thermodynamics and analysis of rate independent adhesive contact at small strains we address a model for adhesive unilateral frictionless signorini type contact between bodies of heatconductive viscoelastic material in the linear kelvin voigt rheology undergoing thermal expansion the flow rule for debonding the adhesion is considered rate independent and unidirectional and a thermodynamically consistent model is derived and analysed as far as the existence of a weak solution is concerned

a vanishing viscosity approach to quasistatic evolution in plasticity with softening we deal with quasistatic evolution problems in plasticity with softening in the framework of small strain associative elastoplasticity the presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rate independent problems to the case of a nonconvex energy functional we argue that in this case the use of global minimizers in the corresponding incremental problems is not justified from the mechanical point of view thus we analyse a different selection criterion for the solutions of the quasistatic evolution problem based on a viscous approximation this leads to a generalized formulation in terms of young measures developed in the first part of the paper in the second part we apply our approach to some concrete examples

robust output feedback model predictive control of constrained linear systems this paper provides a solution to the problem of robust output feedback model predictive control of constrained linear discrete time systems in the presence of bounded state and output disturbances the proposed output feedback controller consists of a simple stable luenberger state estimator and a recently developed robustly stabilizing tube based model predictive controller the state estimation error is bounded by an invariant set the tube based controller ensures that all possible realizations of the state trajectory lie in a simple uncertainty tube the center of which is the solution of a nominal disturbance free system and the cross section of which is also invariant satisfaction of the state and input constraints for the original system is guaranteed by employing tighter constraint sets for the nominal system the complexity of the resultant controller is similar to that required for nominal model predictive control

on fuzzy measure and fuzzy integral on fuzzy set abstract on a fuzzy algebra of fuzzy sets we discuss some structural characteristics of a fuzzy measure the pseudo autocontinuity and some other concepts for a fuzzy measure are introduced and the relations between these cre discussed for the case of fuzzy sets riesz s theorems and lebesgue s theorems for a sequence of measurable functions are proved the concept of the fuzzy integral on a fuzzy set is given and some properties of fuzzy integrals on fuzzy sets are studied finally we prove some convergence theorems of a sequence of fuzzy integrals on fuzzy sets

an ellipsoidal off line model predictive control strategy for linear parameter varying systems with applications in chemical processes abstract in this paper a novel off line model predictive control strategy for linear parameter varying systems is presented the on line computational burdens are reduced by pre computing off line the sequences of state feedback gains corresponding to the sequences of nested ellipsoids the number of sequences of nested ellipsoids constructed is equal to the number of vertices of the polytope at each sampling instant the smallest ellipsoid containing the currently measured state is determined in each sequence of ellipsoids and the scheduling parameter is measured the real time state feedback gain is calculated by linear interpolation between the corresponding state feedback gains an overall algorithm is proved to guarantee robust stability the controller design is illustrated with two examples of continuous stirred tank reactors

correspondence robust stabilization of uncertain time varying discrete systems and comments on an improved approach for constrained robust model predictive control this paper addresses the robust stabilizability problem of linear discrete time systems with time varying polytopic uncertainties a state feedback control law is proposed based on the construction of a parameter dependent lyapunov function also it points out that the main results of cuzzola geromel and morari automatica 38 2002 1183 1189 are incorrect and presents the corrected version of these results

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

explicit mpc for lpv systems stability and optimality this paper considers high speed control of constrained linear parameter varying systems using model predictive control existing model predictive control schemes for control of constrained linear parameter varying systems typically require the solution of a semi definite program at each sampling instance recently variants of explicit model predictive control were proposed for linear parameter varying systems with polytopic representation decreasing the online computational effort by orders of magnitude depending on the mathematical structure of the underlying system the constrained finite time optimal control problem can be solved optimally or close to optimal solutions can be computed constraint satisfaction recursive feasibility and asymptotic stability can be guaranteed a priori by an appropriate selection of the terminal state constraints and terminal cost the paper at hand gathers previous developments and provides new material such as a proof for the optimality of the solution or in the case of close to optimal solutions a procedure to determine a bound on the suboptimality of the solution

semicontinuity problems in the calculus of variations soit f r 3 r une fonction deux fois continument differentiable et pour u w 1 1 a b f u a b a b f x u x u x dx si f r n r m r nm r satisfait 1 f est mesurable en x continue en cs et 2 0 f x s a x c s p p ou p 1 a est une fonction localement sommable non negative et c une constante non negative alors la fonctionnelle f u a b est sequentiellement faiblement semi continue inferieurement sur w 1 p r m si et seulement si f x s est quasi convexe pour chaque s et presque chaque x

output feedback robust mpc of uncertain norm bounded linear systems with disturbance the output feedback robust model predictive control mpc for the linear systems with norm bounded uncertainty and disturbance is studied a new state estimator is formulated where both estimator d

output feedback robust mpc with one free control move for the linear polytopic uncertain system with bounded disturbance in this paper a previous approach for the robust model predictive control mpc for a linear polytopic uncertain system is extended to the case with bounded disturbance and unmeasurable state the controller on line optimizes a free control move followed by an output feedback control law based on the pre specified state estimator a key technique for this controller is an appropriate formulation of the estimation error bound which accounts for recursive feasibility of the optimization problem the quadratic boundedness qb of the augmented state is guaranteed by the proposed approach a numerical example is given to illustrate the effectiveness of the proposed controller

