isometric dilations for infinite sequences of noncommuting operators this paper develops a dilation theory for t n l an infinite sequence of noncommuting operators on a hilbert space when the matrix t1 t2 is a contraction a wold decomposition for an infinite sequence of isometries with orthogonal final spaces and a minimal isometric dilation for tn i are obtained some theorems on the geometric structure of the space of the minimal isometric dilation and some consequences are given this results are used to extend the sz nagy foia lifting theorem to this noncommutative setting this paper is a continuation of 5 and develops a dilation theory for an infinite sequence tn n of noncommuting operators on a hilbert space when en 1 tn tn i i is the identity on s many of the results and techniques in dilation theory for one operator 8 and also for two operators 3 4 are extended to this setting first we extend wold decomposition 8 4 to the case of an infinite sequence vn i of isometries with orthogonal final spaces in 2 we obtain a minimal isometric dilation for tn 1 by extending the schaffer construction in 6 4 using these results we give some theorems on the geometric structure of the space of the minimal isometric dilation finally we give some sufficient conditions on a sequence t7 n to be simultaneously quasi similar to a sequence rn n i of isometries on a hilbert space x with en rnrn n ix in 3 we use the above mentioned theorems to obtain the sz nagy foia5 lifting theorem 7 8 1 4 in our setting in a subsequent paper we will use the results of this paper for studying the characteristic function associated to a sequence tn lo 1 with ez 1 t t i throughout this paper a stands for the set 1 2 k k e n or the set n 1 2 received by the editors september 1 1987 1980 mathematics subject classification 1985 revision primary 47a20 secondary 47a45

models for n tuples of noncommuting operators abstract this paper proves versions of the rota model theorem the de branges rovnyak model theorem and the coisometric extension theorem for n tuples of not necessarily commuting operators this generalizes the work of a e frazho j funct anal 48 1982 1 11 for pairs of operators the methods involve applying the single operator results to matrices of operators

invariant subspaces and hyper reflexivity for free semigroup algebras in this paper we obtain a complete description of the invariant subspace structure of an interesting new class of algebras which we call free semigroup algebras this enables us to prove that they are reflexive and moreover to obtain a quantitative measure of the distance to these algebras in terms of the invariant subspaces such algebras are called hyper reflexive this property is very strong but it has been established in only a very few cases moreover the prototypes of this class of algebras are the natural candidate for a non commutative analytic toeplitz algebra on n variables the case we make for this analogy is very compelling in particular in this paper the key to the invariant subspace analysis is a good analogue of the beurling theorem for invariant subspaces of the unilateral shift this leads to a notion of inner outer factorization in these algebras in a sequel to this paper 13 we add to this evidence by showing that there is a natural homomorphism of the automorphism group onto the group of conformal automorphisms of the ball in cn a free semigroup algebra is the weak operator topology closed algebra generated by a set s1 sn of isometries with pairwise orthogonal ranges these conditions are described algebraically by s i sj iji for 1 i j n f

on the interpretation and identification of dynamic takagi sugeno fuzzy models dynamic takagi sugeno fuzzy models are not always easy to interpret in particular when they are identified from experimental data it is shown that there exists a close relationship between dynamic takagi sugeno fuzzy models and dynamic linearization when using affine local model structures which suggests that a solution to the multiobjective identification problem exists however it is also shown that the affine local model structure is a highly sensitive parametrization when applied in transient operating regimes due to the multiobjective nature of the identification problem studied here special considerations must be made during model structure selection experiment design and identification in order to meet both objectives some guidelines for experiment design are suggested and some robust nonlinear identification algorithms are studied these include constrained and regularized identification and locally weighted identification their usefulness in the present context is illustrated by examples

operator algebras for analytic varieties we study the isomorphism problem for the multiplier algebras of irreducible complete pick kernels these are precisely the restrictionsmv of the multiplier algebram of drury arveson space to a holomorphic subvariety v of the unit ball bd we nd that mv is completely isometrically isomorphic tomw if and only if w is the image of v under a biholomorphic auto morphism of the ball in this case the isomorphism is unitarily implemented this is then strengthend to show that when d 1 every isometric isomorphism is completely isometric the problem of characterizing when two such algebras are al gebraically isomorphic is also studied when v and w are each a nite union of irreducible varieties and a discrete variety in bd with d 1 then an isomorphism betweenmv andmw deter mines a biholomorphism with multiplier coordinates between the varieties and the isomorphism is composition with this function these maps are automatically weak continuous we present a number of examples showing that the converse fails in several ways we discuss several special cases in which the converse does hold particularly smooth curves and blaschke sequences

