every stabilizing controller is l sub 1 and h sub infinity optimal a new formulation is given for the problem of optimally rejecting possibly unbounded disturbances it is shown that for a given plant every particular stabilizing controller is l sub 1 and also h sub infinity optimal for some particular classes of appropriately chosen disturbances an example demonstrates the authors work

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

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

optimal l sub spl infin to l sub spl infin estimation for periodic systems in this paper we consider the problem of finding a filter that minimizes the worst case magnitude l sub spl infin of the estimation error in the case of linear periodically time varying systems subjected to unknown but magnitude bounded l sub spl infin inputs these inputs consist of process and observation noises and the optimization problem is considered over an infinite time horizon lifting techniques are utilized to transform the problem to a time invariant l sub 1 model matching problem subject to additional constraints taking advantage of the particular structure of the estimation problem it is shown how standard methods of l sub 1 optimization in particular the delay augmentation technique can be suitably modified to solve this nonstandard problem

robust performance unknown disturbances and known fixed inputs this paper addresses the robust performance problem when the system under consideration is subjected to norm bounded time varying uncertainty different performance objectives are considered and computable bounds are obtained for the worst case performance in various norms in some important cases it is shown that these bounds are tight giving simple exact formulas for computing robust performance measures one of the important features of these formulas is that they enable the direct and exact calculation of a number of worst cast performance measures while avoiding entirely the iterations needed for computing these measures by existing methods that rely on repeated scalings and spectral radius bound evaluations

bad behavior of godunov mixed methods for strongly anisotropic advection dispersion equations we study the performance of godunov mixed methods which combine a mixed hybrid finite element solver and a godunov like shock capturing solver for the numerical treatment of the advection dispersion equation with strong anisotropic tensor coefficients it turns out that a mesh locking phenomenon may cause ill conditioning and reduce the accuracy of the numerical approximation especially on coarse meshes this problem may be partially alleviated by substituting the mixed hybrid finite element solver used in the discretization of the dispersive diffusive term with a linear galerkin finite element solver which does not display such a strong ill conditioning to illustrate the different mechanisms that come into play we investigate the spectral properties of such numerical discretizations when applied to a strongly anisotropic diffusive term on a small regular mesh a thorough comparison of the stiffness matrix eigenvalues reveals that the accuracy loss of the godunov mixed method is a structural feature of the mixed hybrid method in fact the varied response of the two methods is due to the different way the smallest and largest eigenvalues of the dispersion diffusion tensor influence the diagonal and off diagonal terms of the final stiffness matrix one and two dimensional test cases support our findings

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

on robust stability with structured time variant perturbations abstract we consider the problem of robust stability for uncertain systems described in terms of multiple scalar structured time invariant perturbations which are norm bounded the issue we address is the role that the type of perturbation norm plays in the robust stability conditions to this end the l p induced norm for 1 p on the perturbations is considered and it is shown that the structured singular value is the necessary and sufficient condition for robust stability for all these norms we conclude that for time invariant perturbations in contrast to the time varying case robust stability conditions are independent of the type of perturbation norms

mixed finite element and finite volume discretization for heavy brine simulations in groundwater recently a new theory of high concentration brine transport in groundwater has been developed this approach is based on two nonlinear mass conservation equations one for the fluid flow equation and one for the salt transport equation both having nonlinear diffusion terms in this paper we present and analyze a numerical technique for the solution of such a model the approach is based on the mixed hybrid finite element method for the discretization of the diffusion terms in both the flow and transport equations and a high resolution tvd finite volume scheme for the convective term this latter technique is coupled to the discretized diffusive flux by means of a time splitting approach a commonly used benchmark test elder problem is used to verify the robustness and nonoscillatory behavior of the proposed scheme and to test the validity of two different formulations one based on using pressure head and concentration c as dependent variables and one using pressure p and mass fraction as dependent variables it is found that the latter formulation gives more accurate and reliable results in particular at large times the numerical model is then compared against a semi analytical solution and the results of a laboratory test these tests are used to verify numerically the performance and robustness of the proposed numerical scheme when high concentration gradients i e the double nonlinearity are present

solving the advection diffusion equation on unstructured meshes with discontinuous mixed finite elements and a local time stepping procedure explicit schemes are known to provide less numerical diffusion in solving the advection diffusion equation especially for advection dominated problems traditional explicit schemes use fixed time steps restricted by the global cfl condition in order to guarantee stability this is known to slow down the computation especially for heterogeneous domains and or unstructured meshes to avoid this problem local time stepping procedures where the time step is allowed to vary spatially in order to satisfy a local cfl condition have been developed in this paper a local time stepping approach is used with a numerical model based on discontinuous galerkin mixed finite element methods to solve the advection diffusion equation the developments are detailed for general unstructured triangular meshes numerical experiments are performed to show the efficiency of the numerical model for the simulation of i the transport of a solute on highly unstructured meshes and ii density driven flow where the velocity field changes at each time step the model gives stable results with significant reduction of the computational cost especially for the non linear problem moreover numerical diffusion is also reduced for highly advective problems copyright 2009 john wiley sons ltd