on estimation error bounds for receding horizon filters using quadratic boundedness quadratic boundedness is used to deal with stability and design of receding horizon estimators upper bounds on the norm of the estimation error have been found by means of invariant sets that can be constructed by using quadratic boundedness moreover these bounds are expressed in terms of linear matrix inequalities and are well suited to being minimized for the purpose of design

effective relaxation for microstructure simulations algorithms and applications for a wide class of problems in continuum mechanics like those involving phase transitions or finite elastoplasticity the governing potentials tend to be not quasiconvex this leads to the occurrence of microstructures of in principle arbitrarily small scale which cannot be resolved by standard discretization schemes their effective macroscopic properties however can efficiently be recovered with relaxation theory the paper introduces the variational framework necessary for the implementation of relaxation algorithms with emphasis on problems with internal variables in a time incremental setting the methods developed are based on numerical approximations to notions of generalized convexification the focus is on the thorough analysis of numerical algorithms and their efficiency in applications to benchmark problems an outlook to time evolution of microstructures within the framework of relaxation theory concludes the paper 2004 published by elsevier b v

an energetic formulation of a gradient damage model for concrete and its numerical implementation abstract the energetic formulation of a rate independent system assumes that the evolution of the system is driven by two scalar valued functions the storage energy functional and the dissipation pseudo potential the evolution of the material system is then characterized by two energetic principles the global stability condition and the energy balance between stored and dissipated energies with the work of external loading rate independent generalized standard materials are endowed with such structure whereas the existence of such energetic structure is not so apparent in materials with non associated flow rule in this paper we consider a rate independent gradient damage model for concrete where the evolution of the damage does not follow the normality rule we will show that such model can be nevertheless derived by a dissipation potential at the expense of having a state variable dependent potential and therefore the energetic formulation can be obtained also in this case after introducing the incremental minimization problem consistent with such formulation we obtain a discrete version of the stability condition and establish lower and upper a priori energy bounds met by the energetic solution these are fundamental results for the analysis of the formulation the actual numerical solution of the incremental minimization problem is realized by considering first a variable splitting in order to treat the gradient of the damage field as an independent variable and then by applying the augmented lagrangian method to tackle with the resulting constrained optimization problem we solve the first order stationarity conditions of the augmented lagrangian functional by a path following newton s method based on the energy dissipation rate control we show that we are able to describe highly non linear responses of the material such as softening branches and snap back responses several numerical tests are performed to verify the objectivity of the formulation and of the proposed numerical method details of the numerical implementation are also given

the autocontinuity of set function and the fuzzy integral abstract the autocontinuity and some other concepts of a set function are introduced and sugeno s fuzzy measure with some annexed conditions is studied on a fuzzy measure space egoroffs theorem is proved it is also proved that f mean convergence is equivalent to convergence in measure for a sequence of measurable functions finally some convergence theorems of sequence of fuzzy integrals are proved especially using the concept of autocontinuity a necessary and sufficient condition for the convergence in measure theorem is given

a variational formulation of rate independent phase transformations using an extremum principle we propose a rate independent mesoscopic model for the hysteretic evolution of phase transformations in shape memory alloys the model uses the deformation and phase indicator function as basic unknowns and the potentials for the elastic energy and for the dissipation as constitutive laws using the associated functionals admissible processes are defined to be the ones which are stable at all times and which satisfy the energy inequality

on dynamic output feedback robust mpc for constrained quasi lpv systems this paper considers the dynamic output feedback robust model predictive control mpc of a quasi linear parameter varying quasi lpv system with bounded noise in our previous works for the unknown true state either its ellipsoidal bounds or its polyhedral bounds were solely applied in the main optimisation problem the recursive feasibility of the main optimisation problem was guaranteed by a simple refreshment of the ellipsoidal bound but might be lost by applying the polyhedral bounds this paper shows how and to what extent the recursive feasibility can be restored when the polyhedral bounds are still utilised first we propose a new approach which at each sampling time utilises either the ellipsoidal bound or the polyhedral bound in the main optimisation problem the latter being used if and only if it is contained in the former then we show the sufficient conditions under which the approaches based on polyhedral bounds preserve the property of recursive feasibility a numerical example is

toward a general theory of fuzzy variables abstract a general framework for a theory is presented that encompasses both statistical uncertainty which falls within the province of probability theory and nonstatistical uncertainty which relates to the concept of a fuzzy set and possibility theory l a zadeh j fuzzy sets 1 1978 3 28 the concept of a fuzzy integral is used to define the expected value of a random variable properties of the fuzzy expectation are stated and a mean value theorem for the fuzzy integral is proved comparisons between the fuzzy and the lebesgue integral are presented after a new concept of dependence is formulated various convergence concepts are defined and their relationships are studied by using a chebyshev like inequality for the fuzzy integral the possibility of using this theory in bayesian estimation with fuzzy prior information is explored

