existence results for the flow of viscoelastic fluids with a differential constitutive law where 2 is the symmetric extra stress tensor the total stress is given by g pl i where p is the hydrodynamic pressure 4 is the rate of deformation tensor g u vu vu u being the velocity field a is the relaxation time a2 the retardation time 0 i a a1 and q is the fluid viscosity the symbol a d t denotes an objective frame indifferent derivative i 181 more precisely

a note on a class of observability problems for pdes abstract the question of observability arises naturally in the analysis of control problems if the solution of a pde initial boundary value problem is known to be zero in a part of the domain does this guarantee it is zero everywhere the most popular techniques to establish such results are based on local unique continuation results holmgren s theorem or carleman estimates the purpose of this note is to draw attention to a class of problems where the observed region is bounded by characteristics and local unique continuation fails nevertheless observability may hold a problem of this nature arose in recent work by the author on control of viscoelastic flows m renardy are viscoelastic flows under control or out of control system control lett 54 2005 1183 1193 in this note we first analyze a simple example which shares the same essential features specifically we consider the problem u x t u for spatially periodic solutions we show that observability holds for data given on the line x 0 we shall show however that there is no observability estimate we shall then show how the methods used in the more elementary example can be extended to the case of viscoelastic shear flows

a robust incomplete factorization based on value and space constraints this paper describes an incomplete factorization method for computing a preconditioning matrix for the conjugate gradient method the incomplete factorization satisfies the stability requirement that the incomplete factor remains positive definite throughout the factorization when selecting a preconditioner for the conjugate gradient method the number of non zero entries to be retained in the incomplete factor should be limited so that the amount of computations involving the preconditioning matrix is minimized this paper introduces a method to generate an effective preconditioning matrix within a predefined space numerical results are presented to demonstrate the effectiveness of the incomplete factor as a preconditioner for the conjugate gradient method for solving large scale structural engineering problems

minimization of a regulated response to a fixed input the problem of minimizing a regulated output due to a specific bounded input is solved in the siso single input single output discrete time case it is shown that in most situations the optimal solution will not exist but given any epsilon 0 it is possible to find a suboptimal solution with performance within epsilon of the optimal performance the proposed approach is extended to the problem of shaping the error transient response it is shown how time domain templates can be used in this problem in the same way that frequency weighting functions are used in the h sup infinity and h sup 2 problems

minimization of the maximum peak to peak gain the general multiblock problem a comprehensive study of the general l sub 1 optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are presented by formulating the interpolation conditions in a concise and natural way the general theory is developed in simpler terms and with a minimum number of assumptions in addition further insight is gained into the structure of the optimal solution and different classes of multiblock problems are distinguished this leads to a conceptually attractive iterative method for finding approximate solutions

approximate controllability for linearized compressible barotropic navier stokes system in one and two dimensions abstract in this paper we consider compressible barotropic navier stokes equations in one and two dimensions linearized around a constant steady state with dirichlet boundary conditions we explore the controllability of this linearized system using a control only for the velocity equation we prove that the system with homogeneous dirichlet boundary conditions is approximately controllable by a localized interior control when time is sufficiently large

single input single output h control with time domain constraints standard h optimization cannot handle specifications or constraints on the time response of a closed loop system exactly in this paper the problem of h optimization subject to time domain constraints over a finite horizon is considered following an idea from helton and sideris 1989 ieee trans aut control ac 34 427 434 the problem is transformed into a finite dimensional optimization program that is shown to be convex although generically nondifferentiable the objective function is constructed via state space methods and several properties of the optimal constrained controller are discussed together with a robust algorithm for computation it is shown how satisfying the constraints over a finite horizon can imply overall good behavior

approximate controllability of the fitzhugh nagumo equation in one dimension abstract the fitzhugh nagumo fhn equation is a simplified model of a nerve axon we explore the controllability of this model using a localized interior control only for the first equation the linearized system is not null controllable using a localized interior control since the spectrum of the linearized system has an accumulation point though it is approximate controllable we show that the solution of the fhn equation fails to be globally approximate controllable in a given time but it is possible to move from any steady state to any other steady state arbitrarily close after some appropriate time by a localized interior control provided that both steady states are in the same connected component of the set of steady states finally we make some additional remarks and comments and we mention some open questions for our system for the sake of completeness we give the details of the existence uniqueness and uniform bound of the solution in appendix