the necessity of the small gain theorem for time varying and nonlinear systems it is shown that an appropriately modified version of the small gain theorem which uses the asymptotic gain of a fading memory system leads to a necessary and sufficient condition for the stable invertibility of certain feedback operators this modified small gain theorem is then used to obtain conditions for robust finite energy input output stability of 1 nonlinear plants subject to nonlinear time varying perturbations and 2 linear time varying plants subject to linear time varying perturbations these conditions are shown to be necessary as well as sufficient

on l robust stability and performance with l 2 and l perturbations ubscrpt perturbations in this paper we will consider systems with linear time invariant perturbations we will analyze robust performance in the l2 and l settings the l2 setting gives rise to the familiar case of structured singular values and a stability criterion is given by the small theorem we show that although the necessary and sufficient criterion of robust stability for the l case l stability with structured l gain bounded perturbations is the same small criterion a system with l2 gain bounded perturbations is never l stable

a simple solution to the l 1 optimization problem abstract it is pointed out in this brief paper that the l 1 optimization problem min q l qp 1 h u q v 1 h l mn 1 u l mq 1 v l pn 1 can be solved in one step rather than two the solution of the dual problem is obviated by the direct solution of the primal problem via linear programming the method here is applicable to finite dimensional problems or approximating finite dimensional problems in the general case

l sub 1 analysis and design of sampled data systems the focus of this work is l sub 1 optimal control of sampled data systems a converging approximation procedure is derived to compute the l sub infinity induced norm of closed loop finite dimensional linear time invariant lti sampled data systems an approximation method is developed to synthesize l sub 1 optimal sampled data regulators finally an example is provided that illustrates the l sub 1 analysis and design techniques presented

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

bezout factors and l sup 1 optimal controllers for delay systems using a two parameter compensator scheme the authors consider the simultaneous problem of optimal robust stabilization and optimal tracking for single input single output siso systems in an l sup spl infin setting using a two parameter compensator scheme optimal robustness is linked to the work done by georgiou and smith 1992 in the l sup 2 setting optimal tracking involves the resolution of l sup 1 optimization problems the authors consider in particular the robust control of delay systems they determine explicit expressions of the bezout factors for general delay systems which are in the callier desoer class spl bscr spl circ 0 finally they solve several general l sup 1 optimization problems and give an algorithm to solve the optimal robust control problem for a large class of delay systems

star order automorphisms on the poset of type 1 operators abstract let h be a complex infinite dimensional hilbert space and b h the algebra of all bounded linear operators on h the star partial order is defined by a b if and only if a a a b and a a a b for any a and b in b h we give a type decomposition of operators with respect to star order for any a b h there are unique type 1 operator a 1 which is 0 or the supremum of those rank 1 operators less than a 1 and type 2 operator a 2 which is not greater than any rank 1 operator under star order such that a i a i 1 2 and a a 1 a 2 moreover we determine all automorphisms on the poset of type 1 operators as a consequence we characterize continuous automorphisms on b h

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

l sup 1 optimal estimation for discrete time linear systems a linear multichannel estimation problem with discrete time linear shift invariant models is formulated in the time domain as a minimum l sup 1 norm approximation problem it is shown using some key results from optimization theory that solving the approximation problem is equivalent to solving a sequence of linear programming problems which terminates when an optimal or near optimal solution is reached the motivation for considering an l sup 1 optimal design versus l sup 2 or h sup infinity optimal designs is presented a sample problem is solved to illustrate the computational procedure as well as to compare the relative performances of the l sup 1 l sup 2 and h sup infinity optimal estimators in a practical situation

brief q domain optimization method for l1 optimal controllers the l 1 optimal control problem is most commonly solved through a linear programming optimization approach in this paper we present a q domain solution procedure and suggest when such an approach is advantageous in the proposed method the coefficients of q are used as optimization parameters q being a matrix of iir filters for multi block problems the q domain optimization method requires only a small number of optimization variables and can converge to the desired optimal value more efficiently than is the case for linear programming optimization

on the stabilization of nonlinear systems we extend the applicability of the global q parametrization method of controller design to a large class of unstable nonlinear plants the main result is a two step compensation theorem analogous to that of zames for unstable linear plants if p l e2 rightarrow l e1 is a nonlinear possibly unstable plant and f 0 is any incrementally stable controller such that p 1 p i f 0 p 1 is incrementally stable then the class of controllers f which yields an f g stable closed loop system in the unity feedback configuration for p is globally parametrized by finite gain stable maps q l e1 rightarrow l e2 with f f 0 q i p 1 q 1

