approximately optimal solutions to the finite dimensional witsenhausen counterexample recently a vector version of witsenhausen s counterexample was considered and it was shown that in the asymptotic limit of infinite vector length certain vector quantization based control strategies are provably within a constant factor of the asymptotically optimal cost for all possible problem parameters while suggestive a constant factor result for the finite dimensional problem has remained elusive in this paper we provide a resolution to this issue by applying a large deviation sphere packing philosophy we derive a lower bound to the optimal cost for the finite dimensional case that uses appropriate shadows of an existing vector lower bound that is the same for all dimensions using this new lower bound we show that good lattice quantization based control strategies achieve within a constant factor of the optimal cost uniformly over all possible problem parameters including the vector length for witsenhausen s original problem which is the scalar case the gap between regular lattice quantization based strategies and the lower bound is provably never more than a factor of 100 and computer calculations strongly suggest that the factor in fact may be no larger than 8 finally to obtain a numerical understanding of the possible room for improvement in costs using alternative strategies we also include numerical comparison with strategies that are conjectured to be optimal using this comparison we posit that there is more room for improvement in our lower bounds than in our upper bounds

radial basis function based adaptive fuzzy systems and their applications to system identification and prediction abstract in this paper we describe a neuro fuzzy system with adaptive capability to extract fuzzy if then rules from input and output sample data through learning the proposed system called radial basis function rbf based adaptive fuzzy system afs employs the gaussian functions to represent the membership functions of the premise part of fuzzy rules three architectural deviations of the rbf based afs are also presented according to different consequence types such as constant first order linear function and fuzzy variable these provide versatility of the network to handle arbitrary fuzzy inference schemes we present examples of system identification and time series prediction to illustrate how to solve these problems and to demonstrate its validity and effectiveness using the rbf based afs

optimal distributed controllers realizable over arbitrary networks in this paper we provide a general networked controller design methodology for networked plants and apply it to solve the optimal mathcal h 2 networked control problem both the plant and the controller are interconnected systems interacting over the same arbitrary directed network with noiseless and delay free communication links we introduce the notions of network implementability and network realizability and analyze the structure of network implementable and realizable systems based on the structural property of network implementable systems under certain network related constraints we characterize the set of all stabilizing controllers that are implementable over the given network using the state space version of youla parametrization moreover we provide a constructive procedure to implement the controllers as sub systems interacting over the given network without affecting the stability of the feedback networked system the distributed mathcal h 2 control problem is then cast as a convex optimization problem and its solution is shown to provide the optimal distributed controller over the given network in terms of its network interacting components the results of this paper allow one to apply many classical results and approaches of multi variable robust control theory to networked systems

stochastic nestedness and the belief sharing information pattern solutions to decentralized stochastic optimization problems lead to recursions in which the state space enlarges with the time horizon thus leading to non tractability of classical dynamic programming a common joint information state supplied to each of the agents leads to a tractable recursion as is evident in the one step delayed information sharing structure case or when deterministic nestedness in information holds when there is a causality relationship as in the case of partially nested information structure however communication requirements for such conditions require exchange of very large data noiselessly hence these assumptions are generally impractical in this paper we present a weaker notion of nestedness which we term as stochastic nestedness which is characterized by a sequence of markov chain conditions it is shown that if the information structure is stochastically nested then an optimization problem is tractable and in particular for lqg problems the team optimal solution is linear despite the lack of deterministic nestedness or partial nestedness one other contribution of this paper is that by regarding the multiple decision makers as a single decision maker and using witsenhausen s equivalent model for discrete stochastic control it is shown that the common state required need not consist of observations and it suffices to share beliefs on the state and control actions a pattern we refer to as k stage belief sharing pattern we discuss the minimum amount of information exchange required to achieve such an information pattern for k 1 the information exchange needed is generally strictly less than what is needed for deterministic nestedness and is zero whenever stochastic nestedness applies in view of nestedness we present a discussion on the monotone values of information channels