multilevel aggregation method for solving large scale generalized eigenvalue problems in structural dynamics in this paper a novel iterative method of multilevel type for solving large scale generalized eigenvalue problems encountered in structural dynamics is presented a preconditioned iterative technique which can be viewed as a modification of the subspace iteration method is used for simultaneous calculation of a group of lowest modes and frequencies the paper demonstrates that a coarse aggregation model can be employed in the hierarchical structure of the preconditioner in order to provide a good resemblance of the latter to the stiffness matrix of the finite element approximation with respect to low frequency modes this leads to a fast convergent procedure of subspace iterations as opposed to the coarse grid used in methods of multigrid type this model allows for solving problems with different finite elements including reticulated structures in the framework of large comprehensive finite element software systems numerical experiments performed for three dimensional truss frame and solid structures demonstrate an excellent performance of the method 1997 by john wiley sons ltd

reachability problems for a class of integro differential equations abstract we study control problems for some integro differential equations using the hilbert uniqueness method to do that we follow a harmonic analysis approach our results can be applied to concrete examples in viscoelasticity theory

some controllability results for linear viscoelastic fluids we analyze the controllability properties of systems which provide a description at first approximation of a kind of viscoelastic fluid we consider linear maxwell fluids first we establish the large time approximate finite dimensional controllability of the system with distributed or boundary controls supported by arbitrary small sets then we prove the large time exact controllability of fluids of the same kind with controls supported by suitable large sets the proofs of these results rely on classical arguments in particular the approximate controllability result is implied by appropriate unique continuation properties while exact controllability is a consequence of observability inverse inequalities we also discuss questions concerning the controllability of viscoelastic fluids and some related open problems

block subspace projection preconditioned conjugate gradient method in modal structural analysis abstract this paper considers the preconditioned block conjugate gradient method for solving the algebraic generalized partial eigenvalue problem which arises when the finite element method is applied to dynamic analysis in structural and solid mechanics the focus is on the development of an algorithm that keeps constant the iterable subspace dimension independently of the number of eigenpairs required novelties in this approach include a preconditioning strategy based on block incomplete factorization of the shifted stiffness matrix and analysis of unremovable errors which accumulate with increasing numbers of eigenpairs

a lifting technique for linear periodic systems with applications to sampled data control abstract a lifting technique is developed for periodic linear systems and applied to the h and h 2 sampled data control problems

infinite dimensional convex optimization in optimal and robust control theory many engineering problems can be shown to be equivalent to solving semidefinite programs sps i e convex optimization problems involving linear matrix inequalities lmis powerful computation tools are available for such problems in the finite dimensional case however the problems arising in optimal and robust control theory are often infinite dimensional and so adequate computation tools are not available the key to tackling such problems with finite computation tools is to have a primal dual formulation of the problem without duality gap in this paper we study infinite dimensional sps and present a lifting technique to recast sps as parameterized linear programs lps this enables the wealth of theoretical tools available for infinite dimensional lps to be extended to infinite dimensional sps in particular we develop some new sufficient conditions for the lack of a duality gap for infinite dimensional sps and give an exact characterization of the primal and dual problems for these cases both primal and dual problems are formed as infinite dimensional sp problems with finite truncations to each giving upper and lower bounds respectively on the exact solution to the infinite dimensional problem thus these results can form the basis of practical computation schemes for infinite dimensional problems which require only finite dimensional computation tools to illustrate the power of these tools we apply the results to two previously unsolved optimization problems namely minimizing the l sub 1 norm of a closed loop system subject to bounds on the frequency response magnitude at a finite number of points and or bounds on the h sub 2 norm

are viscoelastic flows under control or out of control we discuss the controllability of viscoelastic shear flows both linear and nonlinear results are reviewed an interesting aspect of the problem is that the nonlinear problem introduces new stress components which are automatically zero in the linear case it is therefore a challenging problem to determine to what extent these stresses are controllable

integral type approximate controllability of linear parabolic integro differential equations abstract this paper addresses the study of the integral type approximate controllability of linear parabolic integro differential equations this new controllability is defined by imposing some additional integral type constraints on the usual approximate controllability and therefore can be used to keep the state close to the target the paper is concerned with a special choice of integral kernels which are multiples of the same exponential function we reduce the problem of new controllability to the obtention of a unique continuation property for the suitable adjoint system

the four block model matching problem in l 1 and infinite dimensional linear programming the purpose of this work is fourfold first the reader is introduced to the present state of the theory behind the solution of the general model matching problem in l 1 this solution is based on the fact that the model matching problem can be recast as an infinite dimensional linear programming problem however the transformation into linear programming form is highly nonunique which leads to the second question of discussion namely how to find a good linear programming formulation it is shown that the presently available formulations contain some redundancies that limit the applicability of the theory and lead to linear programming systems containing unnecessary degeneracies the third object of this work is to study problems related to the computational complexity of two different approximation methods for the solution of the infinite dimensional linear programming systems both of these methods are needed in order to get two sided error bounds on the cutoff error one complication is that ev

