system analysis via integral quadratic constraints this paper introduces a unified approach to robustness analysis with respect to nonlinearities time variations and uncertain parameters from an original idea by yakubovich 1967 the approach has been developed under a combination of influences from the western and russian traditions of control theory it is shown how a complex system can be described using integral quadratic constraints iqc for its elementary components a stability theorem for systems described by iqcs is presented that covers classical passivity dissipativity arguments but simplifies the use of multipliers and the treatment of causality a systematic computational approach is described and relations to other methods of stability analysis are discussed last but not least the paper contains a summarizing list of iqcs for important types of system components

brief paper an anti windup technique for lmi regions the anti windup problem seeks to minimize closed loop performance deterioration due to input nonlinearities such as saturation for a given linear time invariant plant and controller this paper presents a linear matrix inequality lmi based method that attempts to minimize performance deterioration while explicitly restricting the anti windup closed loop dynamics the restriction placed on the dynamics is described via lmi regions which is a form of regional pole placement finally the techniques discussed in this paper are demonstrated on an electro hydraulic testbed

a new perspective on static and low order anti windup synthesis by viewing the anti windup problem as a decoupled set of subsystems and relating this configuration to a general static anti windup set up lmi conditions are established which guarantee stability and performance of the resulting closed loop system the approach taken and the mapping used for the performance index are logical and intuitive and it is argued central to the true anti windup objective the approach enables one to construct static anti windup compensators in a systematic and numerically tractable manner the idea is extended to allow low order anti windup compensators to be synthesized which while being sub optimal can improve transient performance and possess several desired properties such as low computational overhead and sensible closed loop pole locations in addition low order anti windup synthesis is often feasible when the corresponding static synthesis is not

generalized sector synthesis of output feedback control with anti windup structure this paper considers the control synthesis problem for linear time invariant lti continuous time systems with actuator saturation nonlinearities the control architecture is standard a nominal lti output feedback with an anti windup aw mechanism traditional approaches have focused on aw synthesis where the nominal controller is first designed to achieve a local performance in the linear region of the actuators and then the aw compensator is added to guarantee stability performance properties when the actuators saturate in contrast this paper proposes a synthesis method to design both the nominal controller and the aw compensator simultaneously using the generalized sector gs approach in the multiplier setting a sufficient condition is given in terms of linear matrix inequalities so that a given ellipsoid is synthesized as a domain of attraction for the closed loop system our result is shown to include the existing results on the simultaneous circle synthesis and the anti windup gs synthesis as special cases this paper also shows that the direct feed through term in the aw compensator does not contribute to enlarging the achievable domain of attraction within the multiplier gs framework

brief paper anti windup and bumpless transfer schemes this paper considers the problem of windup which occurs when a controller with unstable integrator modes is subjected to input saturation or multi mode operation an optimal strategy for the so called model based approach is proposed based on an h optimisation framework this has been found to give good results on numerical examples taken from the literature

fuzzy set based multiobjective allocation of resources and its applications this paper presents results of research into the use of the bellman zadeh approach to decision making in a fuzzy environment for solving multiobjective optimization problems its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems the use of the bellman zadeh approach has served as a basis for solving a problem of multiobjective allocation of resources or their shortages and developing a corresponding adaptive interactive decision making system aidms1 its calculating kernel permits one to solve maxmin problems using an algorithm based on a nonlocal search modification of the gelfand s and tsetlin s long valley method the aidms1 includes procedures for considering linguistic variables to reflect conditions that are difficult to formalize as well as procedures for constructing and correcting vectors of importance factors for goals the use of these procedures permits one to realize an adaptive approach to processing information of a decision maker to provide successive improving of the solution quality c windows of the aidms1 are presented for input output and special possibilities related to considering linguistic variables and constructing and correcting vectors of importance factors the results of the paper are universally applicable and are already being used to solve power engineering problems

