered control law first we convert the problem into the event triggered global robust stabilization problem of a well defined augmented system based on the internal model approach then we design an output based event triggered control law together with an output based event triggered mechanism to solve the stabilization problem which in turn leads to the solution to the original problem by an output based event triggered control law finally we illustrate our approach by an example

minimization of the l sup infinity induced norm for sampled data systems it is shown that given any degree of accuracy there exists a standard discrete time l sup 1 problem that can be determined a priori whose solution yields a controller that is almost optimal in terms of the hybrid l sup infinity induced norm this is accomplished by first converting the hybrid system into an equivalent infinite dimensional discrete time system using the lifting technique in continuous time and then approximating the infinite dimensional parts of the system which model the intersample dynamics a thorough analysis of the approximation procedure is presented and it is shown that it is convergent at the rate of 1 n explicit bounds that are independent of the controller are obtained to characterize the approximation it is also shown that the geometry of the induced norm for the sampled data problem is different from that of the standard l sup 1 norm and hence there might not exist a linear isometry that maps the sampled data problem exactly to a standard discrete time problem

on slowly time varying systems abstract a characterization of stabilizing controllers for slowly time varying systems based on input output descriptions of the plant and the controller is presented this approach generalizes standard results on slowly time varying systems with finite dimensional state space representation and allows both the plant and the controller to be infinite dimensional the controller design will be based on frozen time versions of the plant obtained at equally spaced instances in time

design of spl lscr sub 1 optimal controllers with flexible disturbance rejection level this note presents a new design methodology that allows for flexible management of the tradeoff between the ability of a system to attenuate disturbance signals versus its expected worst peak to peak amplification the proposed strategy applies to linear time invariant systems which are subject to persistent disturbance signals and combines a recently developed quasi robust linear programming concept with a well known spl lscr sub 1 optimal controller synthesis approach the benefit of the resulting technique is demonstrated using an example

optimal pole placement design for siso discrete time systems in this paper we incorporate the placement of one real closed loop pole into a compensator design framework based upon the youla parameterization duality theory and linear programming this framework has been used to design discrete time compensators to solve the l sub 1 controller design problem as well as other related time domain optimization problems previous work on these problems has focused on deadbeat systems it is known that these can require high order controllers part of the motivation for this work is to improve the tradeoff between controller order and performance over that using deadbeat control

optimal disturbance reduction in linear multivariable systems this paper presents a computational solution to an important optimization problem arising in optimal sensitivity theory the approach is to treat the multivariable problem exactly as the scalar problem in that stability constraints are handled via interpolation the resulting computations are easily implemented using existing methods

combined effect of magnetic field and heat absorption on unsteady free convection and heat transfer flow in a micropolar fluid past a semi infinite moving plate with viscous dissipation using element free galerkin method abstract the fully developed electrically conducting micropolar fluid flow and heat transfer along a semi infinite vertical porous moving plate is studied including the effect of viscous heating and in the presence of a magnetic field applied transversely to the direction of the flow the darcy brinkman forchheimer model which includes the effects of boundary and inertia forces is employed the differential equations governing the problem have been transformed by a similarity transformation into a system of non dimensional differential equations which are solved numerically by element free galerkin method profiles for velocity microrotation and temperature are presented for a wide range of plate velocity viscosity ratio darcy number forchhimer number magnetic field parameter heat absorption parameter and the micropolar parameter the skin friction and nusselt numbers at the plates are also shown graphically the present problem has significant applications in chemical engineering materials processing solar porous wafer absorber systems and metallurgy

numerical solution of the momentum and heat transfer equations for a hydromagnetic flow due to a stretching sheet of a non uniform property micropolar liquid a study of the hydromagnetic flow due to a stretching sheet and heat transfer in an incompressible micropolar liquid is made temperature dependent thermal conductivity and a non uniform heat source sink render the problem analytically intractable and hence a numerical study is made using the shooting method based on runge kutta and newton raphson methods the two problems of horizontal and vertical stretching are considered to implement the numerical method the former problem involves one way coupling between linear momentum and heat transport equations and the latter involves two way coupling further both the problems involve two way coupling between the non linear equations of conservation of linear and angular momentums a similarity transformation arrived at for the problem using the lie group method facilitates the reduction of coupled non linear partial differential equations into coupled non linear ordinary differential equations the algorithm for solving the resulting coupled two point non linear boundary value problem is presented in great detail in the paper extensive computation on velocity and temperature profiles is presented for a wide range of values of the parameters for prescribed surface temperature pst and prescribed heat flux phf boundary conditions