a quadratic programming approach for solving the l sub 1 multiblock problem the authors present a new method to compute solutions to the general multiblock l sub 1 control problem the method is based on solving a standard h sub 2 problem and a finite dimensional semidefinite quadratic programming problem of appropriate dimension the new method has most of the properties that separately characterize many existing approaches in particular as the dimension of the quadratic programming problem increases this method provides converging upper and lower bounds on the optimal l sub 1 norm and for well posed multiblock problems ensures the convergence in norm of the suboptimal solutions to an optimal l sub 1 solution the new method does not require the computation of the interpolation conditions and it allows the direct computation of the suboptimal controller

an improved iterative optimization technique for the leftmost eigenpairs of large symmetric matrices abstract an accelerated optimization technique combined with a stepwise deflation procedure is presented for the efficient evaluation of the p p 20 leftmost eigenvalues and eigenvectors of finite element symmetric positive definite p d matrices of very large size the optimization is performed on the rayleigh quotient of the deflated matrices by the aid of a conjugate gradient cg scheme effectively preconditioned with the incomplete cholesky factorization no a priori estimate of acceleration parameters is required numerical experiments on large arbitrarily sparse problems taken from the engineering finite elements f e practice show a very fast convergence rate for any value of p within the explored interval and particularly so for the minimal eigenpair in this case the number of iterations needed to achieve an accurate solution may be as much as 2 orders of magnitude smaller than the problem size several results concerning the spectral behavior of the cg preconditioning matrices are also given and discussed

explicit observability estimate for the wave equation with potential and its application by means of the carleman type estimate we obtain an explicit observability estimate for the wave equation with a potential as its application we get the exact internal controllability of the semilinear wave equations in any space dimensions

approximate controllability results for viscoelastic flows with infinitely many relaxation modes abstract we prove results on approximate controllability for linear viscoelastic flows with a localized distributed control in the momentum balance equation the constitutive law is a multimode maxwell or jeffreys model with an infinite number of relaxation modes

on the control of viscoelastic jeffreys fluids abstract this paper is devoted to analyzing the control of vicoelastic fluids of the jeffreys kind also known as oldroyd models we will present the interesting problems with special emphasis in the difficulties that they involve then we will consider appropriate linear approximations and we will establish some partial approximate finite dimensional controllability results in an arbitrarily small time with distributed or boundary controls supported by arbitrarily small sets the proofs rely on some specific unique continuation properties which are implied by the structure of the solutions

well posedness for the fene dumbbell model of polymeric flows we prove local and global well posedness for the fene dumbbell model for a very general class of potentials indeed in prior local or global well posedness results conditions on the strength of the singularity or on the parameter b were made here we give a proof in the general case we also prove global existence results if the data is small or if we restrict to the co rotational model in dimension 2 2008 wiley periodicals inc

some controllability results for the n dimensional navier stokes and boussinesq systems with n 1 scalar controls in this paper we deal with some controllability problems for systems of the navier stokes and boussinesq kind with distributed controls supported in small sets our main aim is to control n dimensional systems n 1 scalar unknowns in the case of the navier stokes equations with n 1 scalar control functions in a first step we present some global carleman estimates for suitable adjoint problems of linearized navier stokes and boussinesq systems in this way we obtain null controllability properties for these systems then we deduce results concerning the local exact controllability to the trajectories we also present global null controllability results for some truncated approximations of the navier stokes equations

null controllability of the linearized compressible navier stokes system in one dimension in this paper we consider the one dimensional compressible navier stokes equations linearized around a constant steady state q0 v0 q0 0 v0 0 with periodic boundary conditions in the interval i2 0 2 we explore the controllability of this linearized system using a control only for the velocity equation we prove that the linearized system with homogeneous periodic boundary conditions is null controllable in h 1 per i2 l 2 i2 by a localized interior control when time is sufficiently large where h 1 per i2 denotes the sobolev space of periodic functions with mean value zero we show null controllability of the system by proving an observability inequality with the help of two types of ingham inequality

a necessary and sufficient condition for robust bibo stability abstract this paper is concerned with obtaining necessary and sufficient conditions for robustly stabilizing a class of plants characterized by a known linear shift invariant plant with additive perturbations of the form of possibly nonlinear time varying l stable operators we will show that in some sense the small gain theorem is necessary and sufficient even when the perturbations are restiricted to a class of linear operators

control problems for weakly coupled systems with memory abstract we investigate control problems for wave petrovsky coupled systems in the presence of memory terms by writing the solutions as fourier series we are able to prove ingham type estimates and hence reachability results our findings have applications in viscoelasticity theory and linear acoustic theory