fuzzy preference modeling and its application to multiobjective decision making this paper reflects results of research into the construction and analysis of models within the framework of a general approach to solving optimization problems with fuzzy coefficients this approach involves a modification of traditional mathematical programming methods and is associated with formulating and solving one and the same problem within the framework of mutually interrelated models the use of the approach allows one to maximally cut off dominated alternatives the subsequent contraction of the decision uncertainty region is based on reducing the problem to models of multiobjective choosing alternatives in a fuzzy environment with the use of fuzzy preference relation techniques for analyzing these models three techniques for fuzzy preference modeling are discussed in the paper the first technique is based on the construction of membership functions of subsets of nondominated alternatives with simultaneous considering of all criteria fuzzy preference relations the second technique is of a lexicographic character and consists of step by step introducing of fuzzy preference relations the third technique is based on aggregating membership functions of subsets of nondominated alternatives corresponding to each preference relation these techniques have served for developing a corresponding system for multiobjective decision making mdms c windows of the mdms are presented for input output and some intermediate procedures the results of the paper are of a universal character and are already being used to solve power engineering naval engineering and management problems

nonlinear bounded control for norm bounded uncertain systems in this paper a method to derive a bounded continuous feedback control function which stabilizes a norm bounded uncertain linear system in a certain region is proposed the aim is to ensure a certain performance level in a neighborhood ellipsoid of the origin through a guaranteed cost state feedback control outside this neighborhood a linear like control with state dependent gains is obtained from the solutions of a family of parameter dependent algebraic riccati equation similar to the one arising in h sub spl infin control

the effect of maps permutation on the global attractor of a periodic beverton holt model abstract consider a p periodic difference equation x n 1 f n x n with a global attractor how does a permutation f p 1 f 1 f 0 of the maps affect the global attractor in this paper we limit this general question to the beverton holt model with p periodic harvesting we fix a set of harvesting quotas and give ourselves the liberty to permute them the total harvesting yield is unchanged by the permutation but the population geometric mean may fluctuate we investigate this notion and characterize the cases in which a permutation of the harvesting quotas has no effect or tangible effect on the population geometric mean in particular as long as persistence is assured all permutations within the dihedral group give same population geometric mean other permutations may change the population geometric mean a characterization theorem has been obtained based on block reflections in the harvesting quotas finally we associate directed graphs to the various permutations then give the complete characterization when the periodicity of the system is four or five

technical communique a convex characterization of dynamically constrained anti windup controllers based on a recent description of deadzone nonlinearities via local sector conditions a new lmi characterization is proposed to compute full order continuous time anti windup controllers with pole constraints more precisely an upper bound is introduced on the real part of the controller poles to avoid slow dynamics which often leads to poor time domain performance as is demonstrated in a short applicative part the introduction of such a bound allows us to efficiently handle the trade off between stability domain enlargement and time domain response relevance

optimal impulsive harvesting on non autonomous beverton holt difference equations many recent advances in the theory of the optimal economic exploitation of renewable fish resources have been gained by applying optimal control theory however despite these successes much less is known about how seasonal environments affect the maximum sustainable yield msy or population persistence and any effects of relations between intensity and frequency of harvesting assuming that fish populations follow beverton holt equations we investigated impulsive harvesting in seasonal environments focusing on both economic aspects and resource sustainability we first investigated the existence and stability of a periodic solution and its analytic formula and then showed that the population persistence depends on the intensity and frequency of harvesting with the msy as a management objective we investigated optimal impulsive harvesting policies the optimal harvesting effort that maximizes the sustainable yield the corresponding optimal population level and the msy are obtained by using discrete euler lagrange equations and product formulae and their explicit expressions were obtained in terms of the intrinsic growth rate the carrying capacity and the impulsive moments these results imply that harvest timing is of crucial importance to the msy since impulsive differential equations incorporate elements of continuous and discrete systems we can apply all results obtained for beverton holt equations with impulsive effects to periodic logistic equations with impulsive harvesting