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

some results on a starlike log harmonic mapping of order alpha let h d be the linear space of all analytic functions defined on the open unit disc email protected c z 0 g 0 1 on the other hand if f vanishes at z 0 but it is not identically zero then f admits the following representation 0 3 f z z z 2 bh z g z where email protected 12 h z and g z are analytic in the open disc d with the normalization h 0 0 g 0 1 abdulhadi and bshouty 1988 2 abdulhadi and hengartner 1996 3 in the present paper we will give the extent of the idea which was introduced by abdulhadi and bshouty 1988 2 one of the interesting applications of this extent idea is an investigation of the subclass of log harmonic mappings for starlike log harmonic mappings of order alpha

separable and localized system level synthesis for large scale systems a major challenge faced in the design of large scale cyber physical systems such as power systems the internet of things or intelligent transportation systems is that traditional distributed optimal control methods do not scale gracefully neither in controller synthesis nor in controller implementation to systems composed of a large number e g on the order of billions of interacting subsystems this paper shows that this challenge can now be addressed by leveraging the recently introduced system level approach sla to controller synthesis in particular in the context of the sla we define suitable notions of separability for control objective functions and system constraints such that the global optimization problem or iterate update problems of a distributed optimization algorithm can be decomposed into parallel subproblems we then further show that if additional locality i e sparsity constraints are imposed then these subproblems can be solved using local models and local decision variables the sla is essential to maintain the convexity of the aforementioned problems under locality constraints as a consequence the resulting synthesis methods have o 1 complexity relative to the size of the global system we further show that many optimal control problems of interest such as localized lqr and lqg mathcal h 2 optimal control with joint actuator and sensor regularization and localized mixed mathcal h 2 mathcal l 1 optimal control problems satisfy these notions of separability and use these problems to explore tradeoffs in performance actuator and sensing density and average versus worst case performance for a large scale power inspired system

fuzzy input output controllers are universal approximators abstract in this paper we show that a fuzzy input output controller can approximate to any degree of accuracy a continuous fuzzy system this generalizes the known result that fuzzy controllers crisp input output can approximate continuous functions

on limitations in h suboptimal decentralized control derived from the generalized structured singular value abstract we study how the maximum minimum gain of a decentralized or sparse controller over a frequency interval influences the maximum minimum gain of the corresponding closed loop transfer function over that interval in doing so we derive lower bounds on the best closed loop performance achievable by decentralized and sparse controllers satisfying additional frequency domain restrictions and sufficient conditions for a structured controller to guarantee a desired level of closed loop performance this results in graphical tests for the controller s singular value plots these bounds are obtained by using tools inspired by generalizations of the structured singular value and can be computed by solving linear matrix inequalities lmi we close by applying our results to an active sound control problem

a certain class of starlike log harmonic mappings in this paper we investigate some properties of log harmonic starlike mappings for this aim we use the subordination principle or lindelof principle lewandowski 1961 7

fuzzy set based models of neurons and knowledge based networks we will introduce and study different fuzzy set oriented computational models of neurons the generic topologies of the neurons emerging there are significantly influenced by basic logic operators and or not encountered in the theory of fuzzy sets the logical flavor of the proposed constructs is expressed in terms of operators used in their formalization and a way of their superposition in the neurons the two broad categories of neurons embrace basic aggregation neurons named and and or neurons and referential processing units such as matching dominance inclusion neurons the specific features of the neurons are flexibly modeled with the aid of triangular norms the inhibitory and excitatory characteristics are captured by embodying direct and complemented negated input signals we will propose various topologies of neural networks put together with the use of these neurons and demonstrate straightforward relationships coming off between the problem specificity and the resulting architecture of the network this limpid way of mapping the domain knowledge onto the structure of the network contributes significantly toward enhancements in learning processes in the network and substantially facilitates its interpretation

