the global well posedness and global attractor for the solutions to the 2d boussinesq system with variable viscosity and thermal diffusivity abstract global well posedness of strong solutions and existence of the global attractor to the initial and boundary value problem of 2d boussinesq system in a periodic channel with non homogeneous boundary conditions for the temperature and viscosity and thermal diffusivity depending on the temperature are proved

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

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

initial boundary value problem for two dimensional viscous boussinesq equations we study the initial boundary value problem of two dimensional viscous boussinesq equations over a bounded domain with smooth boundary we show that the equations have a unique classical solution for h3 initial data and the no slip boundary condition in addition we show that the kinetic energy is uniformly bounded in time

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

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

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

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

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

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

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

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

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

the generalized h 2 control problem abstract in this paper we consider the problem of finding an internally stabilizing controller such that the controlled or regulated signals have a guaranteed maximum peak value in response to arbitrary but bounded energy exogenous inputs more specifically we give a complete solution to the problem of finding a stabilizing controller such that the closed loop gain from l 2 0 to l 0 is below a specified level we consider both state feedback and output feedback problems in the state feedback case it is shown that if this synthesis problem is solvable then a solution can be chosen to be a constant state feedback gain necessary and sufficient conditions for the existence of solutions as well as a formula for a state feedback gain that solves this control problem are obtained in terms of a finite dimensional convex feasibility program after showing the separation properties of this synthesis problem the output feedback case is reduced to a state feedback problem it is shown that in the output feedback case generalized h 2 controllers can be chosen to be observer based controllers the theory is demonstrated with a numerical example

infinite prandtl number limit of rayleigh benard convection we rigorously justify the infinite prandtl number model of convection as the limit of the boussinesq approximation to the rayleigh benard convection as the prandtl number approaches infinity this is a singular limit problem involving an initial layer 2003 wiley periodicals inc

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

parabolic equations with vmo coefficients in sobolev spaces with mixed norms an lq lp theory of divergence and non divergence form parabolic equations is presented the main coefficients are supposed to belong to the class vmox which in particular contains all measurable functions depending only on t the method of proving simplifies the methods previously used in the case p q

on linear models for nonlinear systems best linear time invariant lti approximations are analysed for several interesting classes of discrete nonlinear time invariant systems these include nonlinear finite impulse response systems and a class of nonsmooth systems called bi gain systems the frechet derivative of a smooth nonlinear system is studied as a potential good lti model candidate the frechet derivative is determined for nonlinear finite memory systems and for a class of wiener systems most of the concrete results are derived in an signal setting applications to linear controller design to identification of linear models and to estimation of the size of the unmodelled dynamics are discussed

continuous time control model validation using finite experimental data the application of robust control theory requires models containing unknown bounded perturbations and unknown bounded input signals model validation is a means of assessing the applicability of a given model with respect to experimental data this paper develops a theoretical framework and a computational solution for the model validation problem in the case where the model including unknown perturbations and signals is given in the continuous time domain yet the experimental datum is a finite sampled signal the continuous nature of the unknown components is treated directly with a sampled data lifting theory this gives results which are valid for any sample period and any datum length explicit calculation of whether sufficient data for invalidation has been obtained arises naturally in this framework a common class of robust control models is treated and leads to a convex matrix optimization problem a simulation example illustrates the approach

stationary statistical properties of rayleigh benard convection at large prandtl number this is the third in a series of our study of rayleigh benard convection at large prandtl number here we investigate whether stationary statistical properties of the boussinesq system for rayleigh benard convection at large prandtl number are related to those of the infinite prandtl number model for convection that is formally derived from the boussinesq system via setting the prandtl number to infinity we study asymptotic behavior of stationary statistical solutions or invariant measures to the boussinesq system for rayleigh benard convection at large prandtl number in particular we show that the invariant measures of the boussinesq system for rayleigh benard convection converge to those of the infinite prandtl number model for convection as the prandtl number approaches infinity we also show that the nusselt number for the boussinesq system a specific statistical property of the system is asymptotically bounded by the nusselt number of the infinite prandtl number model for convection at large prandtl number we discover that the nusselt numbers are saturated by ergodic invariant measures moreover we derive a new upper bound on the nusselt number for the boussinesq system at large prandtl number of the form