on nonlinear state feedback controllers for persistent disturbance rejection abstract an l 1 optimal linear time invariant lti compensator may have an order significantly higher than that of the plant in the state feedback case there has been recent work exploring the use of nonlinear static feedback controllers which provide near optimal performance in the case of d 12 square and invertible we show that it is enough to have the nonlinearity on a particular substate which can be used to significantly simplify the design problem

optimal and robust controllers for periodic and multirate systems the problem of optimal rejection of bounded persistent disturbances is solved in the case of linear discrete time periodic systems the solution consists of solving an equivalent time invariant standard l sup 1 optimization problem subject to an additional constraint this constraint assures the causality of the resulting periodic controller by the duality theory the problem is shown to be equivalent to a linear programming problem which is no harder than the standard l sup 1 problem also it is shown that the method of solution presented applies exactly to the problem of disturbance rejection in the case of multirate sampled data systems finally the results are applied to the problem of robust stabilization of periodic and multirate systems

robust decoupling of discrete systems using spl lscr sup 1 optimization we address a control design problem related to decoupling namely robust decoupling the idea of robust decoupling is defined and shown to be equivalent to robust performance of a hadamard weighted spl lscr sup 1 performance measure a necessary and sufficient condition to determine if a compensator satisfies robust performance of a hadamard weighted spl lscr sup 1 performance measure in the presence of structured uncertainty is given this condition can be used to determine if a compensator robustly decouples a plant finally an iterative scheme for synthesizing a robust decoupling controller is discussed

minimization of the worst case peak to peak gain via dynamic programming state feedback case considers the problem of designing a controller that minimizes the worst case peak to peak gain of a closed loop system in particular we concentrate on the case where the controller has access to the state of a linear plant and it possibly knows the maximal disturbance input amplitude we apply the principle of optimality and derive a dynamic programming formulation of the optimization problem under mild assumptions we show that at each step of the dynamic program the cost to go has the form of a gauge function and can be recursively determined through simple transformations we study both the finite horizon and the infinite horizon case under different information structures the proposed approach allows us to encompass and improve earlier results based on viability theory in particular we present a computational scheme alternative to the standard bisection algorithm or gamma iteration that allows us to compute the exact value of the worst case peak to peak gain for any finite horizon we show that the sequence of finite horizon optimal costs converges as the length of the horizon goes to infinity to the infinite horizon optimal cost the sequence of such optimal costs converges from below to the optimal performance for the infinite horizon problem we also show the existence of an optimal state feedback strategy that is globally exponentially stabilizing and derive suboptimal globally exponentially stabilizing strategies from the solutions of finite horizon problems

a contraction property for state feedback design of linear discrete time systems abstract the contraction property is proposed as a tool for design of linear discrete time control systems explicit formulae are given for all linear time invariant state feedback controllers that imply the contraction property the obtained controllers are tuned with only two user parameters the two parameters are closely connected to the settling time and the damping of the closed loop system respectively the approach is illustrated by means of simulations

bibo stability robustness in the presence of coprime factor perturbations a necessary and sufficient condition for robustly stabilizing a family of plants described by perturbations of fixed coprime factors of a plant is given the computation of the largest stability margin is discussed via solving a nonsquare l sup 1 optimal control problem an algorithm for obtaining lower approximations of the minimum value of the optimization problem mu sub 0 is proposed this together with the standard algorithm which provides upper approximations allows mu sub 0 to be computed within any degree of accuracy