iterative inversion of fuzzified neural networks the inversion of a neural network is a process of computing inputs that produce a given target when fed into the neural network the inversion algorithm of crisp neural networks is based on the gradient descent search in which a candidate inverse is iteratively refined to decrease the error between its output and the target in this paper we derive an inversion algorithm of fuzzified neural networks from that of crisp neural networks first we present a framework of learning algorithms of fuzzified neural networks and introduce the idea of adjusting schemes for fuzzy variables next we derive the inversion algorithm of fuzzified neural networks by applying the adjusting scheme for fuzzy variables to total inputs in the input layer finally we make three experiments on the parity three problem examine the effect of the size of training sets on the inversion and investigate how the fuzziness of inputs and targets of training sets affects the inversion

lq suboptimal decentralised controllers with disturbance rejection property for hierarchical systems this article is concerned with decentralised output regulation of hierarchical systems subject to input and output disturbances it is assumed that the disturbance can be represented as the output of an autonomous linear time invariant lti system with an unknown initial state the primary objective is to design a decentralised controller with the property that not only does it reject the degrading effect of the disturbance on the output to achieve a satisfactory steady state performance it also results in a small linear quadratic lq cost function implying a good transient behaviour to this end the underlying problem is treated in two phases in the first step a number of modified systems are defined in terms of the original system the problem of designing an lq centralised controller which stabilises all the modified systems and rejects the disturbance in the original system is considered and it is shown that this centralised controller can be found efficiently by solving a linear matrix ine

block wise discretization accounting for structural constraints this paper presents an approximate discretization method named mixed euler zoh me zoh which can be applied to any continuous time linear system this method has been explicitly developed to preserve the system sparsity a property that is particularly important when dealing with the analysis and design of distributed controllers for large scale systems in terms of stability preservation as a function of the sampling interval we show that me zoh outperforms the classical forward euler fe approach which is the only known discretization method guaranteeing the preservation of sparsity for all possible sampling times it is then shown that this new discretization method is capable of preserving stability for all sampling times for a wide classes of dynamical systems including the important class of positive systems besides stability also positivity of the resulting discrete time system is preserved contrarily to what happens for the fe approach a couple of examples are reported to illustrate the main theoretical results of the paper

fuzzy regression analysis using neural networks abstract in this paper we propose simple but powerful methods for fuzzy regression analysis using neural networks since neural networks have high capability as an approximator of nonlinear mappings the proposed methods can be applied to more complex systems than the existing lp based methods first we propose learning algorithms of neural networks for determining a nonlinear interval model from the given input output patterns a nonlinear interval model whose outputs approximately include all the given patterns can be determined by two neural networks next we show two methods for deriving nonlinear fuzzy models from the interval model determined by the proposed algorithms nonlinear fuzzy models whose h level sets approximately include all the given patterns can be derived last we show an application of the proposed methods to a real problem

optimal finite time consensus on fixed and periodic graphs synthesis of optimal controllers achieving finite time consensus for multiagent networks described by fixed or periodic connectivity graphs is considered the solution procedure involves posing a partially nested finite horizon decentralized control problem and converting it to a static convex optimization problem by a quadratic invariance argument the dynamic feedback controller thus synthesized optimizes a transient performance measure and guarantees consensus within a minimal number of steps

algebraic decompositions of dp problems with linear dynamics abstract we consider dynamic programming dp problems in which the dynamics are linear the cost is a function of the state and the state space is finite dimensional but defined over an arbitrary field starting from the natural decomposition of the state space into a direct sum of invariant subspaces consistent with the rational canonical form and assuming the cost functions exhibit an additive structure compatible with this decomposition we extract from the original problem two distinct families of smaller dp problems associated with the invariant subspaces each family constitutes a decomposition of the original problem when the optimal policy and value function can be reconstructed from the optimal policies and value functions of the smaller problems we derive necessary and sufficient conditions for these decompositions to exist propose a readily verifiable sufficient condition for the first decomposition and establish a hierarchy relating the two notions of decomposition