regular ordered semigroups in terms of fuzzy subsets given a set s a fuzzy subset of s or a fuzzy set in s is by definition an arbitrary mapping f s 0 1 where 0 1 is the usual interval of real numbers if the set s bears some structure one may distinguish some fuzzy subsets of s in terms of that additional structure this important concept of a fuzzy set was first introduced by zadeh fuzzy groups have been first considered by rosenfeld fuzzy semigroups by kuroki a theory of fuzzy sets on ordered groupoids and ordered semigroups can be developed some results on ordered groupoids semigroups have been already given by the same authors in n kehayopulu m tsingelis fuzzy sets in ordered groupoids semigroup forum 65 2002 128 132 n kehayopulu m tsingelis the embedding of an ordered groupoid into a poe groupoid in terms of fuzzy sets inform sci 152 2003 231 236 n kehayopulu m tsingelis fuzzy bi ideals in ordered semigroups inform sci 171 2004 13 28 where s has been endowed with the structure of an ordered semigroup and defined fuzzy analogous for several notions that have been proved to be useful in the theory of ordered semigroups the characterization of regular rings in terms of right and left ideals is well known the characterization of regular semigroups and regular ordered semigroups in terms of left and right ideals or in terms of left right ideals and quasi ideals is well known as well the characterization of regular le semigroups that is lattice ordered semigroups having a greatest element in terms of right ideal elements and left ideal elements or right left and quasi ideal elements is also known in the present paper we first give the main theorem which characterizes the regular ordered semigroups by means of fuzzy right and fuzzy left ideals then we characterize the regular ordered semigroups in terms of fuzzy right fuzzy left ideals and fuzzy quasi ideals the paper serves as an example to show that one can pass from the theory of ordered semigroups to the theory of fuzzy ordered semigroups some of our results are true for ordered groupoids in general

ranking function based solutions of fully fuzzified minimal cost flow problem the aim of minimal cost flow problem mcfp is to find the least transportation cost of a single commodity through a capacitated network this paper presents a model to deal with one particular group of such problems in which the supply and demand of nodes and the capacity and cost of edges are represented as fuzzy numbers for easier reference hereafter we refer to this group of problems as fully fuzzified mcfp to represent our model hukuhara s difference and approximated multiplication are used thereafter we sort fuzzy numbers by an order using a ranking function and show that it is a total order i e a reflexive anti symmetric transitive and complete binary relation utilizing the proposed ranking function we transform the fully fuzzified mcfp into three crisp problems solvable in polynomial time from this standpoint combinatorial algorithms are provided to solve the above mentioned problem and find the fuzzy optimal flow furthermore the proposed order is related to the importance weights of the center the left spread and the right spread of each fuzzy number thus this method is capable of handling the decision maker s risk taking by comparing some previous ranking function based works with our method the efficiency of the latter is revealed finally an application of our proposed method to petroleum industry is presented

quadratic stability and singular siso switching systems in this note we consider the problem of determining necessary and sufficient conditions for the existence of a common quadratic lyapunov function for a pair of stable linear time invariant systems whose system matrices are of the form a a ght and where one of the matrices is singular a necessary and sufficient condition for the existence of such a function is given in terms of the spectrum of the product a a ght the technical note also contains a spectral characterization of strictly positive real transfer functions which are strictly proper examples are presented to illustrate our results

comments on disturbance decoupling of boolean control networks a systematic method of disturbance decoupling for boolean control networks has been developed in paper however the purpose of this note is to show that the necessary and sufficient condition for the existence of disturbance decoupling controllers needs a mild modification which is provided

dynamic anti windup scheme for feedback linearizable nonlinear control systems with saturating inputs this paper proposes a dynamic compensation scheme for input constrained feedback linearizable nonlinear systems to cope with the windup phenomenon given a dynamic feedback linearizing controller designed without considering its input constraint an additional dynamic compensator is proposed to account for the constraint this dynamic anti windup is based on the minimization of a reasonable performance index the proposed strategy is a nonlinear extended version of park j k choi c h 1995 dynamic compensation method for multivariable control systems with saturating actuators ieee transactions on automatic control 40 9 1635 1640 with simplified derivation of an optimization solution under relaxed assumptions the parameter matrices and structure of the solution are explicitly decided by mathematical optimization for infinite horizon without tuning of design parameters unlike previous schemes during input saturation the role of the anti windup scheme with the proposed dynamic feedback compensator is to maintain the controller states to be exactly the same as those without input saturation the local asymptotic stability and the total stability of the resulting systems are proved the usefulness of the proposed design method is illustrated by comparative simulations for a constrained control system