a generalized block fsai preconditioner for nonsymmetric linear systems the efficient solution to nonsymmetric linear systems is still an open issue especially on parallel computers in this paper we generalize to the unsymmetric case the block factorized sparse approximate inverse block fsai preconditioner which has already proved very effective on symmetric positive definite spd problems block fsai is a hybrid approach combining an inner preconditioner with the aim of transforming the system matrix structure to block diagonal with an outer one a block diagonal incomplete or exact factorization intended to improve the conditioning of each block the proposed algorithm is experimented with in a number of large size matrices showing both a good robustness and scalability

on the modeling of brine transport in porous media the problem of concentrated brine transport arises in the study of transport of pollutants released from a repository in a rock salt formation an important characteristic of brine as compared to other solutions normally encountered in groundwater problems is that it contains a high concentration of solutes this factor requires special attention in the development of mathematical models for brine transport problems in this work we discuss certain important physical and mathematical differences between low and high concentration situations in particular we consider three primary aspects of a model basic equations boundary conditions and numerical techniques recognizing the fact that in high concentration situations the fluid motion is not independent of the solutes movement a new formulation of darcy s and fick s law are proposed the basic equations comprise a set of two nonlinear coupled partial differential equations to be solved for the pressure p and the solute mass fraction these equations have to be solved by means of iterative methods various possibilities involving finite difference methods have been studied in one case after discretizing the equations in a fully implicit way the newton raphson method has been employed to solve the system of nonlinear difference equations simultaneously in another case after removing part of the nonlinearity by a transformation of the dependent variable a procedure of sequential solution of the two equations by successive substitution is employed it turns out that the latter method is considerably faster than the former one as a result of the quasi linearization finally considering boundary conditions it is shown that often they are also nonlinear and coupled appropriate conditions for a rock salt boundary and an outflow boundary are developed and their significance in high concentration situations are discussed in particular a nonlinear time dependent boundary condition at a rock salt boundary is developed which takes into account the process of salt dissolution and cap rock formation

the mast fv fe scheme for the simulation of two dimensional thermohaline processes in variable density saturated porous media a novel methodology for the simulation of 2d thermohaline double diffusive processes driven by heterogeneous temperature and concentration fields in variable density saturated porous media is presented the stream function is used to describe the flow field and it is defined in terms of mass flux the partial differential equations governing system is given by the mass conservation equation of the fluid phase written in terms of the mass based stream function as well as by the advection diffusion transport equations of the contaminant concentration and of the heat the unknown variables are the stream function the contaminant concentration and the temperature the governing equations system is solved using a fractional time step procedure splitting the convective components from the diffusive ones in the case of existing scalar potential of the flow field the convective components are solved using a finite volume marching in space and time mast procedure this solves a sequence of small systems of ordinary differential equations one for each computational cell according to the decreasing value of the scalar potential in the case of variable density groundwater transport problem where a scalar potential of the flow field does not exist a second mast procedure has to be applied to solve again the odes according to the increasing value of a new function called approximated potential the diffusive components are solved using a standard galerkin finite element method the numerical scheme is validated using literature tests

nonlinear time varying controllers for robust stabilization in this paper we consider the problem of robust stabilizallon for a certain class of plants with unstructured infinite dimensional uncertainty we demonstrate that for the problem of robustly stabilizing this class of plants linear time invariant controllers perform as well as nonlinear time varying nltv ones ihis in particular implies that adaptive control laws offer no advantage as far as the problem of robust stabilization of this class of plants is concerned as a corollary we demonstrate that the small gain theorem is both necessary and sufficient for a certain class of nltv operators

synthesis of globally optimal controllers for robust performance to unstructured uncertainty this paper solves the problem of synthesis of controllers achieving globally optimal robust performance against unstructured time varying and or nonlinear uncertainty the performance measure considered is the infinity to infinity induced norm of a system s transfer function the solution utilizes sensitivity analysis of linear programming and the theory of parametric programming

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

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

an input output approach to structured stochastic uncertainty we consider linear time invariant systems with exogenous stochastic disturbances and in feedback with structured stochastic uncertainties this setting encompasses linear systems with both additive and multiplicative noise our concern is to characterize second order properties such as mean square stability mss and performance a purely input output treatment of these systems is given without recourse to state space models and thus the results are applicable to certain classes of distributed systems we derive necessary and sufficient conditions for mss in terms of the spectral radius of a linear matrix operator whose dimension is that of the number of uncertainties rather than the dimension of any underlying state space models our condition is applicable to the case of correlated uncertainties and reproduces earlier results for uncorrelated uncertainties for cases where state space realizations are given linear matrix inequality equivalents of the input output conditions are given