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

exact controllability stabilization and perturbations for distributed systems exact controllability is studied for distributed systems of hyperbolic type or for petrowsky systems like plate equations the control is a boundary control or a local distributed control exact controllability consists in trying to drive the system to rest in a given finite time the solution of the problems depends on the function spaces where the initial data are taken and also depends on the function space where the control can be chosen a systematic method named hum for hilbert uniqueness method is introduced as the terminology indicates it is based on uniqueness results classical or new and on hilbert spaces constructed in infinitely many ways by using uniqueness a number of applications are indicated having a general method for exact controllability implies having a general method for stabilization this leads to new and complicated nonlinear riccati s type pdes to be compared with direct methods when available in the last part of the paper we consider how all this behaves fo

performance robustness of discrete time systems with structured uncertainty given an interconnection of a nominal discrete time plant and a stabilizing controller together with structured norm bounded nonlinear time varying perturbations necessary and sufficient conditions for robust stability and performance of the system are provided it is shown that performance robustness is equivalent to stability robustness in the sense that both problems can be dealt with in the framework of a general stability robustness problem the resulting stability robustness problem is shown to be equivalent to a simple algebraic one the solution of which provides the desired necessary and sufficient conditions for performance stability robustness these conditions provide an effective tool for robustness analysis and can be applied to a large class of problems in particular it is shown that some known results can be obtained immediately as special cases of these conditions

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

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

model invalidation in spl lscr sub 1 using frequency domain data in this note we study the problem of invalidating uncertain models with an additive uncertainty the problem is to check the existence of an uncertainty and a measurement noise which fit to the given model structure and the uncertainty noise description as well as the experimental data used for invalidation we consider a mixed setting in which the uncertainty is characterized in time domain by the spl lscr sub 1 induced system norm while the available data are frequency response samples of the system we show that this problem which by formulation poses an infinite dimensional primal optimization problem can be solved in a dual finite dimensional space with finitely many constraints

approximate controllability of the semilinear heat equation this article is concerned with the study of approximate controllability for the semilinear heat equation in a bounded domain when the control acts on any open and nonempty subset of or on a part of the boundary in the case of both an internal and a boundary control the approximate controllability in l p for 1 p l in the case of the interior control we also prove approximate controllability in c 0 the proof combines a variational approach to the controllability problem for linear equations and a fixed point method we also prove that the control can be taken to be of quasi bang bang form

on the mathematical foundations of nondifferentiable optimization in engineering design it is shown by example that a large class of engineering design problems can be transcribed into the form of a canonical optimization problem with inequality constraints involving mar functions such problems are commonly referred to as semi infinite optimization problems the bulk of this paper is devoted to the development of a mathematical theory for the construction of first order nondifferentiable optimization algorithms related to phase i phase ii methods of feasible directions which solve these semi infinite optimization problems the applicability of the theory is illustrated with examples that are relevant to engineering design

h sub spl infin optimization with time domain constraints standard h sub spl infin optimization cannot handle specifications or constraints on the time response of a closed loop system exactly in this paper the problem of h sub spl infin optimization subject to time domain constraints over a finite horizon is considered more specifically given a set of fixed inputs w sup i it is required to find a controller such that a closed loop transfer matrix has an h sub spl infin norm less than one and the time responses y sup i to the signals w sup i belong to some prespecified sets spl omega sup i first the one block constrained h sub spl infin optimal control problem is reduced to a finite dimensional convex minimization problem and a standard h sub spl infin optimization problem then the general four block h sub spl infin optimal control problem is solved by reduction to the one block case the objective function is constructed via state space methods and some properties of h sub spl infin optimal constrained controllers are given it is shown how satisfaction of the constraints over a finite horizon can imply good behavior overall an efficient computational procedure based on the ellipsoid algorithm is also discussed