inherent observer property in a class of anti windup compensators owing to the types of non linearities involved the analysis and the comparison of different anti windup compensators that are available in the literature become difficult towards achieving a better understanding of the mechanisms of these anti windup compensators we here expose the observer property inherent in a class of anti windup compensators this observer property allows us to unify these anti windup compensators as special cases of the generalized anti windup compensator due to astrom and wittenmark 1984 and provides a general framework to investigate their performance

design of a nonlinear anti windup gain by using a composite quadratic lyapunov function this technical note revisits the problem of designing a static anti windup gain for enlarging the domain of attraction of the resulting closed loop system by utilizing a composite quadratic lyapunov function which was originally proposed to study the stabilization problem for linear systems under actuator saturation an existing lmi based design algorithm is enhanced to result in a nonlinear possibly continuous anti windup gain this nonlinear anti windup gain enables us to obtain an estimate of the domain of attraction in the form of the convex hull of a group of ellipsoids instead of a single ellipsoid that would result from a single lyapunov function based design simulation results demonstrate the features of the proposed design the composite quadratic lyapunov function brings about

a unified framework for the study of anti windup designs we present a unified framework for the study of linear time invariant lti systems subject to control input nonlinearities the framework is based on the following two step design paradigm design the linear controller ignoring control input nonlinearities and then add anti windup bumpless transfer awbt compensation to minimize the adverse eflects of any control input nonlinearities on closed loop performance the resulting awbt compensation is applicable to multivariable controllers of arbitrary structure and order all known lti anti windup and or bumpless transfer compensation schemes are shown to be special cases of this framework it is shown how this framework can handle standard issues such as the analysis of stability and performance with or without uncertainties in the plant model the actual analysis of stability and performance and robustness issues are problems in their own right and hence not detailed here the main result is the unification of existing schemes for awbt compensation under a general framework

folding and unfolding in periodic difference equations abstract given a p periodic difference equation x n 1 f n mod p x n where each f j is a continuous interval map j 0 1 p 1 we discuss the notion of folding and unfolding related to this type of non autonomous equations it is possible to glue certain maps of this equation to shorten its period which we call folding on the other hand we can unfold the glued maps so the original structure can be recovered or understood here we focus on the periodic structure under the effect of folding and unfolding in particular we analyze the relationship between the periods of periodic sequences of the p periodic difference equation and the periods of the corresponding subsequences related to the folded systems

a hopfield neural network applied to the fuzzy maximum cut problem under credibility measure this paper deals with maximum cut problem on a graph with fuzzy edges this problem is studied to cluster data under imprecise dependency applying the credibility measure this fuzzy problem is transformed into a nonlinear mixed integer programming problem to solve the problem an adaptive hopfield neural network is proposed with modern simulated annealing cooling schedule which converges into an equilibrium status within few iterations to illustrate the efficiency of this network it is simulated on some benchmark examples also webpage clustering problem is solved to illustrate the application of the studied fuzzy problem and neural network solutions

robust anti windup controller design of time delay fuzzy systems with actuator saturations this study presents a robust anti windup fuzzy control approach for uncertain nonlinear time delay systems with actuator saturations the discussed system dynamics is presented by the takagi sugeno t s fuzzy model to facilitate the design process the nonlinearity of input saturation is characterized by a specific sector condition given a stabilizing dynamic output feedback fuzzy controller an anti windup control approach is then developed to maximize the size of estimate of the domain of attraction significantly the convergence of all admissible initial states within this region could be ensured based on the lyapunov krasovskii delay independent and delay dependent analyses sufficient conditions for the robust stabilization are derived these conditions are formulated as a convex optimization problem with constraints represented by a set of linear matrix inequalities allowing the fuzzy controller to be synthesized more efficiently finally numeric simulations are given to validate the proposed approach