on stability analysis methods for large scale discrete time systems this paper proposes a set of lyapunov type conditions that are suited for stability analysis of large scale discrete time systems a time wise relaxation of the lyapunov function decrease condition is employed to derive a set of global and distributed stability conditions essentially these conditions allow to make a trade off between complexity and conservatism by extending the time horizon over which the decrease condition should hold it is shown that for exponentially stable dynamics and any candidate lyapunov function there exists a finite time for which the proposed global or distributed stability conditions hold hence it is possible to use functions with a particular structure to make verification of stability scalable for large scale systems the developed results are applied to establish stability of a benchmark power systems example

absolute stability of systems under block diagonal memoryless uncertainties abstract absolute stability of systems under block diagonal uncertainties is studied a quadratic lyapunov function is used it is found that the quadratic stability condition of such a system is equivalent to that of systems with uncertainties restricted to be rank one matrices the main technique used is exact penalization in nonsmooth analysis

necessary and sufficient conditions for the robustness of time varying systems with applications to sampled data systems necessary and sufficient conditions for robustness of time varying systems with structured norm bounded uncertainty are provided the l sup infinity signal norm is used and the conditions are given in terms of the spectral radii of certain matrices obtained from the kernel representation of the time varying system at hand the derived conditions are then applied to continuous time linear time invariant systems and for sampled data systems

l1 control using linear programming for systems with asymmetric bounds in this paper a novel way to handle the analysis and design of control systems with bounded asymmetrical signals is presented instead of the standard peak to peak norm normally used in l1 optimal control this paper proposes to use an asymmetric objective functional which simplifies the consideration of asymmetrically bounded signals necessary and sufficient conditions are derived to check if some performance specifications expressed using this objective functional are fulfilled the analysis and the synthesis problems are also formulated with respect to this objective functional as in the standard l1 control this approach leads to a linear programming problem which can be solved by available optimization tools a numerical example is also studied to clarify this proposed approach

robust disturbance rejection in e 1 optimal control systems abstract given a class of plants formed by perturbing a nominal discrete time linear shift invariant plant with norm bounded unstructured perturbation the problem of finding a single compensator that will stabilize all plants in this class and at the same time minimize the worst case norm of a certain performance measure is addressed assuming the performance measure of interest is the sensitivity function first an expression for the supremum over all plants in this class of such a measure is derived for a system with a robustly stabilizing compensator this is achieved by first showing that the proposed expression is an upper bound for the worst case sensitivity norm and then by constructing a plant in the allowable class that will achieve this upper bound combined with already known necessary and sufficient conditions for robust stability the derived expression provides an effective way of combining both robust stability and performance in one easy to compute measure secondly a scheme for finding a controller that minimizes the worst case norm of the sensitivity function while achieving robust stability is provided this makes possible the incorporation of stability and performance robustness requirements in one design procedure

finite settling time stabilisation the robust siso case this article deals with the problem of robustness to multiplicative plant perturbations for the case of finite settling time stabilisation fsts of single input single output siso linear discrete time systems fsts is a generalisation of the deadbeat control and as in the case of deadbeat control the main feature of fsts is the placement of all closed loop poles at the origin of the z plane this makes fsts sensitive to plant perturbations hence the need of robust design an efficient robustness index is introduced and the problem is reduced to a finite linear programme where all the benefits of the simplex method such as effectiveness efficiency and ability to provide complete solution to the optimisation problem can be exploited

robust stability and performance analysis of sampled data systems the authors consider the robust stability and performance analysis of a general linear interconnection of a continuous time plant and a discrete time controller via sample and hold devices they obtain necessary and sufficient conditions for the robust stability of the feedback system consisting of an uncertain plant represented as a known linear time invariant nominal model with time varying norm bounded uncertainty and a shift invariant discrete time controller these results show that the condition arising from the small gain theorem is necessary and sufficient when the uncertainties belong to a class of linear systems also similar results are derived for a case of structured uncertainty both l sub 2 and l sub infinity signal norms are considered robust performance analysis problem is solved by converting it to a robust stability analysis problem

best achievable decentralized performance in this paper a novel parameterization of all decentralized stabilizing controllers is employed in mathematically formulating the best achievable decentralized performance problem as an infinite dimensional optimization problem finite dimensional optimization problems are then constructed that have values arbitrarily close to this infinite dimensional problem an algorithm which identifies the best achievable performance over all linear time invariant decentralized controllers is then presented it employs a global optimization approach to the solution of these finite dimensional approximating problems

dual periodicity in l 1 norm minimisation problems the topic of this paper is the discrete time l1 norm minimisation problem with convolution constraints we find primal initial conditions for which the dual optimal solution is periodic periodicity of the dual optimal solution implies satisfaction of a simple linear recurrence relation by the primal optimal solution