global regularity results for the 2d boussinesq equations with vertical dissipation abstract the two dimensional 2d incompressible boussinesq equations model geophysical fluids and play an important role in the study of the raleigh bernard convection mathematically this 2d system retains some key features of the 3d navier stokes and euler equations such as the vortex stretching mechanism the issue of whether the 2d boussinesq equations always possess global in time classical solutions can be difficult when there is only partial dissipation or no dissipation at all this paper obtains the global regularity for two partial dissipation cases and proves several global a priori bounds for two other prominent partial dissipation cases these results take us one step closer to a complete resolution of the global regularity issue for all the partial dissipation cases involving the 2d boussinesq equations

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

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

rational suboptimal continuous time controller design we obtain rational suboptimal continuous time solutions to some optimal control problems specified via time domain performance criteria these include spl lscr sub 1 and spl lscr sub spl infin norms and peak overshoot the approach uses linear semi infinite programming to compute weights for a given finite set of rational basis functions and makes the best possible use of the basis the closed loop transfer functions obtained satisfy appropriate interpolation constraints for internal stability and the formulation allows additional linear constraints to be incorporated

l1 robust performance of discrete time systems with structured uncertainty abstract this paper addresses the robust performance problem when a linear time invariant system is subjected to both norm bounded time varying uncertainty and worst case external bounded input the tightest upper bounds for steady state robust performance measures over classes of finite memory and fading memory perturbations are computed in the regulation and tracking problems since the classes of finite memory and fading memory perturbations are inappropriate to the purposes of model validation and adaptive control approximating subclasses of bounded memory perturbations and perturbations with exponentially decreasing impulse responses are considered it is shown that the robust performance bounds obtained are nonconservative in the case of bounded memory perturbations the worst case steady state robust performance measures for siso system under coprime factor perturbations are computed for illustration

l_ 1 discretization for sampled data controller synthesis via piecewise linear approximation this paper develops a new discretization method with piecewise linear approximation for the l 1 optimal controller synthesis problem of sampled data systems which is the problem of minimizing the l infty induced norm of sampled data systems we apply fast lifting on the top of the lifting technique by which the sampling interval 0 h is divided into m subintervals with an equal width the signals on each subinterval are then approximated by linear functions by introducing two types of linearizing operators for input and output which leads to piecewise linear approximation of sampled data systems by using the arguments of preadjoint operators we provide an important inequality that forms a theoretical basis for tackling the l 1 optimal controller synthesis problem of sampled data systems more efficiently than the conventional method more precisely a mathematical basis for the piecewise linear approximation method associated with the convergence rate is shown through this inequality and this suggests that the piecewise linear approximation method may drastically outperform the conventional method in the l 1 optimal controller synthesis problem of sampled data systems we then provide a discretization procedure of sampled data systems by which the l 1 optimal controller synthesis problem is converted to the discrete time l 1 optimal controller synthesis problem finally effectiveness of the proposed method is demonstrated through a numerical example

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

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

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

global well posedness for the euler boussinesq system with axisymmetric data abstract in this paper we prove the global well posedness for the three dimensional euler boussinesq system with axisymmetric initial data without swirl this system couples the euler equation with a transport diffusion equation governing the temperature

global regularity for the initial boundary value problem of the 2 d boussinesq system with variable viscosity and thermal diffusivity abstract we prove the global existence of strong solution to the initial boundary value problem of the 2 d boussinesq system and 3 d infinite prandtl number model with viscosity and thermal conductivity depending on the temperature