noncommutative hyperbolic geometry on the unit ball of b h n in this paper we introduce a hyperbolic poincare bergman type distance on the noncommutative open ball b h n 1 x1 xn b h n x1x1 xnxn 1 2 1 where b h is the algebra of all bounded linear operators on a hilbert space h it is proved that is invariant under the action of the free holomorphic automorphism group of b h n 1 i e x y x y x y b h n 1 for all aut b h n 1 moreover we show that the topology and the usual operator norm topology coincide on b h n 1 while the open ball b h n 1 is not a complete metric space with respect to the operator norm topology we prove that b h n 1 is a complete metric space with respect to the hyperbolic metric we obtain an explicit formula for in terms of the reconstruction operator rx x1 r1 xn rn x x1 xn b h n 1 associated with the right creation operators r1 rn on the full fock space with n generators in the particular case when h c we show that the hyperbolic distance coincides with the poincare bergman distance on the open unit ball bn z z1 zn cn z 2 1 we obtain a schwarz pick lemma for free holomorphic functions on b h n 1 with respect to the hyperbolic metric i e if f f1 fm is a contractive f 1 free holomorphic function then f x f y x y x y b h n 1 as consequences we show that the caratheodory and the kobayashi distances with respect to coincide with on b h n 1 the results of this paper are presented in the more general context of harnack parts of the closed ball b h n 1 which are noncommutative analogues of the gleason parts of the gelfand spectrum of a function algebra

fuzzy gain scheduling controller and observer design based on lyapunov method and convex optimization addresses model based fuzzy control a constructive and automated method for the design of a gain scheduling controller is presented based on a given takagi sugeno fuzzy model of the plant the controller is designed such that stability and prescribed performance of the closed loop are guaranteed these properties are valid in a wide working range around an equilibrium without restrictions to slowly varying trajectories the synthesis is based on linear matrix inequalities and convex optimization techniques if required a fuzzy state estimator and an extended controller can be included providing a zero steady state error in the presence of disturbances and modeling errors the proposed method has been applied to a control of a laboratory liquid level process hence the performance has been evaluated in simulations as well as in real time control

pointwise boundary differentiability for the infinity laplace equations abstract in this paper we study the boundary differentiability for infinity harmonic functions at some general corner points we prove the slope estimate and provide a necessary and sufficient condition of the boundary differentiability for infinity harmonic function at less than corner points or greater than corner points as defined in the introduction the boundary differentiable conclusions of the homogeneous infinity laplace equations also apply to the inhomogeneous case

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

the algebraic structure of non commutative analytic toeplitz algebras the non commutative analytic toeplitz algebra is the wot closed algebra generated by the left regular representation of the free semigroup on n generators we develop a detailed picture of the algebraic structure of this algebra in particular we show that there is a canonical homomorphism of the automorphism group onto the group of conformal automorphisms of the complex n ball the k dimensional representations form a generalized maximal ideal space with a canonical surjection onto the ball of k kn matrices which is a homeomorphism over the open ball analogous to the fibration of the maximal ideal space of h over the unit disk in 6 17 18 20 a good case is made that the appropriate analogue for the analytic toeplitz algebra in n non commuting variables is the wotclosed algebra generated by the left regular representation of the free semigroup on n generators the papers cited obtain a compelling analogue of beurling s theorem and inner outer factorization in this paper we add further evidence the main result is a short exact sequence determined by a canonical homomorphism of the automorphism group onto this algebra onto the group of conformal automorphisms of the unit ball of cn the kernel is the subgroup of quasi inner automorphisms which are trivial modulo the wot closed commutator ideal additional evidence of analytic properties comes from the structure of k dimensional completely contractive representations which have a structure very similar to the fibration of the maximal ideal space of h over the unit disk an important tool in our analysis is a detailed structure theory for wot closed right ideals curiously left ideals remain more obscure the non commutative analytic toeplitz algebra ln is determined by the left regular representation of the free semigroup fn on n generators z1 zn which acts on 2 fn by w v wv for v w in fn in particular the algebra ln is the unital wot closed algebra generated by the isometries li zi for 1 i n this algebra and its norm closed version the noncommutative disk algebra were introduced by popescu 19 in an abstract sense in connection with a non commutative von neumann inequality and 1991 mathematics subject classification 47d25 march 9 1997 october 9 1997 final draft first author partially supported by an nserc grant and a killam research fellowship second author partially supported by an nsf grant