robust steady state tracking this paper addresses the robust performance problem when the performance measure is the steady state value of an error signal necessary and sufficient conditions are derived for robust steady state tracking of fixed inputs in the presence of structured time varying uncertainty are derived these conditions are easily computable and fit well with existing conditions on stability robustness and performance robustness when the performance measure is the level of disturbance rejection using these conditions it is shown that time varying perturbations of a nominal linear time invariant plant can result in large steady state tracking errors to fixed inputs even if the nominal plant and controller give zero steady state tracking errors the derived expressions for the worst case steady state tracking error give insight into how the time variation in the plant affects tracking errors and suggest that certain transfer function norms should be minimized to reduce the effect of these perturbations on the steady state value of error signals

study of the acoustic feedback problem of active noise control by using the l1 and l2 vector space optimization approaches this study attempts to explore the acoustic feedback problem that is frequently encountered in feedforward active noise control anc structure from the standpoint of control theories the analysis is carried out on the basis of the youla s parametrization and the l1 norm and l2 norm vector space optimization the anc problem is formulated as a model matching procedure and is solved via linear programming in the dual vector space these methods alleviate the problems caused by the nonminimum phase nmp zeros of the cancellation path the anc algorithms are implemented by using a digital signal processor various types of noises were chosen for validating the developed algorithms the proposed methods are also compared with the well known filtered u least mean square fulms method the experimental results show that the acoustic feedback problem significantly degrades the performance and stability of the anc system regardless which method is used insights into the difficulties due to acoustic feedback a

robust synthesis in sub 1 a globally optimal solution in this paper a method to synthesize controllers that achieve globally optimal robust performance within any prespecified tolerance against structured norm bounded time varying and or nonlinear uncertainty is developed the performance measure considered is the infinity to infinity induced norm of a system s transfer function the method developed utilizes linear relaxation techniques to solve the infinite dimensional nonconvex problem via finite dimensional linear programming problems

a new approach to the solution of the l sub 1 control problem the scaled q method we explore an approach for solving multiple input multiple output mimo l sub 1 optimal control problems this approach which we refer to as the scaled q approach is introduced to alleviate many of the difficulties facing the numerical solution of optimal l sub 1 control problems in particular the computations of multivariable zeros and their directions are no longer required the scaled q method also avoids the pole zero cancellation difficulties that existing methods based on zero interpolation face when attempting to recover the optimal controller from an optimal closed loop map because the scaled q approach is based on solving a regularized auxiliary problem for which the solution is always guaranteed to exist it can be used no matter where the system zeros are including the stability boundary upper and lower bounds that converge to the optimal cost are provided and all solutions are based on finite dimensional linear programming for which efficient software exists

l sub 1 suboptimal pole placement design we incorporate an arbitrary number of candidate positive distinct poles into the scalar l sub 1 optimization framework in order to obtain low order rational suboptimal solutions to constrained l sub 1 optimization problems our approach uses a single linear program to minimize an upper bound on the l sub 1 norm and gives a solution which uses only the best out of the prespecified poles rational suboptimal solutions to a scalar two block problem are obtained similarly

a polynomial approach to the l sub 1 mixed sensitivity optimal control problem it is shown how discrete time mixed sensitivity l sub 1 optimal control problems can be converted via polynomial techniques to linear least absolute data fitting problems and solved via efficient and stable numerical methods in particular two new sub superoptimization schemes are introduced by expressing the closed loop sensitivity and complementary sensitivity maps in terms of the free parameter of a stabilizing deadbeat controller parameterization and exploiting the underlying algebraic structure this approach induces the application of a consistent truncation strategy that leads to a redundance free constraint formulation and as a consequence to linear programming problems less affected by degeneracy further more insight on the algebraic structure of the problem and on the achievement of exact rational solutions is provided allowing the development of a simple and conceptually attractive theory

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

a construction of rational wavelets and frames in hardy sobolev spaces with applications to system modeling using the daubechies wavelet theory we establish rational wavelet decompositions of the hardy sobolev classes on the half plane the decay of wavelet coefficients is analyzed and error bounds for approximation are given we give applications to the modeling of linear systems and to the model reduction of infinite dimensional systems

mixed finite elements and newton type linearizations for the solution of richards equation we present the development of a two dimensional mixed hybrid finite element mhfe model for the solution of the non linear equation of variably saturated flow in groundwater on unstructured triangular meshes by this approach the darcy velocity is approximated using lowest order raviart thomas rt0 elements and is exactly mass conserving hybridization is used to overcome the ill conditioning of the mixed system the scheme is globally first order in space nevertheless numerical results employing non uniform meshes show second order accuracy of the pressure head and normal fluxes on specific grid points the non linear systems of algebraic equations resulting from the mhfe discretization are solved using picard or newton iterations realistic sample tests show that the mhfe newton approach achieves fast convergence in many situations in particular when a good initial guess is provided by either the picard scheme or relaxation techniques copyright 1999 john wiley sons ltd