deconvolution filter design via l sub 1 optimization technique a new l sub 1 optimal deconvolution filter design approach for systems with uncertain or unknown but bounded inputs and external noises is proposed the purpose of this deconvolution filter is to minimize the peak gain from the input signal and noise to the error by the viewpoint of the time domain the solution consists of two steps in the first step the l sub 1 norm minimization problem is transferred to an equivalent a norm minimization problem and the minimum value of the peak gain is calculated in the second step based on the minimum peak gain the l sub 1 optimal deconvolution filter is constructed by solving a set of constrained linear equations some techniques of inner outer factorization polynominal spectral factorization linear programming and some optimization theorems found in a book by luenberger are applied to treat the l sub 1 optimal deconvolution filter design problem although the analysis of the algorithm seems complicated the calculation of the proposed design algorithm for actual systems is simple finally one numerical example is given to illustrate the proposed design approach several simulation results have confirmed that the proposed l sub 1 optimal deconvolution filter has more robustness than the l sub 2 optimal deconvolution filter under uncertain driving signals and noises

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

a parametrization of stabilizing controllers for multirate sampled data systems all linear multirate controllers for a given multirate sampled data system plant are parameterized in terms of a single parameter q z that is allowed to be any stable transfer matrix provided that certain causality conditions are met the result parallels a well known parameterization result for single rate sampled data plants the parameterization suggests architectures for multirate controllers

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

the vanishing diffusivity limit for the 2 d boussinesq equations with boundary effect abstract in this paper we tackle the issue of the vanishing diffusivity limit of the 2 d incompressible boussinesq equations in the half plane our main purpose is to study the boundary layer effect and the convergence rates as the thermal diffusion parameter goes to zero under the homogeneous dirichlet boundary condition of velocity and the nonhomogeneous dirichlet boundary condition in the x direction for temperature we show that the boundary layer thickness is of the order o with 0 2 3 in contrast with jiang et al 2011 the bl thickness we got is thinner than that in jiang et al 2011 moreover we prove that as diffusivity tends to zero the solutions of the fully viscous equations converge strongly to those of zero diffusion equations we also obtain the convergence rates of the vanishing diffusivity limit

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

on the blowup criteria and global regularity for the non diffusive boussinesq equations with temperature dependent viscosity coefficient abstract in this paper we consider the boussinesq equations with temperature dependent viscosity and zero thermal diffusivity a blowup criterion of classical solution depending only on l q 0 t l p with p 2 and 1 p 1 q 1 2 is obtained for the two dimensional equations this is in particular consistent with the results in chae 2006 hou and li 2005 lai et al 2011 where the global regularity of the 2d non diffusive boussinesq equations with constant viscosity coefficient i e const was proved a serrin s type blowup criterion depending on u l s 0 t l r l q 0 t l p with r p 3 3 r 2 s 1 and 3 p 2 q 1 is obtained for the three dimensional case we also study the global regularity with large data for the two dimensional equations in a non divergence form

fuzzy observer based fuzzy control design for nonlinear systems with persistent bounded disturbances to date nonlinear l gain control problems have not been solved by the conventional control methods for the nonlinear dynamic systems with persistent bounded disturbances this study introduces a fuzzy control design to deal with the nonlinear l gain output feedback control problem first the takagi and sugeno t s fuzzy model is employed to approximate the nonlinear dynamic system next based on the fuzzy model a fuzzy observer based fuzzy controller is developed to minimize the upper bound of l gain of the closed loop system under some linear matrix inequality lmi constraints therefore the nonlinear l gain control problem is transformed into a suboptimal control problem i e to minimize the upper bound of the l gain of the closed loop system subject to some lmi constraints in this situation the nonlinear l gain output feedback control problem can be easily solved by a lmi based optimization method the proposed methods which efficiently attenuate the peak of perturbation due to persistent bounded disturbances extend the l gain control problems from linear dynamic systems to nonlinear dynamic systems