decentralized control via grobner bases and variable elimination we consider the problem of optimal decentralized controller synthesis there are several classes of such problems for which effective solution methods are known including the quadratically invariant one in this technical note we use grobner bases and elimination theory to characterize all closed loop maps achievable by forming a feedback loop with decentralized controllers we show that this approach allows solution of a wide class of optimal decentralized control problems it includes not only quadratically invariant problems under a technical condition but also some other problems which are not quadratically invariant

on using a cuts to evaluate fuzzy equations abstract consider an equation y f x1 xn where the extension principle is used to find y f x 1 x n when we subtitute fuzzy numbers x i for the xi 1 i n if x i denotes an cut of x i then we argue that for only certain simple equations will one obtain y equal to f x 1 x n where f is evaluated using interval arithmetic

a study on relationship between generalization abilities and fuzziness of base classifiers in ensemble learning we investigate essential relationships between generalization capabilities and fuzziness of fuzzy classifiers viz the classifiers whose outputs are vectors of membership grades of a pattern to the individual classes the study makes a claim and offers sound evidence behind the observation that higher fuzziness of a fuzzy classifier may imply better generalization aspects of the classifier especially for classification data exhibiting complex boundaries this observation is not intuitive with a commonly accepted position in traditional pattern recognition the relationship that obeys the conditional maximum entropy principle is experimentally confirmed furthermore the relationship can be explained by the fact that samples located close to classification boundaries are more difficult to be correctly classified than the samples positioned far from the boundaries this relationship is expected to provide some guidelines as to the improvement of generalization aspects of fuzzy classifiers

controllability and observability of coordinated linear systems abstract this paper develops concepts of controllability and observability for the class of coordinated linear systems a special class of linear hierarchical systems with a top to bottom information structure the usual concepts of reachability and indistinguishability for linear systems are refined taking into account the decentralized nature of coordinated linear systems the corresponding controllability and observability decompositions are derived and several concepts of controllability and observability for coordinated linear systems are introduced and discussed these results are then combined to a definition and characterization of stabilizability via dynamic measurement feedback for this class of systems

rspop rough set based pseudo outer product fuzzy rule identification algorithm system modeling with neuro fuzzy systems involves two contradictory requirements interpretability verses accuracy the pseudo outer product pop rule identification algorithm used in the family of pseudo outer product based fuzzy neural networks popfnn suffered from an exponential increase in the number of identified fuzzy rules and computational complexity arising from high dimensional data this decreases the interpretability of the popfnn in linguistic fuzzy modeling this article proposes a novel rough set based pseudo outer product rspop algorithm that integrates the sound concept of knowledge reduction from rough set theory with the pop algorithm the proposed algorithm not only performs feature selection through the reduction of attributes but also extends the reduction to rules without redundant attributes as many possible reducts exist in a given rule set an objective measure is developed for popfnn to correctly identify the reducts that improve the inferred consequence experimental results are presented using published data sets and real world application involving highway traffic flow prediction to evaluate the effectiveness of using the proposed algorithm to identify fuzzy rules in the popfnn using compositional rule of inference and singleton fuzzifier popfnn cri s architecture results showed that the proposed rough set based pseudo outer product algorithm reduces computational complexity improves the interpretability of neuro fuzzy systems by identifying significantly fewer fuzzy rules and improves the accuracy of the popfnn

augmented lagrangian approach to design of structured optimal state feedback gains we consider the design of optimal state feedback gains subject to structural constraints on the distributed controllers these constraints are in the form of sparsity requirements for the feedback matrix implying that each controller has access to information from only a limited number of subsystems the minimizer of this constrained optimal control problem is sought using the augmented lagrangian method notably this approach does not require a stabilizing structured gain to initialize the optimization algorithm motivated by the structure of the necessary conditions for optimality of the augmented lagrangian we develop an alternating descent method to determine the structured optimal gain we also utilize the sensitivity interpretation of the lagrange multiplier to identify favorable communication architectures for structured optimal design examples are provided to illustrate the effectiveness of the developed method