comment on conditions for stable zeros of sampled systems upo90 from the submatrix u a which is a submatrix of the previous submatrix containing xpq this process of constructing xpq goes on until the last submatrix the nth submatrix which is equal to the matrix a containing xpq has been reached example find the 30 60 th entry of the 10th kronecker power of the matrix upoqoup1 l pkqk

mimo l 1 optimal control problems via the polynomial equations approach the general mimo multi block l 1 optimal control problem is considered a novel solution is derived by resorting to polynomial techniques and simple algebraic conditions on the free parameter of the yjbk parameterization as a result we arrive at unconstrained lp formulations less affected by redundancy and solvable by standard lp solvers as usual because the optimal controller is in general infinite dimensional a solution scheme based on solving sequences of increasing larger finite dimensional sub super optimal optimization problem is proposed viz sequences of finite dimensional optimization problems whose solutions provide lower and respectively upper bounds to the optimum monotonically converging to it finally an example is presented in order to exemplify the theory and show the effectiveness of the method

high order godunov mixed methods on tetrahedral meshes for density driven flow simulations in porous media two dimensional godunov mixed methods have been shown to be effective for the numerical solution of density dependent flow and transport problems in groundwater even when concentration gradients are high and the process is dominated by density effects this class of discretization approaches solves the flow equation by means of the mixed finite element method thus guaranteeing mass conserving velocity fields and discretizes the transport equation by mixed finite element and finite volumes techniques combined together via appropriate time splitting in this paper we extend this approach to three dimensions employing tetrahedral meshes and introduce a spatially variable time stepping procedure that improves computational efficiency while preserving accuracy by adapting the time step size according to the local courant friedrichs lewy cfl constraint careful attention is devoted to the choice of a truly three dimensional limiter for the advection equation in the time splitting technique so that to preserve second order accuracy in space in the sense that linear functions are exactly interpolated the three dimensional elder problem and the saltpool problem recently introduced as a new benchmark for testing three dimensional density models provide assessments with respect to accuracy and reliability of this numerical approach

controller design for plants with structured uncertainty this paper addresses the problem of designing feedback controllers to achieve good performance in the presence of structured plant uncertainty and bounded but unknown disturbances a general formulation for the performance robustness problem is presented and exact computable conditions are furnished these conditions are then utilized for synthesizing robust controllers which involves solving l1 optimization problems these solutions are computed using the duality theory of lagrange multipliers approximations and computational issues are discussed

fading memory feedback systems and robust stability abstract this paper considers fading memory for nonlinear time varying systems and associated problems of robust stability we define two notions of fading memory for stable dynamical systems uniform and pointwise we then provide conditions under which stable linear or nonlinear systems exhibit uniform or pointwise fading memory in particular we show that 1 all stable discrete time linear time varying ltv systems have uniform fading memory 2 all stable continuous time ltv systems have pointwise fading memory and 3 stable finite dimensional continuous time ltv systems have uniform fading memory we then show that a version of the small gain theorem which employs the asymptotic gain of a fading memory system is necessary for the stable invertibility of certain feedback operators these results are presented for both continuous time and discrete time systems using general lp or l p notions of input output stability and generalize existing results for l2 stability we further investigate fading memory in a closed loop context for linear plants we parametrize all nonlinear controllers which lead to closed loop pointwise fading memory

some properties on the star order of bounded operators abstract in this paper we give various characterizations of star order and present some new relationships between the logic order and the star order we present some necessary and sufficient conditions for which the infimum or upper bound exists with respect to given orders

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

practical output feedback stabilisation for a class of continuous time dynamic systems under sample data outputs this article deals with a class of continuous nonlinear control systems in the presence of sampled outputs the dynamical models under consideration are described by ordinary differential equations with additive bounded uncertainties the linear feedback control design proposed in this article is based on an extended version of the classical invariant ellipsoid method the stability robustness analysis of the resulting closed loop system involves the celebrated descriptor techniques from the extended lyapunov methodology finally the implementability of the proposed control design scheme is illustrated by a computational example a brief discussion on the principal numerical issues is also included

star partial order on b h abstract let h be an infinite dimensional complex hilbert space and let b h be the algebra of all bounded linear operators on h in the paper the equivalent definition of the star partial order on b h using selfadjoint idempotent operators is introduced also some properties of the generalized concept of order relations on b h defined with the help of idempotent operators are investigated

analysis of robust performance with multiple objectives performance robustness with multiple objectives of linear control systems having structured norm bounded uncertainty is considered in order to deal with any two objective functions 1 and 2 associated with a single feedback control system the combined criterion 1 2 s 1 is often used the paper however considers 1 1 and w 11 1 directly it is shown that it is possible to assess robust performance of two objectives by a single test if repeated nonscalar blocks are adequately introduced in the structure of in other words a performance robustness problem with multiple objectives is proved to be equivalent to a stability robustness problem with extra repeated uncertainty blocks this equivalence theorem is applicable to various system and norm setups including sampled data systems