an anti windup design for linear systems with input saturation abstract an anti windup design problem is posed and it is shown that all observer based anti windup modifications solve this problem at least locally sufficient conditions for an observer based anti windup modification to solve the global version of this problem are presented a novel observer based anti windup design is then proposed such that the anti windup problem can be interpreted in terms of a reduced order system in particular the proposed anti windup design induces an invariant subspace for the dynamic behavior of the mismatch between the constrained and unconstrained closed loops the dynamics in this invariant subspace are identical to the behavior of the plant with input saturation starting at the origin stabilized by linear state feedback and driven by the mismatch between the unconstrained input and this input passed through a saturation function the second part of the paper shows how the original dynamic compensator can be modified while retaining those dynamic features that produce a desirable closed loop steady state response to ensure that the requisite invariant subspace exists and it is reasonably tuned for input saturation two case studies are carried out on systems that have been investigated in the literature

fuzzy preference relations in models of decision making abstract analysis of x r models is considered as part of a general approach to solving optimization problems with fuzzy coefficients this approach involves a modification of traditional optimization methods and is associated with formulating and solving one and the same problem within the framework of mutually interrelated models by constructing equivalent analogs with fuzzy coefficients in objective functions alone the use of the approach allows one to maximally cut off dominated alternatives the subsequent contraction of the decision uncertainty region is based on reducing the problem to multiobjective choice of alternatives in a fuzzy environment three techniques for processing of fuzzy preference relations reflecting criteria of quantitative as well as qualitative character are discussed the results of the paper are universally applicable and are already being used to solve power engineering problems

brief multiplier theory for stability analysis of anti windup control systems we apply the passivity theorem with appropriate choice of multipliers to develop a general framework for analyzing stability of anti windup bumpless transfer awbt schemes for appropriate choices of the multipliers we reduce the resulting sufficient conditions for stability to equivalent linear matrix inequalities lmis we show that a number of previously reported attempts to analyze awbt stability using seemingly diverse techniques such as the popov circle and off axis circle criteria the optimally scaled small gain theorem generalized m upper bound and describing functions can all be generalized within the framework of this paper

a procedure for ordering fuzzy subsets of the unit interval abstract we introduce a function to help in the ordering of fuzzy subsets of the unit interval this function is the integral of the mean of the level sets associated with the fuzzy subsets various properties of this function are studied

incremental l2 gain stability of piecewise affine systems with piecewise polynomial storage functions abstract this paper concerns the incremental l 2 gain stability of piecewise affine pwa systems we propose sufficient conditions derived from dissipativity theory to compute an upper bound on the incremental l 2 gain this is achieved by constructing piecewise polynomial storage functions through the use of sum of squares sos relaxations the constraints are expressed as linear matrix inequalities lmis which can be solved numerically in an efficient way the proposed conditions are verified to be less conservative than previous results found in the literature by means of a numerical example

linear discrete time global and regional anti windup an lmi approach in this article we address linear anti windup design for linear discrete time control systems guaranteeing regional and global stability and performance the techniques that we develop are the discrete time counterpart of existing techniques for anti windup augmentation which lead to convex constructions by way of linear matrix inequalities lmis when adopting static and plant order anti windup augmentation interesting system theoretic interpretations of the performance bounds for the non linear closed loop can also be given we show here that parallel results apply to the discrete time case we derive the corresponding conditions and prove their effectiveness by adapting the continuous time approaches to the discrete time case

a dynamic consensus scheme based on a nonreciprocal fuzzy preference relation modeling in this paper we propose a dynamical consensus scheme which makes use of an index of comparability and of an index of concordance to regulate the information flow in the discussion among the experts in addition to the traditional use of a concordance index to identify the discordant expert who can be invited to review his opinion or to explain his judgment to the other experts here an index of comparability is utilized to identify the experts that have faced difficulties in expressing their preferences with this information at hand a moderator can invite the experts that are confident on their opinions to support the experts that are hesitating in the construction of the fuzzy preference relations

semi global exponential stabilization of linear systems subject to input saturation via linear feedbacks abstract it is known that a linear time invariant system subject to input saturation can be globally asymptotically stabilized if it has no eigenvalues with positive real parts it is also shown by fuller 1997 and sussmann and yang 1991 that in general one must use nonlinear control laws and only some special cases can be handled by linear control laws in this paper we show the existence of linear state feedback and or output feedback control laws for semi global exponential stabilization rather than global asymptotic stabilization of such systems we explicitly construct linear static state feedback laws and or linear dynamic output feedback laws that semi globally exponentially stabilize the given system our results complement the negative result of fuller 1977 and sussmann and yang 1991