intractable problems in control theory this paper is an attempt to understand the apparent intractability of problems in decentralized decision making using the concepts and methods of computational complexity we first establish that the discrete version of an important paradigm for this area proposed by witsenhausen is np complete thus explaining the failures reported in the literature to attack it computationally in the rest of the paper we show that the computational intractability of the discrete version of a control problem the team decision problem in our particular example can imply that there is no satisfactory continuous algorithm for the continuous version to this end we develop a theory of continuous algorithms and their complexity and a quite general proof technique which can prove interesting by themselves

metric spaces of fuzzy sets two classes of metrics are introduced for spaces of fuzzy sets their equivalence is discussed and basic properties established a characterisation of compact and locally compact subsets is given in terms of boundedness and p mean equileft continuity and the spaces shown to be locally compact complete and separable metric spaces

design of optimal controllers for spatially invariant systems with finite communication speed we consider the problem of designing optimal distributed controllers whose impulse response has limited propagation speed we introduce a state space framework in which all spatially invariant systems with this property can be characterized after establishing the closure of such systems under linear fractional transformations we formulate the h 2 optimal control problem using the model matching framework we demonstrate that even though the optimal control problem is non convex with respect to some state space design parameters a variety of numerical optimization algorithms can be employed to relax the original problem thereby rendering suboptimal controllers in particular for the case in which every subsystem has scalar input disturbance scalar measurement and scalar actuation signal we investigate the application of the steiglitz mcbride gauss newton and newton iterative schemes to the optimal distributed controller design problem we apply this framework to examples previously considered in the literature to demonstrate that by designing structured controllers with infinite impulse response superior performance can be achieved compared to finite impulse response structured controllers of the same temporal degree

principal component analysis of fuzzy data using autoassociative neural networks this paper describes an extension of principal component analysis pca allowing the extraction of a limited number of relevant features from high dimensional fuzzy data our approach exploits the ability of linear autoassociative neural networks to perform information compression in just the same way as pca without explicit matrix diagonalization fuzzy input values are propagated through the network using fuzzy arithmetics and the weights are adjusted to minimize a suitable error criterion the inputs being taken as target outputs the concept of correlation coefficient is extended to fuzzy numbers allowing the interpretation of the new features in terms of the original variables experiments with artificial and real sensory evaluation data demonstrate the ability of our method to provide concise representations of complex fuzzy data

a characterization of convex problems in decentralized control ast we consider the problem of constructing optimal decentralized controllers we formulate this problem as one of minimizing the closed loop norm of a feedback system subject to constraints on the controller structure we define the notion of quadratic invariance of a constraint set with respect to a system and show that if the constraint set has this property then the constrained minimum norm problem may be solved via convex programming we also show that quadratic invariance is necessary and sufficient for the constraint set to be preserved under feedback these results are developed in a very general framework and are shown to hold in both continuous and discrete time for both stable and unstable systems and for any norm this notion unifies many previous results identifying specific tractable decentralized control problems and delineates the largest known class of convex problems in decentralized control as an example we show that optimal stabilizing controllers may be efficiently computed in the case where distributed controllers can communicate faster than their dynamics propagate we also show that symmetric synthesis is included in this classification and provide a test for sparsity constraints to be quadratically invariant and thus amenable to convex synthesis