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

i 1 optimal control of multivariable systems with output norm constraints in this paper we consider the l1 optimal control problem for general rational plants it is shown that for plants with no poles or zeros on the unit circle an optimal compensator exists and that the resulting closed loop transfer function is polynomial whenever there are at least as many controls as regulated outputs and at least as many measurements as exogeneous inputs exactly or approximately optimal rational compensators can be obtained by solving a sequence of finite linear programs for the coefficients of a polynomial closed loop transfer function no assumptions on plant poles or zeros are required to obtain at least approximately optimal compensators it is shown that constrained problems in which a set of outputs is regulated subject to l norm constraints on another set of outputs can be solved using a slight modification of the same algorithm

h optimal feedback controllers for linear multivariable systems this paper treats the problem of designing for a linear multivariable plant a feedback controller which minimizes the h infty norm of a weighted sensitivity matrix there exists a family of optimal improper feedbacks this family is determined by application of a theory of ball and helton a method for computing optimal feedbacks is described in detail and a numerical example is included it is shown that an optimal improper feedback can be approximated by a proper one under certain conditions on the weighting matrices

robust fuzzy observer based fuzzy control design for nonlinear systems with persistent bounded disturbances a novel decoupled approach unlike the l 2 gain h control case the l gain control problem is dealing with persistent bounded disturbances this study introduces l gain fuzzy observer based fuzzy control design where the premise variables depend on the state variables estimated by a fuzzy observer for nonlinear systems via t s fuzzy models the fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables do not depend on the state variables estimated by a fuzzy observer a novel decoupled method is proposed in this study to transform the non lmi conditions into some lmi forms by the proposed decoupled method and the genetic algorithm the l gain fuzzy observer based fuzzy control problem can be easily solved by an lmi based method

rational approximation of l sub 1 optimal controllers for siso systems the l sub 1 optimal control problem with rational controllers for continuous time systems is considered in which it is shown that the optimal l sub 1 performance index with rational controllers is equal to that of irrational controllers a sequence of rational controllers that approximates the optimal index is constructed convergence properties of such a sequence are studied that the corresponding sequence of objective transfer functions is shown to converge in weak topology in bv r sub in the time domain and uniformly in a wider sense in the frequency domain

l 1 optimal feedback controllers for mimo discrete time systems the problem considered in this paper is the design of a closed loop system consisting of a mimo discrete time plant and compensator in such a way that the system is internally stable and optimally tracks all persistent bounded inputs the solution consists of two parts first the calculation of the minimum value of the performance index a weighted transfer function which is done by solving a linear programming problem and second construction of the optimal transfer function by solving a set of linear equations it is shown that in general the discrete time problem will have a rational solution and thus appears to be of considerable practical significance

chebyshev finite difference approximation for the boundary value problems this paper presents a numerical technique for solving linear and non linear boundary value problems for ordinary differential equations this technique is based on using matrix operator expressions which applies to the differential terms it can be regarded as a non uniform finite difference scheme the values of the dependent variable at the gauss lobatto points are the unknown one solves for the application of the method to boundary value problems leads to algebraic systems the method permits the application of iterative method in order to solve the algebraic systems the effective application of the method is demonstrated by four examples

two properties of l sub 1 optimal controllers the solution of the l sub 1 sensitivity minimization problem is shown to have two properties which contrast markedly with properties of the solutions to the better known h infinity sensitivity minimization problem or the lqg linear quadratic gaussian problem is given of a one parameter family of first order plants where the order of the l sub 1 optimal compensator can be arbitrarily large and thus it is impossible to bound the order of an l sub 1 optimal compensator in terms of the order of the plant a plant is considered which has a continuous one parameter family of l sub 1 optimal compensators and thus l sub 1 optimal compensators need not be unique the author s two examples are considered to answer two questions left open by m a daleh and j b pearson ibid vol 32 p 314 23 1987