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

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

h sub infinity optimal control as a weighted wiener hopf problem it is shown that h sub infinity optimization is equivalent to weighted h sub 2 optimization in the sense that the solution of the latter problem also solves the former the weighting rational matrix that achieves this equivalence is explicitly computed in terms of a state space realization the authors do not suggest transforming h sub infinity optimization problems to h sub 2 optimization problems as a computational approach rather their results reveal an interesting connection between h sub infinity and h sub 2 optimization problems which is expected to offer additional insight for example h sub 2 optimal controllers are known to have an optimal observer full state feedback structure the result obtained shows that the minimum entropy solution of h sub infinity optimal control problems can be obtained as an h sub 2 optimal solution therefore it can be expected that the corresponding h sub infinity optimal controller has an optimal observer full state feedback structure

interior approximate and null controllability of the heat equation with memory in this paper we study the approximate and null controllability of the heat equation with memory we mainly consider the distributed control case with an arbitrarily small support of the control function for each positive final time t we deduce that the approximate controllability property holds and the null controllability property fails

controller design with multiple objectives in this paper we study multi objective control problems that give rise to equivalent convex optimization problems we develop a uniform treatment of such problems by showing their equivalence to linear programming problems with equality constraints and an appropriate positive cone we present some specialized results on duality theory and we apply them to the study of three multi objective control problems the optimal l sub 1 control with time domain constraints on the response to some fixed input the mixed h sub 2 l sub 1 control problem and the l sub 1 control with magnitude constraint on the frequency response what makes these problems complicated is that they are often equivalent to infinite dimensional optimization problems the characterization of the duality relationship between the primal and dual problem allows us to derive several results these results establish connections with special convex problems linear programming or linear matrix inequality problems uncover finite dimensional structures in the optimal solution when possible and provide finite dimensional approximations to any degree of accuracy when the problem does not appear to have a finite dimensional structure to illustrate the theory and highlight its potential several numerical examples are presented

global well posedness of viscoelastic fluids of oldroyd type in besov spaces abstract we investigate a system of equations concerning an incompressible viscoelastic fluid of the oldroyd type which describes one class of non newtonian fluid with memory making use of a regularization method in conjunction with bony s paraproduct decomposition we obtain the existence and uniqueness of a small global solution for the above system in the besov spaces b 2 s with s d 2 and which implies global well posedness for small data in h s with s d 2 since the sobolev space h s is embedded in b 2 s

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

optimal rejection of persistent disturbances robust stability and mixed sensitivity minimization the problem of optimal disturbance rejection of bounded persistent disturbances is solved in the general nonsquare case the minimum value of the objective function can be obtained by solving a semi infinite linear programming problem and an iterative procedure for obtaining approximate solutions is introduced application of the l sup 1 optimal problem to robustness is discussed a mixed sensitivity problem is formulated and shown to guarantee good disturbance rejection in the presence of plant perturbations

simplifying the h theory via loop shifting matrix pencil and descriptor concepts the 2 riccati h controller formulae and derivations are simplified via various loop shifting transformations that are naturally expressed in terms of a degree one polynomial system matrix psm closely related to the luenberger descriptor form of a system the technique enables one without loss of generality to restrict attention to the simple case in which d 11 0 d 22 0 d t 12 0 l d 21 0 l d l 12 c1 0 and b 1 d t 21 0 matrix fraction descriptions mfds for the algebraic riccati equation solutions afford another change of variables which brings the 2 riccati h controller formulae into a cleaner more symmetric descriptor form having the important practical advantage that it eliminates the numerical difficulties that can occur in cases where one or both of the riccati solutions pi and q blow up and in cases where l qp is nearly singular numerical difficulties previously associated with verifying the existence conditions p 0 q 0 and maxlpar qp 1 are largely eliminated by e

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

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

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

state space formulae for discrete time h optimization abstract state space formulae and proofs are given for ail the important steps in discrete time h 8 optimization the steps closely follow the algorithms for continuous time systems but there are some technically involved differences in the detail that make their derivation non trivial

sign weighted peak minimization problem for feedback systems this note studies the problem of minimizing a parameterized convex combination of the overshoot and undershoot of a single input single output siso discrete time system to a fixed input we provide a simple condition for the solution existence and characterize the structure of optimal solutions it is shown that a known l sub spl infin suboptimal scheme also works in our problem in addition we make a comparative analysis with the l sub spl infin problem

a characterization of all solutions to the four block general distance problem all solutions to the four block general distance problem which arises in h infty optimal control are characterized the procedure is to embed the original problem in an all pass matrix which is constructed it is then shown that part of this all pass matrix acts as a generator of all solutions special attention is given to the characterization of all optimal solutions by invoking a new descriptor characterization of all pass transfer functions as an application necessary and sufficient conditions are found for the existence of an h infty optimal controller following that a descriptor representation of all solutions is derived

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