parameterized tube model predictive control this paper develops a parameterized tube model predictive control mpc synthesis method the most relevant novel feature of our proposal is the online use of a single tractable linear program that optimizes parameterized minkowski decomposable state and control tubes and an associated fully separable nonlinear control policy the induced control policy enjoys a higher degree of nonlinearity than existing tube mpc and robust mpc using disturbance affine control policy our proposal offers greater generality than the state of the art robust mpc methods it is conjectured and also established in three cases that our proposal is equivalent feasibility wise to dynamic programming dp it is also shown that under natural assumptions our method is computationally efficient while it possesses rather strong system theoretic properties

on the calculation of the acoustic eigenfrequencies for anisotropic materials with uncertainty abstract in this work a numerical method based on a boundary integral formulation is used to calculate approximately the acoustic eigenfrequencies or eigenvalues in a bounded domain filled with an anisotropic material we assume that the knowledge about the anisotropy is uncertain or incomplete and we use fuzzy numbers to model it using the zadeh s extension principle and affine transformations we get approximate fuzzy solutions to the posed problem finally some numerical examples are shown

quasistatic crack growth in nonlinear elasticity in this paper we prove a new existence result for a variational model of crack growth in brittle materials proposed in 19 we consider the case of n dimensional nonlinear elasticity for an arbitrary n 1 with a quasiconvex bulk energy and with prescribed boundary deformations and applied loads both depending on time

dynamic output feedback predictive control for nonlinear systems represented by a takagi sugeno model this paper addresses the output feedback predictive control for a takagi sugeno t s fuzzy system with bounded noise the controller optimizes an infinite horizon objective function respecting the input and state constraints the control law is parameterized as a dynamic output feedback that is dependent on the membership functions and the closed loop stability is specified by the notion of quadratic boundedness online algorithms that guarantee the recursive feasibility of the convex optimization problem and the convergence of the augmented state to a neighborhood of the equilibrium point are proposed in this paper a numerical example is given to illustrate the effectiveness of the proposed output feedback controllers

quasi static small strain plasticity in the limit of vanishing hardening and its numerical approximation the quasi static rate independent evolution of the prager ziegler type model of plasticity with hardening is shown to converge to the rate independent evolution of the prandtl reuss elastic perfectly plastic model based on the concept of energetic solutions we study the convergence of the solutions in the limit for hardening coefficients converging to 0 by using the abstract method of gamma convergence for rate independent systems an unconditionally convergent numerical scheme is devised and two and three dimensional numerical experiments are presented a two sided energy inequality is a posteriori verified to document experimental convergence rates

existence and convergence for quasi static evolution in brittle fracture this paper investigates the mathematical well posedness of the variational model of quasi static growth for a brittle crack proposed by francfort and marigo in 15 the starting point is a time discretized version of that evolution which results in a sequence of minimization problems of mumford and shah type functionals the natural weak setting is that of special functions of bounded variation and the main difficulty in showing existence of the time continuous quasi static growth is to pass to the limit as the time discretization step tends to 0 this is performed with the help of a jump transfer theorem which permits under weak convergence assumptions for a sequence un of sbv functions to its bv limit u to transfer the part of the jump set of any test field that lies in the jump set of u onto that of the converging sequence un in particular it is shown that the notion of minimizer of a mumford and shah type functional for its own jump set is stable under weak convergence assumptions furthermore our analysis justifies numerical methods used for computing the time continuous quasi static evolution 2003 wiley periodicals inc

output feedback model predictive control for lpv systems based on quasi min max algorithm this paper proposes a robust output feedback model predictive control mpc scheme for linear parameter varying lpv systems based on a quasi min max algorithm this approach involves an off line design of a robust state observer for lpv systems using linear matrix inequality lmi and an on line robust output feedback mpc algorithm using the estimated state the proposed mpc method for lpv systems is applicable for a variety of systems with constraints and guarantees the robust stability of the output feedback systems a numerical example for an lpv system subject to input constraints is given to demonstrate its effectiveness

transformation theorems for fuzzy integrals on fuzzy sets abstract in this paper sugeno s fuzzy integrals studied in 5 8 9 are generalized some equivalent definitions of fuzzy integrals on fuzzy sets are given and several transformation theorems of such type of fuzzy integrals are proved these results reveal the relations between the fuzzy integrals on fuzzy sets and on classical sets

dynamic output feedback predictive control of a takagi sugeno model with bounded disturbance this paper considers predictive control of a takagi sugeno fuzzy model with bounded disturbance strictly satisfying the input and state constraints the membership function dependent dynamic output feedback law as in a previous work is utilized the novelty lies in the following technical improvements for the notion of quadratic boundedness which specifies closed loop stability and invariance properties the full lyapunov matrix is utilized the real time ellipsoidal bound of true state is recursively optimized by invoking the s procedure some relaxation scalars being optimized by the norm bounding technique are introduced for better handling the input and state constraints the multistep approach where a sequence of dynamic output feedback laws are optimized at each sampling instant is given to improve the single step approach numerical examples are given to illustrate the effectiveness of the proposed controllers