technical communique static output feedback stabilization an ilmi approach in this note the static output feedback stabilization problem is addressed using the linear matrix inequality technique a necessary and sufficient condition for static output feedback stabilizability for linear time invariant systems is derived in the form of a matrix inequality the extension of the result to h control is studied an iterative lmi ilmi algorithm is proposed to compute the feedback gain numerical examples are employed to demonstrate the effectiveness and the convergence of the algorithm

antiwindup for stable linear systems with input saturation an lmi based synthesis this paper considers closed loop quadratic stability and l sub 2 performance properties of linear control systems subject to input saturation more specifically these properties are examined within the context of the popular linear antiwindup augmentation paradigm linear antiwindup augmentation refers to designing a linear filter to augment a linear control system subject to a local specification called the unconstrained closed loop behavior building on known results on h sub spl infin and lpv synthesis the fixed order linear antiwindup synthesis feasibility problem is cast as a nonconvex matrix optimization problem which has an attractive system theoretic interpretation the lower bound on the achievable l sub 2 performance is the maximum of the open and unconstrained closed loop l sub 2 gains in the special cases of zero order static and plant order antiwindup compensation the feasibility conditions become convex linear matrix inequalities it is shown that if and only if the plant is asymptotically stable plant order linear antiwindup compensation is always feasible for large enough l sub 2 gain and that static antiwindup compensation is feasible provided a quasi common lyapunov function between the open loop and unconstrained closed loop exists using the solutions to the matrix feasibility problems the synthesis of the antiwindup augmentation achieving the desired level of l sub 2 performance is then accomplished by solving an additional lmi

anti windup synthesis using riccati equations the aim of this paper is to give a novel solution to the full order anti windup aw compensation problem for stable systems with input saturation the solution is obtained by completing the square in three steps and requires the solution to a single bounded real riccati equation characterized by the open loop plant s norm the riccati equation plays the role of the lmis usually found in anti windup synthesis but in addition to its numerical advantages it yields a family of anti windup compensators with the same performance this family of compensators is parameterized by a matrix which is intimately linked with both the poles of the anti windup compensator and the robustness properties of the closed loop saturated system thus this matrix allows a robust anti windup problem to be solved in a straightforward and intuitive manner the effectiveness of the proposed technique is demonstrated on a simple example

nonlinear regulation the piecewise linear approach this paper approaches nonlinear control problems through the use of discrete time piecewise linear systems these are systems whose next state and output maps are both described by pl maps i e by maps which are affine on each of the components of a finite polyhedral partition various results on state and output feedback observers and inverses standard for linear systems are proved for pl systems many of these results are then used in the study of more general both discrete and continuous time systems using suitable approximations

a framework for multivariable algebraic loops in linear anti windup implementations abstract this brief paper addresses the implementation and well posedness aspects of multivariable algebraic loops which arise naturally in many anti windup control schemes using the machinery of linear complementarity problems a unified framework is developed for establishing well posedness of such algebraic loops enforcing well posedness is reduced to a linear matrix inequality feasibility problem that can be solved during the anti windup design stage several existing anti windup implementations appear as special cases of the unified framework presented in this brief paper

a magnitude and rate saturation model and its use in the solution of a static anti windup problem in this paper we address the anti windup design problem for linear control systems with strictly proper controllers in the presence of input magnitude and rate saturation using generalized sector condition we provide an lmi based procedure for the construction of a linear anti windup gain acting on the controller state equation such that regional closed loop stability is guaranteed and suitable performance measures are optimized the approach is successfully illustrated on a simulation example

w stability of feedback systems abstract this paper introduces the notion of w stability of feedback systems this is a generalization of a concept of well posedness discussed by willems w stability requires that a feedback system should remain stable under a certain class of perturbations which may not be vanishingly small when measured by the gap metric the paper derives necessary and sufficient conditions for a feedback system to be w stable further an investigation of well posedness is given for feedback systems where high frequency roll off has been suppressed for modelling simplicity this question is pertinent in standard pid control