free holomorphic functions on the unit ball of b h n abstract in this paper we continue the study of free holomorphic functions on the noncommutative ball b h n 1 x 1 x n b h n x 1 x 1 x n x n 1 2 1 where b h is the algebra of all bounded linear operators on a hilbert space h and n 1 2 or n several classical results from complex analysis have free analogues in our noncommutative setting we prove a maximum principle a naimark type representation theorem and a vitali convergence theorem for free holomorphic functions with operator valued coefficients we introduce the class of free holomorphic functions with the radial infimum property and study it in connection with factorizations and noncommutative generalizations of some classical inequalities obtained by schwarz and harnack the borel caratheodory theorem is extended to our noncommutative setting using a noncommutative generalization of schwarz s lemma and basic facts concerning the free holomorphic automorphisms of the noncommutative ball b h n 1 we obtain an analogue of julia s lemma for free holomorphic functions f b h n 1 b h m 1 we also obtain pick julia theorems for free holomorphic functions with operator valued coefficients we provide a noncommutative generalization of a classical inequality due to lindelof which turns out to be sharper then the noncommutative von neumann inequality finally we introduce a pseudohyperbolic metric on b h n 1 which is invariant under the action of the free holomorphic automorphism group of b h n 1 and turns out to be a noncommutative extension of the pseudohyperbolic distance on b n the open unit ball of c n in this setting we obtain a schwarz pick type lemma we also provide commutative versions of these results for operator valued multipliers of the drury arveson space

stabilizing controller design for uncertain nonlinear systems using fuzzy models a lyapunov based stabilizing control design method for uncertain nonlinear dynamical systems using fuzzy models is proposed the controller is constructed using a design model of the dynamical process to be controlled the design model is obtained from the truth model using a fuzzy modeling approach the truth model represents a detailed description of the process dynamics the truth model is used in a simulation experiment to evaluate the performance of the controller design a method for generating local models that constitute the design model is proposed sufficient conditions for stability and stabilizability of fuzzy models using fuzzy state feedback controllers are given the results obtained are illustrated with a numerical example involving a four dimensional nonlinear model of a stick balancer

boundary differentiability of infinity harmonic functions abstract we prove that an infinity harmonic function u x c is differentiable at a boundary point x 0 if both and the boundary data g x are differentiable at x 0 this work improved a former result of changyou wang and yifeng yu 2012 10 they obtained the boundary differentiability of u x with the c 1 assumption on and g x

on fixed points of self maps of the free ball abstract in this paper we study the structure of the fixed point sets of noncommutative self maps of the free ball we show that for such a map that fixes the origin the fixed point set on every level is the intersection of the ball with a linear subspace we provide an application for the completely isometric isomorphism problem of multiplier algebras of noncommutative complete pick spaces

elliptic equations on convex domains with nonhomogeneous dirichlet boundary conditions abstract in this paper we will study the differentiability on the boundary of solutions of elliptic non divergence differential equations on convex domains the results are divided into two cases i at the boundary points where the blow up of the domain is not the half space if the boundary function is differentiable then the solution is differentiable ii at the boundary points where the blow up of the domain is the half space the differentiability of the solution needs an extra dini condition for the boundary function counterexample is given to show that our results are optimal

c1 regularity for infinity harmonic functions in two dimensions a continuous function open image in new window is said to be infinity harmonic if it satisfies the pde

slope estimate and boundary differentiability for inhomogeneous infinity laplace equation on convex domains abstract we study the boundary differentiability for inhomogeneous infinity laplace equations on convex domains with the inhomogeneous term f c l and differentiable boundary data g at a flat point the boundary point where the blow up of the domain is the half space u is differentiable due to a previous result of the second author in hong 2014 at a corner point the boundary point where the blow up of the domain is not the half space we establish a slope estimate for u and provide a necessary and sufficient condition for the boundary differentiability of u in this paper