ground states of simple bodies that may undergo brittle fractures abstract equilibrium states of elastic brittle solids that may suffer nucleation of cracks in finite deformation setting are analyzed crack patterns are described in terms of appropriate radon measures namely curvature varifolds with boundary a new form of the energy is presented it includes terms associated with the curvature of margins and tips of possible cracks existence of minima of the energy is established in classes of pairs of deformation and families of varifolds configurational balances in weak form are determined with reference to generic curvature varifolds with boundary they include non standard terms associated with the curvatures involved in the energy pointwise balances of configurational actions are also evaluated in a special case new pointwise balances at the tips and along the margins of the crack pattern emerge

robust constrained model predictive control using linear matrix inequalities abstract the primary disadvantage of current design techniques for model predictive control mpc is their inability to deal explicitly with plant model uncertainty in this paper we present a new approach for robust mpc synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation the uncertainty is expressed in both the time and frequency domains the goal is to design at each time step a state feedback control law that minimizes a worst case infinite horizon objective function subject to constraints on the control input and plant output using standard techniques the problem of minimizing an upper bound on the worst case objective function subject to input and output constraints is reduced to a convex optimization involving linear matrix inequalities lmis it is shown that the feasible receding horizon state feedback control design robustly stabilizes the set of uncertain plants several extensions such as application to systems with time delays problems involving constant set point tracking trajectory tracking and disturbance rejection which follow naturally from our formulation are discussed the controller design is illustrated with two examples

worst case formulations of model predictive control for systems with bounded parameters two different predictive control formulations are developed based on minimization of the worst case quadratic cost for systems with bounded parameters the two formulations differ on the assumptions made about the future inputs in optimizing the current input one assumes open loop control while the other considers closed loop control their closed loop properties such as asymptotic stability are examined we then focus on a moving average model with an integrator and derive computationally simpler suboptimal algorithms

a density result in two dimensional linearized elasticity and applications we show that in a two dimensional bounded open set whose complement has a finite number of connected components the vector fields u h 1 2 are dense in the space of fields whose symmetrized gradient e u is in l 2 4 this allows us to show the continuity of some linearized elasticity problems with respect to variations of the set with applications to shape optimization or the study of crack evolution

on the convergence of sequences of fuzzy measures and generalized convergence theorems of fuzzy integrals abstract in this paper we will investigate further fuzzy measures and fuzzy integrals given by sugeno 1974 our purpose is concentrated on the convergence of sequences of fuzzy measures or fuzzy integrals some concepts such as convergence uniform convergence convergence in integral weak convergence are introduced for the sequence of fuzzy measures then the properties and relations of them are discussed furthermore various kinds of convergence theorems of fuzzy integrals are extended these are generalized monotone convergence theorem generalized fatou s lemma etc

fuzzy number fuzzy measures and fuzzy integrals ii fuzzy integrals of fuzzy valued functions with respect to fuzzy number fuzzy measures on fuzzy sets this is a subsequent paper of 9 by using the concepts of fuzzy number fuzzy measures 9 and fuzzy valued functions 10 a theory of fuzzy integrals of fuzzy valued functions with respect to fuzzy number fuzzy measures is built up so far it is a more general one following sugeno s 5

maximally dissipative local solutions to rate independent systems and application to damage and delamination problems abstract the system of two inclusions u e t u t z t 0 and r z z e t u t z t 0 with the dissipation potential r degree 1 homogeneous and with the stored energy e t separately convex is considered the relation between conventional weak solutions and local solutions is shown and a suitably integrated maximal dissipation principle is devised to select force driven local solutions and eliminate solutions with too early jumps as it may occur in energy driven ones this is illustrated on scalar examples an approximation by a simple and efficient semi implicit time discretization of the fractional step type is shown to converge to local solutions on the scalar examples the approximate solutions are shown to satisfy the integrated maximal dissipation principle asymptotically while in general it is devised only to serve as an a posteriori tool to justify or possibly adaptively adjust thus obtained approximate solutions as in fact force driven applications of such solutions are illustrated on specific examples from continuum mechanics at small strains involving inelastic processes in a bulk or on a surface namely damage and delamination

the gilbert equation with dry friction type damping a modified gilbert equation for micromagnetics is considered obtained by augmenting the standard viscous like dissipation with a rate independent term we prove existence of a weak solution both with and without viscous dissipation by scaling time we show that if the applied field varies very slowly then gyromagnetic effects and viscous dissipation become negligible in the infinitesimally slow loading limit the system thus becomes fully rate independent

implicit improved vertex control for uncertain time varying linear discrete time systems with state and control constraints the problem of regulating an uncertain and or time varying linear discrete time system with state and control constraints to the origin is addressed it is shown that feasibility and a robustly asymptotically stable closed loop can be achieved using an interpolation technique the design method can be seen as an alternative to optimization based control schemes such as robust model predictive control especially for problems requiring complex calculations to find the optimal solution the present method can provide a straightforward suboptimal solution a simulation demonstrates the performance of this class of constrained controllers