modelling of uncertain systems via linear programming abstract real plants are in general time varying and uncertain yet most industrial control loops are designed using linear time invariant lti plant models the present work formalizes the problem of best approximate lti modelling of bibo stable linear time varying ltv systems in a way that is compatible with the notion of induced l norm used in robust l 1 control this setup is closely associated with certain identification methods and controlmotivated model validation invalidation procedures that can be efficiently implemented with special purpose linear programming lp techniques results are given for approximate modelling of bibo stable ltv and lti systems using lti models especially bibo stable fixed pole state space model parametrizations it is shown that such parametrizations are satisfactory from an approximate modelling point of view and can be used in output error type lp identification techniques and in lp model validation procedures various useful constraints on model parameters etc can be included as long as they are linear in the unknown parameters and both insensitive statistically robust and sensitive criteria can be used in identification and model validation simulation examples are included to illustrate that such techniques indeed give good results and can be used to solve problems of realistic size

a maximum principle satisfying modification of triangle based adaptive stencils for the solution of scalar hyperbolic conservation laws a modified triangle based adaptive difference stencil for the numerical approximation of scalar hyperbolic conservation laws in two space dimensions is constructed the scheme satisfies the maximum principle and approximates the flux with second order accuracy

accuracy of galerkin finite elements for groundwater flow simulations in two and three dimensional triangulations summary in standard nite element simulations of groundwater 4ow the correspondence between hydraulic head gradients and groundwater 4uxes is represented by the sti ness matrix in two dimensional problems the use of linear triangular elements on delaunay triangulations guarantees a sti ness matrix of type m this implies that the local numerical 4uxes are physically consistent with darcy s law this condition is fundame ntal to avoid theoccurre nceof local maxima or minima and is of crucial importancewhe n the calculated 4ow eld is used in contaminant transport simulations or pathline evaluation in three spatial dimensions the linear galerkin approach on tetrahedra does not lead to m matrices even on delaunay meshes by interpretation of the galerkin approach as a subdomain collocation scheme we develop a new approach osc orthogonal subdomain collocation that is shown to produce m matrices in three dimensional delaunay triangulations in case of heterogeneous and anisotropic coeacients extra mesh properties required for m sti ness matrices will also be discussed copyright 2001 john wiley sons ltd

on minimizing maximum errors it is shown how a previously published control problem by a g parlos 1988 formulated using ellipsoidal set theoretic control synthesis techniques can be formulated and solved using l sup 1 optimal control theory a complete solution is furnished to the problem it avoids the difficulties of parameter optimization

efficient algorithm for solving semi infinite programming problems and their applications to nonuniform filter bank designs an efficient algorithm for solving semi infinite programming problems is proposed in this paper the index set is constructed by adding only one of the most violated points in a refined set of grid points by applying this algorithm for solving the optimum nonuniform symmetric antisymmetric linear phase finite impulse response fir filter bank design problems the time required to obtain a globally optimal solution is much reduced compared with that of the previous proposed algorithm

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

optimal asymptotic identification under bounded disturbances the intrinsic limitation of worst case identification of linear time invariant systems using data corrupted by bounded disturbances when the unknown plant is known to belong to a given model set is studied this is done by analyzing the optimal worst case asymptotic error achievable by performing experiments using any bounded input and estimating the plant using any identification algorithm it is shown that under some topological conditions on the model set there is an identification algorithm which is asymptotically optimal for any input and the optimal asymptotic error is characterized as a function of the inputs these results which hold for any error metric and disturbance norm are applied to three specific identification problems identification of stable systems in the l sub 1 norm identification of stable rational systems in the h sub infinity norm and identification of unstable rational systems in the gap metric for each of these problems the general characterization of optimal asymptotic error is used to find near optimal inputs to minimize the error

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

lattice properties of the order for complex matrices abstract it is shown that the set c m n of complex m n matrices forms a lower semilattice under the partial ordering a b defined by a a a b aa ba where a denotes the conjugate transpose of a as a special case of a result for division rings it is further shown that over any field f for m n 2 and any proper involution of f2 2 the corresponding intersections a b all exist