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

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

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

global well posedness for the 2 d boussinesq system with the temperature dependent viscosity and thermal diffusivity abstract we prove the global well posedness for the 2 d boussinesq system with the temperature dependent viscosity and thermal diffusivity

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

persistent disturbance rejection via static state feedback in contrast with spl hscr sub spl infin and spl hscr sub 2 control theories the problem of persistent disturbance rejection l sup 1 optimal control leads to dynamic controllers even when the states of the plant are available for feedback using viability theory shamma showed 1993 in a nonconstructive way that in the state feedback case the same performance achieved by any dynamic linear time invariant controller can be achieved using memoryless nonlinear state feedback in this paper we give an alternative constructive proof of these results for discrete and continuous time systems the main result of the paper shows that in both cases the l sup 1 norm achieved by any stabilizing state feedback linear dynamic controller can be also achieved using a memoryless variable structure controller

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

structure and optimality of multivariable periodic controllers a linear periodic plant to be controlled by measurement feedback is considered the general optimal synthesis problem in which the objective is to select a compensator to minimize the norm of the induced map between the controlled output and the exogeneous input is analyzed it is shown that the performance of any linear compensator possibly time varying nonperiodic can be matched by a compensator contained in the restricted class of periodic controllers this result is established in the discrete time case for bounded amplitude l sub infinity signals in the continuous time case the result is shown for bounded energy signals l sub 2 l sub 2

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

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

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

global well posedness for 2 d boussinesq system with the temperature dependent viscosity and supercritical dissipation abstract the present paper is dedicated to the global well posedness issue for the boussinesq system with the temperature dependent viscosity in r 2 motivated by the work abidi and zhang adv math 305 2017 1202 1249 on the critical dissipation d with 1 in the temperature equation of the system we consider the extension of their work to the supercritical dissipation for 2 3 1

book review actuator saturation control v kapila k m grigoriadis marcel dekker new york isbn 0 8247 0751 6

initial boundary value problem to 2d boussinesq equations for mhd convection with stratification effects abstract this paper is concerned with the initial boundary value problem to 2d magnetohydrodynamics boussinesq system with the temperature dependent viscosity thermal diffusivity and electrical conductivity first we establish the global weak solutions under the minimal initial assumption then by imposing higher regularity assumption on the initial data we obtain the global strong solution with uniqueness moreover the exponential decay rates of weak solutions and strong solution are obtained respectively

global regularity for the 2d boussinesq equations with partial viscosity terms abstract in this paper we prove the global in time regularity for the 2d boussinesq system with either the zero diffusivity or the zero viscosity we also prove that as diffusivity viscosity tends to zero the solutions of the fully viscous equations converge strongly to those of zero diffusion viscosity equations our result for the zero diffusion system in particular solves the problem no 3 posed by moffatt in r l ricca ed kluwer academic publishers dordrecht the netherlands 2001 pp 3 10

the 2d boussinesq equations with vertical viscosity and vertical diffusivity this paper aims at the global regularity of classical solutions to the 2d boussinesq equations with vertical dissipation and vertical thermal diffusion we prove that the l r norm of the vertical velocity v for any 1 0 would guarantee the global regularity of classical solutions

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

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

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

regularity results for two dimensional flows of multiphase viscous fluids global regularity results for weak solutions of the navier stokes equations for two dimensional multiphase incompressible fluids are proved under suitable conditions on the viscosity without assuming positive lower bounds on the initial density as an application we deduce regularity properties for the integral curves of the corresponding velocity field finally we prove regularity results in the small for strong solutions

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

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

siso controller design to minimize a positive combination of the l 1 and the h 2 norms abstract we consider the problem of minimizing a given positive linear combination of the l1 norm and the square of the h 2 norm of the closed loop over all internally stabilizing controllers the problem is analysed for the discrete time siso linear time invariant case it is shown that a unique optimal solution always exists and can be obtained by solving a finite dimensional convex optimization problem with an a priori determined dimension it is also established that the solution is continuous with respect to changes in the coefficients of the linear combination