robustness analysis of nonlinear feedback systems an input output approach this paper presents an approach to robustness analysis for nonlinear feedback systems we pursue a notion of model uncertainty based on the closeness of input output trajectories which is not tied to a particular uncertainty representation such as additive parametric structured etc the basic viewpoint is to regard systems as operators on signal spaces we present two versions of a global theory where stability is captured by induced norms or by gain functions we also develop local approaches over bounded signal sets and give a treatment for systems with potential for finite time escape we compute the relevant stability margin for several examples and demonstrate robustness of stability for some specific perturbations e g small time delays we also present examples of nonlinear control systems which have zero robustness margin and are destabilized by arbitrarily small gap perturbations the paper considers the case where uncertainty is present in the controller as well as the plant and the generalization of the approach to the case where uncertainty occurs in several subsystems in an arbitrary interconnection

brief incremental gain analysis of piecewise linear systems and application to the antiwindup problem this paper presents an approach to estimating the l 2 incremental gain of piecewise linear systems storage functions satisfying a dissipation inequality are used to derive a set of linear matrix inequalities lmis to provide a bound the application of the results to the antiwindup problem is illustrated by examples

anti windup synthesis for systems with rate limits using riccati equations this article develops an anti windup aw scheme for systems with rate limited actuators the main results show how a full order aw compensator can be synthesised using an algebraic riccati equation and several free parameters a further result then shows how the free parameters may be chosen to influence in an intuitive way the local gain of the system and the size of the region of attraction the results are of interest due to their low computational burden and hence their applicability to the systems of large state dimension

brief multivariable anti windup controller synthesis using linear matrix inequalities we present a general formulation of the problem of multi variable anti windup bumpless transfer awbt controller synthesis which provides sufficient conditions for stability covering a large class of typical input nonlinearities such as saturation deadzone and switching override nonlinearities the resulting synthesis method demonstrates graceful performance degradation whenever input nonlinearities are active through minimization of a weighted l 2 gain the main contribution of the paper is that the awbt controller synthesis using static compensation is cast as a convex optimization over linear matrix inequalities

multiobjective and multiattribute decision making in a fuzzy environment and their power engineering applications two classes of problems requiring the use of a multicriteria approach are defined fuzzy set theory serves for aggregating information arriving from diverse sources combined branches of mathematics of uncertainty serve as a new decision making tool the use of fuzzy set based decision making in power system problems is described benefits of applying fuzzy set theory in problems of power engineering are shown this work presents and generalizes our experience in the use of fuzzy set theory including its combination with another branch of mathematics of uncertainty in developing general approaches and methods for optimization and decision making with considering the uncertainty and multicriteria factors in problems of the design planning operation and control of complex systems two major classes of situations that require the use of a multicriteria approach are identified in accordance with this two general classes of models related to multiobjective x f models and multiattribute x r models problems respectively are considered methods for their analysis based on the use of the bellman zadeh approach to decision making in a fuzzy environment and fuzzy preference modeling techniques respectively are considered although the use of x f and x r models is of an independent character they also serve as parts of a general scheme for multicriteria decision making under conditions of uncertainty this scheme is associated with the use of a generalization of the classic approach to considering the uncertainty of information to multicriteria problems based on analyzing special aggregations of payoff matrices the authors experience in the use of the results indicated above for solving diverse classes of power system planning and operation problems is described this experience convincingly demonstrates diverse advantages of applying fuzzy mathematics in optimization and decision making problems of power engineering

algorithms of discrete optimization and their application to problems with fuzzy coefficients an approach to solving optimization problems with fuzzy coefficients in objective functions and constraints is described it consists in formulating and solving one and the same problem within the framework of mutually related models with constructing equivalent analogs with fuzzy coefficients in objective functions alone it enables one to maximally cut off dominated alternatives from below as well as from above since the approach is applied within the context of fuzzy discrete optimization problems several modified algorithms of discrete optimization are discussed these algorithms are associated with the method of normalized functions are based on a combination of formal and heuristic procedures and allow one to obtain quasi optimal solutions after a small number of steps thus overcoming the computational complexity posed the np completeness of discrete optimization problems the subsequent contraction of the decision uncertainty regions is associated with reduction of the problem to multiobjective decision making in a fuzzy environment with using techniques based on fuzzy preference relations the techniques are also directly applicable to situations in which the decision maker is required to choose alternatives from a set of explicitly available alternatives the results of the paper are of a universal character and can be applied to the design and control of systems and processes of different purposes as well as the enhancement of corresponding cad cam systems and intelligent decision making systems the results of the paper are already being used to solve problems of power engineering