crack growth in polyconvex materials we discuss a model for crack propagation in an elastic body where the crack path is described a priori in particular we develop in the framework of finite strain elasticity a rate independent model for crack evolution which is based on the griffith fracture criterion due to the nonuniqueness of minimizing deformations the energy release rate is no longer continuous with respect to time and the position of the crack tip thus the model is formulated in terms of the clarke differential of the energy generalizing the classical crack evolution models for elasticity with strictly convex energies we prove the existence of solutions for our model and also the existence of special solutions where only certain extremal points of the clarke differential are allowed

asymptotic structural characteristics of fuzzy measure and their applications abstract in fuzzy measure theory as sugeno s fuzzy measures lose additivity in general the concept almost which is well known in classical measure theory splits into two different concepts almost and pseudo almost in order to replace the additivity it is quite necessary to investigate some asymptotic behaviors of a fuzzy measure at sequences of sets which are called waxing and waning and to introduce some new concepts such as autocontinuity converse autocontinuity and pseudo autocontinuity these concepts describe some asymptotic structural characteristics of a fuzzy measure in this paper by means of the asymptotic structural characteristics of fuzzy measure we also give four forms of generalization for both egoroff s theorem riesz s theorem and lebesgue s theorem respectively and prove the almost everywhere pseudo almost everywhere convergence theorem the convergence in measure pseudo in measure theorem of the sequence of fuzzy integrals in the last two theorems the employed conditions are not only sufficient but also necessary

brief an improved approach for constrained robust model predictive control in this paper we present a new technique to address constrained robust model predictive control the main advantage of this new approach with respect to other well known techniques is the reduced conservativeness specifically the technique described in this paper can be applied to polytopic uncertain systems and is based on the use of several lyapunov functions each one corresponding to a different vertex of the uncertainty s polytope

a fast ellipsoidal mpc scheme for discrete time polytopic linear parameter varying systems this paper proposes a fast ellipsoidal model predictive control mpc strategy to address feedback regulation problems for constrained polytopic linear parameter varying lpv systems subject to bounded disturbances in order to deal with the specific non convex structure of the state prediction tubes arising in lpv contexts a new convexification procedure is proposed and based on the off line computation of a sequence of inner ellipsoidal approximations of exact one step controllable sets a computationally low demanding mpc algorithm is presented comparisons with state of the art mpc control algorithms for lpv systems are reported in a final numerical example where several methods are contrasted in terms of achievable domains of attraction control performance numerical burdens and memory requirements

a variational view of partial brittle damage evolution under time dependent loading an elastic material undergoes the simplest form of damage in which it passes from its original state to a weaker elastic state elaborating on prior work 14 we establish the existence of a relaxed variational evolution where at each time the two states of the material combine to form a fine mixture optimal from the standpoint of the applied load at that time yet preserving the irreversibility of the damaging process

technical communique design of state estimators for uncertain linear systems using quadratic boundedness the notion of quadratic boundedness which allows one to address the stability of a dynamic system in the presence of bounded disturbances is applied to the design of state estimators for discrete time linear systems with polytopic uncertainties necessary and sufficient stability conditions are stated and upper bounding sequences on the estimation error are derived for the purpose of design such conditions can be expressed in terms of linear matrix inequalities lmis thus guaranteeing the numerical tractability simulation results are reported to show the effectiveness of the approach

threshold based quasi static brittle damage evolution we introduce models for static and quasi static damage in elastic materials based on a strain threshold and then investigate the relationship between these threshold models and the energy based models introduced in francfort and marigo eur j mech a solids 12 149 189 1993 and francfort and garroni ration mech anal 182 1 125 152 2006 a somewhat surprising result is that while classical solutions for the energy models are also threshold solutions this is shown not to be the case for nonclassical solutions that is solutions with microstructure a new and arguably more physical definition of solutions with microstructure for the energy based model is then given in which the energy minimality property is satisfied by sequences of sets that generate the effective elastic tensors rather than by the tensors themselves we prove existence for this energy based problem and show that these solutions are also threshold solutions a by product of this analysis is that all local minimizers in both the classical setting and for the new microstructure definition are also global minimizers

stability results for doubly nonlinear differential inclusions by variational convergence we present a stability result for a wide class of doubly nonlinear equations featuring general maximal monotone operators and possibly nonconvex and nonsmooth energy functionals the limit analysis consists in the reformulation of the differential evolution as a scalar energy conservation equation with the aid of the so called fitzpatrick theory for the representation of monotone operators in particular our result applies to the vanishing viscosity approximation of rate independent systems

brief an efficient off line formulation of robust model predictive control using linear matrix inequalities the practicality of model predictive control mpc is partially limited by its ability to solve optimization problems in real time moreover on line computational demand for synthesizing a robust mpc algorithm will likely grow significantly with the problem size in this paper we use the concept of an asymptotically stable invariant ellipsoid to develop a robust constrained mpc algorithm which gives a sequence of explicit control laws corresponding to a sequence of asymptotically stable invariant ellipsoids constructed off line one within another in state space this off line approach can address a broad class of model uncertainty descriptions with guaranteed robust stability of the closed loop system and substantial reduction of the on line mpc computation the controller design is illustrated with two examples