the isomorphism problem for some universal operator algebras abstract this paper addresses the isomorphism problem for the universal non self adjoint operator algebras generated by a row contraction subject to homogeneous polynomial relations we find that two such algebras are isometrically isomorphic if and only if the defining polynomial relations are the same up to a unitary change of variables and that this happens if and only if the associated subproduct systems are isomorphic the proof makes use of the complex analytic structure of the character space together with some recent results on subproduct systems restricting attention to commutative operator algebras defined by a radical ideal of relations yields strong resemblances with classical algebraic geometry these commutative operator algebras turn out to be algebras of analytic functions on algebraic varieties we prove a projective nullstellensatz connecting closed ideals and their zero sets under some technical assumptions we find that two such algebras are isomorphic as algebras if and only if they are similar and we obtain a clear geometrical picture of when this happens this result is obtained with tools from algebraic geometry reproducing kernel hilbert spaces and some new complex geometric rigidity results of independent interest the c envelopes of these algebras are also determined the banach algebraic and the algebraic classification results are shown to hold for the wot closures of these algebras as well

h sub spl infin controller synthesis of fuzzy dynamic systems based on piecewise lyapunov functions and bilinear matrix inequalities this work presents an h sub spl infin controller design method for fuzzy dynamic systems based on techniques of piecewise smooth lyapunov functions and bilinear matrix inequalities it is shown that a piecewise continuous lyapunov function can be used to establish the global stability with h sub spl infin performance of the resulting closed loop fuzzy control systems and the control laws can be obtained by solving a set of bilinear matrix inequalities bmis two examples are given to illustrate the application of the proposed methods

models for noncommuting operators abstract this paper develops a model theory for a pair of noncommuting operators using backward shift operators on a fock space rota s theorem is generalized i e it is shown that any two bounded operators on a hilbert space are simultaneously similar to part of a pair of backward shift operators on a fock space these shift operators and the fock space framework are also used to develop a dilation theory for two noncommuting operators

pick interpolation for free holomorphic functions we give necessary and sufficient conditions to solve an interpolation problem for free holomorphic functions bounded in norm on a free polynomial polyhedron as an application we prove that every bounded holomorphic function on a polynomial polyhedron extends to a bounded free function

delay dependent guaranteed cost control for t s fuzzy systems with time delays this study introduces a guaranteed cost control method for nonlinear systems with time delays which can be represented by takagi sugeno t s fuzzy models with time delays the state feedback and generalized dynamic output feedback approaches are considered the generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base it considers both the dynamic part and the output part of t s fuzzy model which guarantees that the controller without any delay information can stabilize time delay t s fuzzy systems based on delay dependent lyapunov functional approach some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation pdc first second the corresponding conditions are extended into the generalized dynamic output feedback closed loop system via so called generalized pdc technique the upper bound of time delay can be obtained using convex optimization such that the system can be stabilized for all time delays whose sizes are not larger than the bound the minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function the effectiveness of the proposed method can be shown by the simulation examples

effective optimization for fuzzy model predictive control this paper addresses the optimization in fuzzy model predictive control when the prediction model is a nonlinear fuzzy model nonconvex time consuming optimization is necessary with no guarantee of finding an optimal solution a possible way around this problem is to linearize the fuzzy model at the current operating point and use linear predictive control i e quadratic programming for long range predictive control however the influence of the linearization error may significantly deteriorate the performance in our approach this is remedied by linearizing the fuzzy model along the predicted input and output trajectories one can further improve the model prediction by iteratively applying the optimized control sequence to the fuzzy model and linearizing along the so obtained simulated trajectories four different methods for the construction of the optimization problem are proposed making difference between the cases when a single linear model or a set of linear models are used by choosing an appropriate method the user can achieve a desired tradeoff between the control performance and the computational load the proposed techniques have been tested and evaluated using two simulated industrial benchmarks ph control in a continuous stirred tank reactor and a high purity distillation column