fuzzy sets and models of decision making abstract results of research into the use of fuzzy sets for handling various forms of uncertainty in optimization problems related to the design and control of complex systems are presented much attention is given to considering the uncertainty of goals that is associated with a multicriteria character of many optimization problems the application of a multicriteria approach is needed to solve 1 1 problems in which solution consequences cannot be estimated on the basis of a single criterion that involves the necessity of analyzing a vector of criteria and 2 2 problems that may be considered on the basis of a single criterion but their unique solutions are not achieved because the uncertainty of information produces so called decision uncertainty regions and the application of additional criteria can serve as a convincing means to contract these regions according to this two classes of models x m and x r models are considered with applying the bellman zadeh approach and techniques of fuzzy preference relations to their analysis the consideration of x r models is associated with a general approach to solving a wide class of optimization problems with fuzzy coefficients this approach consists in formulating and analyzing one and the same problem within the framework of interrelated models with constructing equivalent analogs with fuzzy coefficients in objective functions alone it allows one to maximally cut off dominated alternatives the subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment with its analysis applying one of two techniques based on fuzzy preference relations the results of the paper are of a universal character and are already being used to solve problems of power engineering

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

a general approach to solving a wide class of fuzzy optimization problems results of research into the use of fuzzy sets for handling various forms of uncertainty in the optimal design and control of complex systems are presented a general approach to solving a wide class of optimization problems containing fuzzy coefficients in objective functions and constraints is described it involves a modification of traditional mathematical programming methods and is associated with formulating and solving one and the same problem within the framework of mutually conjugated models this approach allows one to maximally cut off dominated alternatives from below as well as from above the subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment the general approach is applied within the context of a fuzzy discrete optimization model that is based on a modification of discrete optimization algorithms prior to application of these algorithms there is a transition from a model with fuzzy coefficients in objective functions and constraints to an equivalent analog with fuzzy coefficients in objective functions alone the results of the paper are of a universal character and are already being used to solve problems of power engineering

multicriteria analysis in decision making under information uncertainty abstract this paper presents results of research related to multicriteria decision making under information uncertainty the bellman zadeh approach to decision making in a fuzzy environment is utilized for analyzing multicriteria optimization models x m models under deterministic information its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems this circumstance permits one to generalize the classic approach to considering the uncertainty of quantitative information based on constructing and analyzing payoff matrices reflecting effects which can be obtained for different combinations of solution alternatives and the so called states of nature in monocriteria decision making to multicriteria problems considering that the uncertainty of information can produce considerable decision uncertainty regions the resolving capacity of this generalization does not always permit one to obtain unique solutions taking this into account a proposed general scheme of multicriteria decision making under information uncertainty also includes the construction and analysis of the so called x r models which contain fuzzy preference relations as criteria of optimality as a means for the subsequent contraction of the decision uncertainty regions the paper results are of a universal character and are illustrated by a simple example

fuzzy set based multiobjective allocation of resources solution algorithms and applications abstract this paper presents results of research in the use of the bellman zadeh approach to decision making in a fuzzy environment for solving multiobjective optimization problems its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems the application of the approach permits one to realize an effective from the computational standpoint as well as rigorous in view of obtaining solutions from the pareto set method of analyzing multiobjective models the use of the bellman zadeh approach has served as a basis for solving problems of multiobjective allocation of resources or their shortages and developing a corresponding adaptive interactive decision making system aidms its calculating kernel permits one to solve maxmin problems using an algorithm based on a non local search modification of gelfand s and tsetlin s long valley method as well as a genetic algorithm the comparison of their computational performance is given on the basis of solving problems of multiobjective power shortage allocation in power systems