approximation of rate independent optimal control problems this work introduces an abstract approximation scheme for optimal control problems in the energetic theory of rate independent systems this scheme builds upon the usual temporal semidiscretization and a gamma convergence approximation of the functionals in a full discretization this approximation consists of a sequence of discrete functionals defined on finer and finer discrete spaces the main new result of this work is a rigorous convergence analysis for this scheme interestingly it turns out that the usual time discretization is incomplete as a basis for a fully discrete approximation of the optimal control problem and a new nonlocal condition has to be introduced since this new condition is necessary and sufficient for a one to one correspondence of discrete time and continuous time solutions to rate independent systems we also gain a new theoretical insight which might be of independent interest at the heart of the derivation are so called reverse approximation results for which we provide extensions and refinements to give a concrete example and to demonstrate how the abstract theory can be applied in a concrete problem we present a full discretization with finite elements of the optimal control problem for a rate independent partial differential inclusion

receding horizon control strategies for constrained lpv systems based on a class of nonlinearly parameterized lyapunov functions in this technical note we present a receding horizon control rhc design method for linear parameter varying lpv systems subject to input and or state constraints based on a class of nonlinearly parameterized lyapunov functions recently introduced by guerra and vermeiren as it will be made clear their use gives rise to less conservative stabilizability conditions w r t those arising from quadratic lyapunov functions a workable convex optimization procedure is first presented for control design purposes which allows the synthesis of stabilizing scheduling state feedback control laws complying with the prescribed constraints this control design method is then arranged into a receding horizon framework and its feasibility and stability properties are carefully analyzed numerical comparisons with existing rhc methods for lpv systems are reported in the final example

deriving new evolution equations for microstructures via relaxation of variational incremental problems we study material models for rate independent inelasticity in situations where no internal length scale is given and formation of microstructure for the deformation gradients and the internal variables may occur we develop a rational procedure for deriving consistent macroscopic models which allow for the computation of nontrivial effective quantities without resolving the fine scales the method involves the relaxation of variational incremental problems which are derived from an elastic and a plastic potential we use young measures to describe the microscopic distribution of the internal variables as well as the quasiconvexification of the elastic stored energy density with respect to the deformation gradient the resulting model provides a new rate independent model in terms of the deformation and the young measure the approach is based on a derivative free energetic formulation using one functional for elastic energy storage and one for the dissipation distance the latter is derived from a dissipation potential defining the dissipation distance between internal states and hence the wasserstein distance between young measures this approach is strongly linked to an associated time incremental problem which is a minimization problem of the type used for several years now in the engineering literature the update algorithm for the incremental problem is discussed in detail and two simple examples are given

fuzzy integrals of fuzzy valued functions abstract this paper based on the fuzzy measures and integrals given by sugeno first defines fuzzy integrals of set valued functions and then the fuzzy integral of fuzzy valued functions is obtained and discussed next it defines the fuzzy integrals of fuzzy mappings then pays much effort to the fuzzy integral of interval valued functions the properties and convergence theorems are obtained all these are generalizations of earlier results

global higher integrability of minimizers of variational problems with mixed boundary conditions abstract we consider integral functionals with densities of p growth with respect to gradients on a lipschitz domain with mixed boundary conditions the aim of this paper is to prove that under uniform estimates within certain classes of p growth and coercivity assumptions on the density the minimizers are of higher integrability order meaning that they belong to the space of first order sobolev functions with an integrability of order p for a uniform 0 the results are applied to a model describing damage evolution in a nonlinear elastic body and to a model for shape memory alloys

asymptotically necessary and sufficient conditions for stability and performance in fuzzy control applications of polya s theorem stability and performance requirements in fuzzy control of takagi sugeno systems are usually stated as fuzzy summations i e sums of terms related to lyapunov functions which are weighted by membership functions or products of them this paper presents an application to fuzzy control of polya s theorems on positive forms on the standard simplex the result provides a set of progressively less conservative sufficient conditions for proving positivity of fuzzy summations such conditions are less and less conservative as a complexity parameter n increases particular cases of such conditions are those in c h fang y s liu s w kau l hong c h lee a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems ieee trans fuzzy systems 14 2006 286 397 x liu q zhang new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 9 2003 1571 1582 with n 2 and 3 respectively the proposed conditions are asymptotically exact i e necessary and sufficient when n tends to infinity or equivalently when a tolerance parameter tends to zero

non convex potentials and microstructures in finite strain plasticity a mathematical model for a finite strain elastoplastic evolution problem is proposed in which one time step of an implicit time discretization leads to generally non convex minimization problems the elimination of all internal variables enables a mathematical and numerical analysis of a reduced problem within the general framework of calculus of variations and nonlinear partial differential equations the results for a single slip system and von mises plasticity illustrate that finite strain elastoplasticity generates reduced problems with non quasiconvex energy densities and so allows for non attainment of energy minimizers and microstructures