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

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

fuzzy model based predictive control by instantaneous linearization a linearization technique for product sum crisp type fuzzy model and a multistep predictive control strategy for the construction of a model based predictive fuzzy controller is presented in this paper a model based predictive controller is based on a local linear model generated by using the proposed linearization technique that linearizes the product sum crisp type fuzzy process model around the current operating point the control of ph in a continuous stirred tank reactor is chosen as a realistic nonlinear case study for the demonstration of the proposed control algorithm the controller is shown to be capable of controlling the nonlinear processes that operate over a wide range and of providing better overall system performance than the optimal pi controller

topological isomorphisms for some universal operator algebras abstract let i c z 1 z d be a radical homogeneous ideal and let a i be the norm closed non selfadjoint algebra generated by the compressions of the d shift on drury arveson space h d 2 to the co invariant subspace h d 2 i then a i is the universal operator algebra for commuting row contractions subject to the relations in i we ask under which conditions are there topological isomorphisms between two such algebras a i and a j we provide a positive answer to a conjecture of davidson ramsey and shalit a i and a j are topologically isomorphic if and only if there is an invertible linear map a on c d which maps the vanishing locus of j isometrically onto the vanishing locus of i most of the proof is devoted to showing that finite algebraic sums of full fock spaces over subspaces of c d are closed this allows us to show that the map a induces a completely bounded isomorphism between a i and a j

slope estimate and boundary differentiability of infinity harmonic functions on convex domains abstract we study the boundary differentiability of infinity harmonic functions with given differentiable boundary data on convex domains at a flat point the boundary point where the blow up of the domain is the half space the infinity harmonic function u is differentiable due to a previous result of the first author in hong 2013 at a corner point the boundary point where the blow up of the domain is not the half space an example shows that u is not necessarily differentiable in this paper we establish a slope estimate for u at corner points and provide a necessary and sufficient condition for the differentiability of u at corner points

counterexample to c1 boundary regularity of infinity harmonic functions abstract in this short note we construct a planar infinity harmonic function u in a c 1 domain with smooth boundary data g however d u is not continuous on the boundary changyou wang and yifeng yu 2012 proved the c 1 boundary regularity of planar infinity harmonic functions provided that and g are c 2 they asked the question whether the result holds when and g are assumed to be c 1 our counterexample answered this question negatively our construction of the counterexample is strongly inspired by the counterexample of dongsheng li and lihe wang 2006 for uniformly elliptic equations

algebras of noncommutative functions on subvarieties of the noncommutative ball the bounded and completely bounded isomorphism problem abstract given a noncommutative nc variety v in the nc unit ball b d we consider the algebra h v of bounded nc holomorphic functions on v we investigate the problem of when two algebras h v and h w are isomorphic we prove that these algebras are weak continuously isomorphic if and only if there is an nc biholomorphism g w v between the similarity envelopes that is bi lipschitz with respect to the free pseudo hyperbolic metric moreover such an isomorphism always has the form f f g where g is an nc biholomorphism these results also shed some new light on automorphisms of the noncommutative analytic toeplitz algebras h b d studied by davidson pitts and by popescu in particular we find that aut h b d is a proper subgroup of aut b d when d and the varieties are homogeneous we remove the weak continuity assumption showing that two such algebras are boundedly isomorphic if and only if there is a bi lipschitz nc biholomorphism between the similarity envelopes of the nc varieties we provide two proofs in the noncommutative setting our main tool is the noncommutative spectral radius about which we prove several new results in the free commutative case we use a new free commutative nullstellensatz that allows us to bootstrap techniques from the fully commutative case

operator algebras of monomial ideals in noncommuting variables abstract we study operator algebras arising from monomial ideals in the ring of polynomials in noncommuting variables through the apparatus of subproduct systems and c correspondences we provide a full comparison amongst the related operator algebras for our analysis we isolate a partially defined dynamical system to which we refer as the quantised dynamics of the monomial ideal in addition we revisit several previously considered constructions these include matsumoto s subshift c algebras as well as the tensor and the pimsner algebras associated with dynamical systems or graphs we sort out the various relations by giving concrete conditions and counterexamples that orientate the operator algebras of our context it appears that the boundary c algebras do not arise as the quotient with the compact operators unconditionally we establish a dichotomy to this effect by examining the resulting tensor algebras we identify their boundary representations we analyse their c envelopes and we give criteria for hyperrigidity moreover we completely classify them in terms of the data provided by the monomial ideals for tensor algebras of c correspondences and bounded isomorphisms this is achieved up to the level of local conjugacy in the sense of davidson and roydor for the quantised dynamics for tensor algebras of subproduct systems and algebraic isomorphisms this is achieved up to the level of equality of monomial ideals modulo permutations of the variables in the process we accomplish more in different directions most notably we show that tensor algebras form a complete invariant for isomorphic resp similar subproduct systems of homogeneous ideals up to isometric resp bounded isomorphisms the results on local conjugacy are obtained via an alternative proof of the breakthrough result of davidson and katsoulis on piecewise conjugate systems for our purposes we use appropriate compressions of the fock representation we then apply this alternative proof locally for the partially defined quantised dynamics in this way we avoid the topological graphs machinery and pave the way for further applications these include operator algebras of dynamical systems over commuting contractions or over row commuting contractions