an intelligent stock trading decision support system through integration of genetic algorithm based fuzzy neural network and artificial neural network the stock market which has been investigated by various researchers is a rather complicated environment most research only concerned the technical indexes quantitative factors instead of qualitative factors e g political effect however the latter plays a critical role in the stock market environment thus this study develops a genetic algorithm based fuzzy neural network gfnn to formulate the knowledge base of fuzzy inference rules which can measure the qualitative effect on the stock market next the effect is further integrated with the technical indexes through the artificial neural network ann an example based on the taiwan stock market is utilized to assess the proposed intelligent system evaluation results indicate that the neural network considering both the quantitative and qualitative factors excels the neural network considering only the quantitative factors both in the clarity of buying selling points and buying selling performance

sparse stable systems abstract in the design of decentralized networked systems it is important to know whether a given network topology can sustain stable dynamics we consider a basic version of this problem here given a vector space of sparse real matrices does it contain a stable hurwitz matrix said differently is a feedback channel corresponding to a non zero entry necessary for stabilization or can it be done without we provide in this paper a set of necessary conditions and a set of sufficient conditions for the existence of stable matrices in a vector space of sparse matrices we further prove some properties of the set of sparse matrix spaces that contain hurwitz matrices the conditions we exhibit are most easily stated in the language of graph theory which we thus adopt in this paper

incorporating fuzzy membership functions into the perceptron algorithm the perceptron algorithm one of the class of gradient descent techniques has been widely used in pattern recognition to determine linear decision boundaries while this algorithm is guaranteed to converge to a separating hyperplane if the data are linearly separable it exhibits erratic behavior if the data are not linearly separable fuzzy set theory is introduced into the perceptron algorithm to produce a fuzzy algorithm which ameliorates the convergence problem in the nonseparable case it is shown that the fuzzy perceptron like its crisp counterpart converges in the separable case a method of generating membership functions is developed and experimental results comparing the crisp to the fuzzy perceptron are presented

can neural nets be universal approximators for fuzzy functions abstract we first argue that the extension principle is too computationally involved to be an efficient way for a computer to evaluate fuzzy functions we then suggest using cuts and interval arithmetic to compute the valued of fuzzy functions using the method of computing fuzzy functions we then show that neural nets are universal approximators for computable fuzzy functions when we only input non negative or non positive fuzzy numbers

a convex characterization of multidimensional linear systems subject to sqi constraints this technical note proposes a convex characterization of the set of all stable closed loop linear systems that are obtained from a given plant which may be multidimensional by interconnecting it in feedback with controllers that satisfy a certain pre selected constraint we take an approach that is particularly useful when a doubly coprime factorization of the plant is difficult to obtain and a stable stabilizing controller may not exist the plant is not strongly stabilizable or when one may be difficult to find most related work requires one of these we adopt the so called coordinate free approach which unlike youla s parametrization does not rely on a doubly coprime factorization of the plant we show that if constraints which satisfy a condition called strong quadratic invariance sqi are imposed on the controllers then the set of all stable closed loop multidimensional linear systems has a convex representation and norm optimal control problems can be cast in convex form although the sqi condition is in general slightly stronger than quadratic invariance qi which was developed in related work they are equivalent for common classes of problems arising in decentralized control

explicit solutions to separable problems in optimal cooperative control this paper presents explicit state space solutions for a class of networked cooperative control problems we consider the optimal control problem for a class of systems with dynamics defined at the vertices of a directed acyclic graph and dynamic propagation along the edges of the graph the controller is also constrained to use information flowing along the edges of the graph with the additional assumption of transitive closure such problems have linear optimal controllers we show that under the factorization condition that every disturbance non sink takes state feedback these problems separate into several independent subproblems and hence they can be explicitly solved this technique generalizes and unifies several existing approaches for optimal decentralized control and it further provides the optimal controller for many cases in which the optimal control was previously unknown the optimal solutions are expressed in terms of a series of riccati equations whose sizes are bounded by the system order the separated problems highlight the structure of the optimal controller we demonstrate our approach on a salvo guidance problem for a team of networked missiles