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

the supremum of linear operators for the order abstract let b h be the algebra of all bounded linear operators on a complex hilbert space h in 1978 drazin introduced a partial order on b h for a b b h a b if and only if a a a b and aa ba given a b b h let a b be the least upper bound supremum for a and b with respect to the order in this paper we present some necessary and sufficient conditions for which a b exists and give an explicit representation of a b if a b exists

robust stability with time varying structured uncertainty considers the problem of assessing robust stability in the presence of block diagonally structured time varying dynamic uncertainty it is shown that robust stability holds only if there exist constant scalings which lead to a small gain condition the notion of stability here is finite gain stability over finite energy signals in sharp contrast to the case of time invariant dynamic uncertainty this result is not limited by the number uncertainty blocks these results parallel previous results regarding finite gain stability over persistent bounded signals

worst case analysis of identification bibo robustness for closed loop data this paper deals with the worst case analysis of identification of linear shift invariant possibly infinite dimensional systems a necessary and sufficient input richness condition for the existence of robustly convergent identification algorithms in l sup 1 is given a closed loop identification setting is studied to cover both stable and unstable but bibo stabilizable systems identification or modeling error is then measured by distance functions which lead to the weakest convergence notions for systems such that closed loop stability in the sense of bibo stability is a robust property worst case modeling error bounds in several distance functions are included

robust stability under structured and unstructured perturbations the problem of robust stability for linear time invariant single output control systems subject to both structured parametric and unstructured h sub infinity perturbations is studied a generalization of the small gain theorem which yields necessary and sufficient conditions for robust stability of a linear time invariant dynamic system under perturbations of mixed type is presented the solution involves calculating the h sub infinity norm of a finite number of extremal plants the problem of calculating the exact structured and unstructured stability margins is then constructively solved a feedback control system containing a linear time invariant plant which is subject to both structured and unstructured perturbations is considered the case where the system to be controlled is interval is treated and a nonconservative easily verifiable necessary and sufficient condition for robust stability is given the solution is based on the extremal of a finite number of line segments in the plant parameter property of a finite number of line segments in the plant parameter space along which the points closest to instability are encountered

analysis and design for robust performance with structured uncertainty abstract necessary and sufficient conditions for stability and performance robustness of discrete time systems are provided in terms of the spectral radius of a certain nonnegative matrix the conditions are easily computable and provide a simple and efficient method for computation of the robustness conditions for siso as well mimo perturbations the problem of robust controller synthesis is explored and an iteration scheme for controller synthesis is introduced

approximation of distributed delays in this paper we address the approximation problem of distributed delays these elements are convolution operators with kernel having bounded support and appear in the control of time delay systems from the rich literature on this topic we propose a general methodology to achieve such an approximation for this we enclose the approximation problem in the graph topology and working on the convolution banach algebra a constructive approximation is proposed analysis in time and frequency domains is provided this methodology is illustrated on the stabilization control for time delay systems

model reference adaptive control for nonminimum phase systems in this paper we define a new model reference adaptive control problem which allows a large amount of plant uncertainty instead of the usual goal of asymptotic error regulation here we require that the limit superior of the magnitude of the error be less than a predefined constant times the limit superior of the magnitude of the external reference input this provides a natural way to incorporate uncertainty which includes nonminimum phase systems

internal behaviour provided by nonlinear l1 optimal controllers abstract an l 1 optimal linear time invariant lti compensator may have an order significantly higher than that of the plant even when the state is measurable recently there has been work exploring the use of nonlinear static feedback controllers which provide near optimal performance here we consider a class of nonlinear state feedback controllers and derive superposition like bounds on both the plant state and the controlled output in the event that the plant initial condition the disturbance and the noise are all non zero

on optimal e to e filtering abstract in this paper we consider the problem of finding a filter that minimizes the worst case magnitude l of the estimation error in the case of linear time invariant systems subjected to unknown but magnitude bounded l inputs these inputs consist of process and observation noise as well as initial conditions also the optimization problem is considered over an infinite time horizon taking a model matching approach suboptimal solutions are presented that stem from the resulting l induced norm minimization problem

adaptive suboptimal tracking for the first order plant with lipschitz uncertainty a tracking problem for the first order discrete time plant with time invariant uncertainty of the lipschitz type and bounded exogenous disturbance is considered in the adaptive setting and two different adaptive laws are proposed the first law is based on a natural estimation of the unknown linear part of the plant and introduces some conservatism in stability margin and tracking performance the second adaptive law is suboptimal and includes additionally the estimation of the unknown lipshitz constant and the unknown norm of exogenous disturbance the suboptimality is achieved by exploiting a cone estimation algorithm and the linearity of the control criterion with respect to unknown parameters both adaptive laws utilize the nonlinear feedback by xie and guo based on nonparametric estimation of the uncertainty

l 1 optimal compensators for continuous time systems previous work has been concerned with minimizing the l 1 norm of an error pulse response for discrete time siso 1 and mimo 2 systems in this paper we study the problem of minimizing the l1 norm of the error impulse response for siso continuous time systems this problem is quite different from the discrete time problem in that irrational solutions are obtained even when the problem data are rational two methods are suggested for the solution of the continuous time problem an exact method which leads to a finite dimensional nonlinear programming problem and an approximate method which leads to a linear programming problem