superposition principle on the viscosity solutions of infinity laplace equations abstract we consider the sum of the solutions of two infinity laplace equations in disjoint variables we prove that the superposed function is a viscosity solution of the infinity laplace equation in the extension domains with the sum of inhomogeneous terms if one of the solutions is in the sense of viscosity and the other is in the classical sense we also construct a counterexample to show that the conclusion may not be true if both of the solutions are merely in the viscosity sense

fuzzy constrained min max model predictive control based on piecewise lyapunov functions this paper proposes two novel stable fuzzy model predictive controllers based on piecewise lyapunov functions and the min max optimization of a quasi worst case infinite horizon objective function the main idea is to design state feedback control laws that minimize the worst case objective function based on fuzzy model prediction and thus to obtain the optimal transient control performance which is of great importance in industrial process control moreover in both of these predictive controllers piecewise lyapunov functions have been used in order to reduce the conservatism of those existent predictive controllers based on common lyapunov functions it is shown that the asymptotic stability of the resulting closed loop discrete time fuzzy predictive control systems can be established by solving a set of linear matrix inequalities moreover the controller designs of the closed loop control systems with desired decay rate and input constraints are also considered simulations on a numerical example and a highly nonlinear benchmark system are presented to demonstrate the performance of the proposed fuzzy predictive controllers

robust stability constraints for fuzzy model predictive control this paper addresses the synthesis of a predictive controller for a nonlinear process based on a fuzzy model of the takagi sugeno t s type resulting in a stable closed loop control system conditions are given that guarantee closed loop robust asymptotic stability for open loop bounded input bounded output bibo stable processes with an additive l sub 1 norm bounded model uncertainty the idea is closely related to small gain based l sub 1 control theory but due to the time varying approach the resulting robust stability constraints are less conservative therefore the fuzzy model is viewed as a linear time varying system rather than a nonlinear one the goal is to obtain constraints on the control signal and its increment that guarantee robust stability robust global asymptotic stability and offset free reference tracking are guaranteed for asymptotically constant reference trajectories and disturbances

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

addition of certain non commuting random variables soit g le groupe libre non commutatif sur deux generateurs et soit u j j 1 2 les unites dans l 2 g correspondant a la translation a gauche par les generateurs et on considere l 2 g la fonction g g e soient x j des operateurs de la forme x j j u j les operateurs x j peuvent etre consideres comme des variables aleatoires de moments ou de facon equivalente avec des distributions donnees par les fonctionnelles analytiques j ou j f avec ces conventions la distribution de x 1 x 2 depend seulement des distributions de x 1 et x 2 on explique cette relation

noncommutative reproducing kernel hilbert spaces abstract the theory of positive kernels and associated reproducing kernel hilbert spaces especially in the setting of holomorphic functions has been an important tool for the last several decades in a number of areas of complex analysis and operator theory an interesting generalization of holomorphic functions namely free noncommutative functions e g functions of square matrix arguments of arbitrary size satisfying additional natural compatibility conditions is now an active area of research with motivation and applications from a variety of areas e g noncommutative functional calculus free probability and optimization theory in linear systems engineering the purpose of this article is to develop a theory of positive kernels and associated reproducing kernel hilbert spaces for the setting of free noncommutative function theory

uniqueness of lipschitz extensions minimizing the sup norm of the gradient in this paper we examine the problem of minimizing the sup norm of the gradient of a function with prescribed boundary values geometrically this can be interpreted as finding a minimal lipschitz extension due to the weak convexity of the functional associated to this problem solutions are generally nonunique by adopting g aronsson s notion of absolutely minimizing we are able to prove uniqueness by characterizing minimizers as the unique solutions of an associated partial differential equation in fact we actually prove a weak maximum principle for this partial differential equation which in some sense is the euler equation for the minimization problem this is significantly difficult because the partial differential equation is both fully nonlinear and has very degenerate ellipticity to overcome this difficulty we use the weak solutions of m g crandall and p l lions also known as viscosity solutions in conjunction with some arguments using integration by parts