quasi min max mpc algorithms for lpv systems in this paper a new model predictive controller mpc is developed for polytopic linear parameter varying lpv systems we adopt the paradigm used in gain scheduling and assume that the time varying parameters are measured on line but their future behavior is uncertain and contained in a given polytope at each sampling time optimal control action is computed by minimizing the upper bound on the quasi worst case value of an infinite horizon quadratic objective function subject to constraints on inputs and outputs the mpc algorithm is called quasi because the first stage cost can be computed without any uncertainty this allows the inclusion of the first move u k k separately from the rest of the control moves governed by a feedback law and is shown to reduce conservatism and improve feasibility characteristics with respect to input and output constraints proposed optimization problems are solved by semi definite programming involving linear matrix inequalities it is shown that closed loop stability is guaranteed by the feasibility of the linear matrix inequalities a numerical example demonstrates the unique features of the mpc design

on fuzzy measures defined by fuzzy integrals on definit une mesure floue comme une fonction ensemble sur 7b f qui est une algebre de sous ensembles de l ensemble x

damage gradient of damage and principle of virtual power a theory of continuum damage mechanics is developed within the framework of the principle of virtual power because the damage in a solid results from microscopic movements we decided to include the power of these microscopic movements in the power of the internal forces the microscopic velocities are related to the damage rate the power of the internal forces we choose depends on the damage velocity and its gradient to take into account the interactions models issued from this theory are presented they are coherent from the mechanical and mathematical points of view the numerical computations show no mesh sensitivity they describe with good agreement the main experimental properties concrete is chosen as an example to illustrate the theory a model using two damage quantities is also presented it yields the correct description of the unilateral phenomenon observed in concrete finally an extension of the existing models is proposed to describe the fatigue damage behaviour

global existence results for viscoplasticity at finite strain we study a model for rate dependent gradient plasticity at finite strain based on the multiplicative decomposition of the strain tensor and investigate the existence of global in time solutions to the related pde system we reveal its underlying structure as a generalized gradient system where the driving energy functional is highly nonconvex and features the geometric nonlinearities related to finite strain elasticity as well as the multiplicative decomposition of finite strain plasticity moreover the dissipation potential depends on the left invariant plastic rate and thus depends on the plastic state variable the existence theory is developed for a class of abstract nonsmooth and nonconvex gradient systems for which we introduce suitable notions of solutions namely energy dissipation balance and energy dissipation inequality solutions hence we resort to the toolbox of the direct method of the calculus of variations to check that the specific energy and dissipation functionals for our viscoplastic models comply with the conditions of the general theory

output feedback robust mpc for lpv system with polytopic model parametric uncertainty and bounded disturbance abstractthe output feedback robust model predictive control mpc for the linear parameter varying lpv system with norm bounded disturbance is addressed where the model parametric matrices are only known to be bounded within a polytope the previous techniques of norm bounding technique quadratic boundedness qb dynamic output feedback and ellipsoid true state bound tsb refreshment formula for guaranteeing recursive feasibility are fused into the newly proposed approaches in the notion of qb the full lyapunov matrix is applied for the first time in this context the single step dynamic output feedback robust mpc where the infinite horizon control moves are parameterised as a dynamic output feedback law is the main topic of this paper while the multi step method is also suggested in order to strictly guarantee the physical constraints the outer bound of the true state replaces the true state itself so tightness of this bound has a major effect on the control performance in order to ti

a model for the quasi static growth of brittle fractures existence and approximation results we give a precise mathematical formulation of a variational model for the irreversible quasi static evolution of brittle fractures proposed by g a francfort and j j marigo and based on griffith s theory of crack growth in the two dimensional case we prove an existence result for the quasi static evolution and show that the total energy is an absolutely continuous function of time although we cannot exclude the possibility that the bulk energy and the surface energy may present some jump discontinuities this existence result is proved by a time discretization process where at each step a global energy minimization is performed with the constraint that the new crack contains all cracks formed at the previous time steps this procedure provides an effective way to approximate the continuous time evolution

gradient damage models toward full scale computations abstract the description of localisation and structural failure through local damage constitutive laws leads to ill posed problems to retrieve a well posed problem the material state is described through the gradients of damage in addition to the strain and the damage under some assumptions it is shown that these gradient laws can be cast into a variational formulation its numerical treatment is reduced to the design of a mixed finite element so that algorithms such as newton s method and path following techniques are still available possible convergence difficulties related to the reduction of the damage band width and the appearance of micro instabilities are removed thanks to the design of a new class of brittle laws finally numerical applications show the convergence with mesh refinement the compatibility with coarser approaches such as griffith s theory and cohesive crack models the robustness in case of unstable multi cracking the applicability to full scale 3d situations and the physical relevance compared to experimental data

numerical simulation of ductile fracture with the rousselier constitutive law this contribution aims at developing robust and reliable tools dedicated to predictive numerical simulation of ductile fracture description of damage mechanisms relies here on the rousselier constitutive law to achieve robustness and objectivity several points need then to be addressed reduction of the set of internal variables so as to recast the model into the framework of generalised standard materials proper expression of the normal plastic flow rule at the vertex of the yield surface finite strain formulation based on a multiplicative split of the deformation gradient fully implicit integration of the constitutive equations leading to a single scalar equation that admits a unique root use of mixed finite elements to avoid volumetric locking strain gradient based nonlocal model to control strain localisation and remedy spurious mesh dependency the capabilities of the resulting numerical formulation are demonstrated through simulating the cup cone fracture of a notched tensile specimen