robust fuzzy observer based fuzzy control design for nonlinear discrete time systems with persistent bounded disturbances to date nonlinear l infin gain control problems have not been solved by the conventional control methods for nonlinear discrete time systems with persistent bounded disturbances this study introduces fuzzy observer based fuzzy control design where the premise variables depend on the state variables estimated by a fuzzy observer to deal with the nonlinear l infin gain control problem the fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables depend on the state variables first the takagi sugeno t s fuzzy model is employed to represent the nonlinear discrete time system next based on the fuzzy model a fuzzy observer based fuzzy controller is developed to minimize the upper bound of l infin gain of the closed loop system under some nonlinear matrix inequality non lmi constraints a novel decoupled method is proposed in this study to transform the non lmi conditions into some linear matrix inequality lmi forms by the proposed decoupled method and the genetic algorithm the l infin gain fuzzy observer based fuzzy control problem for the nonlinear discrete time systems can be easily solved by an lmi based optimization method the proposed methods which efficiently attenuate the peak of perturbation due to persistent bounded disturbances extend the l infin gain control problems from linear discrete time systems to nonlinear discrete time systems a simulation example is given to illustrate the design procedures and to confirm the l infin gain performance of the proposed method

on the design of linear multivariable feedback systems via constrained nondifferentiable optimization in h sup infinity spaces the design discussed is of linear lumped time invariant multivariable feedback systems subject to various frequency and time domain performance specifications the approach is based on the use of stabilizing controller parametrizations which result in the formulation of feedback system design problems as convex nondifferentiable optimization problems these problems are solvable by recently developed nondifferentiable optimization algorithms for the constrained minimization of regular uniformly locally lipschitz continuous functions in r sup n

chebyshev finite difference method for the solution of boundary layer equations a new chebyshev finite difference method is proposed for solving the governing equations of the boundary layer flow the falkner skan equation has been solved as a model problem the more general problem of the equations governing magnetohydrodynamic three dimensional free convection on a vertical stretching surface is solved the comparisons between the data resulting from the present method and those obtained by others are made the results indicate that the suggested method yields more accurate results than those computed by others

optimal rejection of persistent bounded disturbances in this paper we formulate the problem of optimal disturbance rejection in the case where the disturbance is generated as the output of a stable system in response to an input which is assumed to be of unit amplitude but is otherwise arbitrary the objective is to choose a controller that minimizes the maximum amplitude of the plant output in response to such a disturbance mathematically this corresponds to requiring uniformly good disturbance rejection over all time since the problem of optimal tracking is equivalent to that of optimal disturbance rejection if a feedback controller is used see 7 sect 5 6 the theory presented here can also be used to design optimal controllers that achieve uniformly good tracking over all time rather than a tracking error whose l 2 norm is small as is the case with the currently popular h infty theory the present theory is a natural counterpart to the existing theory of optimal disturbance rejection the so called h infty theory which is based on the assumption that the disturbance to be rejected is generated by a stable system whose input is square integrable and has unit energy it is shown that the problem studied here has quite different features from its predecessor complete solutions to the problem are given in several important cases including those where the plant is minimum phase or when it has only a single unstable zero in other cases procedures are given for obtaining bounds on the solution and for obtaining suboptimal controllers

synthesis of linear multivariable regulators this paper generalizes the results obtained by the authors in 1 and presents new results on the construction of proper controllers for linear multivariable regulators these results may lead to efficient computation methods that do not involve smith forms or the order relations used in 1 to construct proper controllers the methods are based on the recently developed theory of generalized polynomials 2 we discuss several numerical algorithms and how they can be applied to the regulator problem we also point out an important computational problem in need of an efficient numerical algorithm

frequency response algorithms for h sub infinity optimization with time domain constraints a very broad framework for control system design is considered that encompasses frequency response methodologies for h sub infinity optimization that solve various aspects of the control design problem and that are less well known that state space methods the focus is on linear programming lawson s algorithm and trefethen s algorithm a modified lawson s algorithm is proposed and related to trefethan s method the modified algorithm is shown to be significantly faster than linear programming and lawson s algorithm it is also shown how to extend the modified lawson s algorithm so as to handle time domain constraints in addition to frequency domain specifications which distinguishes it from other h sub infinity optimization methods some steps are taken toward dealing with time domain constraints within an h sub infinity optimization framework