analysis and synthesis of nonlinear time delay systems via fuzzy control approach takagi sugeno ts fuzzy models 1985 1992 can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input output i o submodels in this paper the ts fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete time nonlinear systems with time delay the ts fuzzy models with time delay are presented and the stability conditions are derived using lyapunov krasovskii approach we also present a stabilization approach for nonlinear time delay systems through fuzzy state feedback and fuzzy observer based controller sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities an illustrative example based on the cstr model is given to design a fuzzy controller

nonlinear state feedback controller for nonlinear systems stability analysis and design based on fuzzy plant model this paper presents the stability analysis of a fuzzy model based control system consisting of a nonlinear plant and a nonlinear state feedback controller and the design of the nonlinear gains of the controller the nonlinear plant is represented by a fuzzy model having p rules a nonlinear state feedback controller is designed to close the feedback loop under this design the stability condition is reduced to p linear matrix inequalities an application example on stabilizing a mass spring damper system will be given

analysis and design for a class of complex control systems part i fuzzy modelling and identification this paper is the first of two dealing with the analysis and design of a class of complex control systems this part deals with fuzzy modelling and identification the second paper is concerned with fuzzy controller design we believe that these two papers show a way to analyze and design complex control systems using a combination of fuzzy logic and modern control theory the complex systems studied in these two papers can be represented by a fuzzy aggregation of a set of local linear models the identification can be divided into two procedures the first procedure is the identification of the membership functions including the determination of the number of fuzzy rules and the estimation of the parameters in the membership functions the second is the identification of the local linear models including the determination of the structure and the parameters of the local rule maps and the global rule interpolation two examples are used to demonstrate the application of the modelling method

fuzzy model predictive control of non linear processes using genetic algorithms abstract this paper introduces a new fuzzy control technique which belongs to the popular family of control algorithms called model predictive controllers the method is based on a dynamic fuzzy model of the process to be controlled which is used for predicting the future behavior of the output variables a non linear optimization problem is then formulated which minimizes the difference between the model predictions and the desired trajectory over the prediction horizon and the control energy over a shorter control horizon the problem is solved on line using a specially designed genetic algorithm which has a number of advantages over conventional non linear optimization techniques the method can be used with any type of fuzzy model and is particularly useful when a direct fuzzy controller cannot be designed due to the complexity of the process and the difficulty in developing fuzzy control rules the method is illustrated via the application to a non linear single input single output reactor where a takagi sugeno model serves as a predictor of the process future behavior

similarity problems in noncommutative polydomains abstract in this paper we consider several problems of joint similarity to tuples of bounded linear operators in noncommutative polydomains and varieties associated with sets of noncommutative polynomials we obtain analogues of classical results such as rota s model theorem for operators with spectral radius less than one sz nagy characterization of operators similar to isometries or unitary operators and the refinement obtained by foias and by de branges and rovnyak for strongly stable contractions we also provide analogues of these results in the context of joint similarity of commuting tuples of positive linear maps on the algebra of bounded linear operators on a separable hilbert space an important role in this paper is played by a class of noncommutative cones associated with positive linear maps the fourier type representation of their elements and the constrained noncommutative berezin transforms associated with these elements it is shown that there is an intimate relation between the similarity problems and the existence of positive invertible elements in these noncommutative cones and the corresponding berezin kernels

piecewise quadratic stability of fuzzy systems presents an approach to stability analysis of fuzzy systems the analysis is based on lyapunov functions that are continuous and piecewise quadratic the approach exploits the gain scheduling nature of fuzzy systems and results in stability conditions that can be verified via convex optimization over linear matrix inequalities examples demonstrate the many improvements over analysis based on a single quadratic lyapunov function special attention is given to the computational aspects of the approach and several methods to improve the computational efficiency are described

controller synthesis of fuzzy dynamic systems based on piecewise lyapunov functions this paper presents a kind of controller synthesis method for fuzzy dynamic systems based on a piecewise smooth lyapunov function the basic idea of the proposed approach is to construct controllers for the fuzzy dynamic systems in such a way that a piecewise continuous lyapunov function can be used to establish the global stability with h sub spl infin performance of the resulting closed loop fuzzy control systems it is shown that the control laws can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software an example is given to illustrate the application of the proposed methods