fuzzy integrals on l fuzzy sets abstract the fuzzy measures and fuzzy integrals for zadeh s fuzzy sets were studied by qiao and wang 5 6 7 12 in this paper we consider the real valued fuzzy measures and fuzzy integrals for l fuzzy sets where l is a pseudocomplemented infinitely distributive complete lattice on a fuzzy algebra of l fuzzy sets the concepts of fuzzy measure and fuzzy integral are introduced some equivalent forms of fuzzy integrals on l fuzzy sets are given moreover we discuss several properties of fuzzy integrals on l fuzzy sets and prove some convergence theorems for a sequence of fuzzy integrals on l fuzzy sets

robust control of constrained linear systems with bounded disturbances this technical note develops a novel robust control algorithm for linear systems subject to additive and bounded disturbances the approach is based on the constraint tightening method while this problem can be tackled using existing robust model predictive control techniques the proposed method has an advantage in that it is computationally efficient and avoids the need to solve repeatedly an online optimization problem while the optimization problem solved at initialization is a simple linear programming problem the algorithm elaborated in this technical note guarantees convergence to a minimal disturbance invariant set and the terminal predicted state constraint set is allowed to be larger than the minimal disturbance invariant set as an illustration the developed algorithm is applied to constrained roll control of a ship operating in a wave field simulation results show that the proposed approach reduces the ship roll motion while the input and dynamic stall constraints are satisfied

homogeneous polynomially nonquadratic stabilization of discrete time takagi sugeno systems via nonparallel distributed compensation law this paper considers stability of discrete time nonlinear systems in takagi sugeno t s form this problem has been studied for more than 20 years with many sufficient conditions and the asymptotically necessary and sufficient ans conditions with respect to the common quadratic lyapunov function having being obtained this paper considers general forms of homogeneous polynomially nonquadratic lyapunov hpnql function and homogeneous polynomially parameterized nonparallel distributed compensation hpp non pdc law by generalization of the procedure based on polya s theorem and techniques used for parameter dependent linear matrix inequality pd lmi which have been studied previously in different contexts ans stability conditions with respect to the general hpnql function are obtained

technical communique min max predictive control strategies for input saturated polytopic uncertain systems a novel robust predictive controller for input saturated ltv discrete time systems with polytopic model uncertainties is presented the solution is based on the minimization at each time instant of an upper bound of the worst case infinite horizon quadratic cost under the constraint of steering the set valued future state evolutions emanating from the current state into a feasible and positive invariant set a condition on the initial state is given that suffices to ensure problem solvability for all subsequent time instants under the latter the proposed predictive controller is proved to robustly asymptotically stabilize the input saturated ltv polytopic system

fuzzy number fuzzy measures and fuzzy integrals i fuzzy integrals of functions with respect to fuzzy number fuzzy measures this paper based on the fuzzy measures and fuzzy integrals given by sugeno first defines interval number fuzzy measures inf measures and fuzzy number fuzzy measures fnf measures and the fuzzy integral of function with respect to inf measures are given then it defines the fuzzy integral of functions with respect to fnf measures and the properties and convergence theorems are obtained all these are generalizations of sugeno s works

homothetic tube model predictive control the robust model predictive control for constrained linear discrete time systems is solved through the development of a homothetic tube model predictive control synthesis method the method employs several novel features including a more general parameterization of the state and control tubes based on homothety and invariance a more flexible form of the terminal constraint set and a relaxation of the controlled dynamics of the sets that define the state and control tubes under natural assumptions the proposed method is computationally efficient and it induces strong system theoretic properties

transformation theorems of abstract integrals on fuzzy sets abstract the concept of abstract integrals on fuzzy sets is introduced and some elementary properties for such type of integrals are given this paper also proves some transformation theorems for abstract integrals on fuzzy sets and presents some convergence theorems of a sequence of abstract integrals

robust distributed model predictive control of linear systems with structured time varying uncertainties abstractin this work synthesis of robust distributed model predictive control mpc is presented for a class of linear systems subject to structured time varying uncertainties by decomposing a global system into smaller dimensional subsystems a set of distributed mpc controllers instead of a centralised controller are designed to ensure the robust stability of the closed loop system with respect to model uncertainties distributed state feedback laws are obtained by solving a min max optimisation problem the design of robust distributed mpc is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints an iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance the simulation results show the effectiveness of the proposed robust distributed mpc algorithm

the explicit constrained min max model predictive control of a discrete time linear system with uncertain disturbances in this technical brief we develop an algorithm to determine the explicit solution of the constrained min max model predictive control problem for a discrete time linear system with bounded additive uncertain disturbance the control law is determined to be piecewise affine from a quadratic cost function and the state space is partitioned into corresponding polyhedral cones by moving the on line implementation to an off line explicit evaluation the computational burden is decreased and the applicability of min max optimization is broadened the results of this approach are shown via computer simulations