t sum of bell shaped fuzzy intervals the usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of zadeh s extension principle based on a t norm t a t norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation if this arithmetic operation is closed for this class it is important to know which t norms are consistent with a particular type of fuzzy intervals recently dombi and gyorbiro proved that addition is closed if the dombi t norm is used with two bell shaped fuzzy intervals a result proved by mesiar on a strict t norm based shape preserving additions of lr fuzzy intervals with unbounded support is recalled as applications we define a broader class of bell shaped fuzzy intervals then we study t norms which are consistent with these particular types of fuzzy intervals dombi and gyorbiro s results are special cases of the results described in this paper

on approximations of zadeh s extension principle in this paper we provide several results concerning the approximation of zadeh s extension of a given function we provide several simple observations due to which we provide a general procedure allowing to approximate zadeh s extension of any continuous map among other things we demonstrated that the technique of f transform can also be used to approximate this extension further we studied how the choice of the metric on the space of fuzzy sets resp fuzzy numbers can affect the quality of the approximation and we clarified that in comparison to recent habits the choice of the levelwise metric need not be the most appropriate one and that the approximation process could be simplified our results are general in the sense that we mostly require nothing but the continuity of the original map

optimal multivariable controller design using an itse performance index this article deals with the design of optimal controllers and as an embedded problem with the computation of achievable performance bounds in the control of non minimum phase unstable multi input multi output systems the cost function comprises a time weighted measure of the tracking error itse and an incremental quadratic penalisation of the control effort the proposed methodology relies on the properties of a frequency domain generalisation of the itse index the solution to the optimisation problem can be computed using orthonormal basis function expansions and a closed form expression is found for the optimal coefficients of the expansion numerical examples are presented to illustrate the results

on the nearest quadratically invariant information constraint quadratic invariance is a condition which has been shown to allow for optimal decentralized control problems to be cast as convex optimization problems the condition relates the constraints that the decentralization imposes on the controller to the structure of the plant in this technical note we consider the problem of finding the closest subset and superset of the decentralization constraint which are quadratically invariant when the original problem is not we show that this can itself be cast as a convex problem for the case where the controller is subject to delay constraints between subsystems but that this fails when we only consider sparsity constraints on the controller for that case we develop an algorithm that finds the closest superset in a fixed number of steps and discuss methods of finding a close subset

regularization for design when designing controllers for large scale systems the architectural aspects of the controller such as the placement of actuators sensors and the communication links between them can no longer be taken as given the task of designing this architecture is now as important as the design of the control laws themselves by interpreting controller synthesis in a model matching setup as the solution of a particular linear inverse problem we view the challenge of obtaining a controller with a desired architecture as one of finding a structured solution to an inverse problem building on this conceptual connection we formulate and analyze a framework called regularization for design rfd in which we augment the variational formulations of controller synthesis problems with convex penalty functions that induce a desired controller architecture the resulting regularized formulations are convex optimization problems that can be solved efficiently these convex programs provide a unified computationally tractable approach for the simultaneous co design of a structured optimal controller and the actuation sensing and communication architecture required to implement it further these problems are natural control theoretic analogs of prominent approaches such as the lasso the group lasso the elastic net and others that are employed in structured inference in analogy to that literature we show that our approach identifies optimally structured controllers under a suitable condition on a signal to noise type ratio

distributed multi parametric quadratic programming one of the fundamental problems in the area of large scale optimization is to study locality features of spatially distributed optimization problems in which the variables are coupled in the cost function as well as constraints such problems can motivate the development of fast and well conditioned distributed algorithms in this paper we study spatial locality features of large scale multi parametric quadratic programming mpqp problems with linear inequality constraints our main application focus is receding horizon control of spatially distributed linear systems with input and state constraints we propose a new approach for analysis of large scale mpqp problems by blending tools from duality theory with operator theory the class of spatially decaying matrices is introduced to capture couplings between optimization variables in the cost function and the constraints we show that the optimal solution of a convex mpqp is piecewise affine represented as convolution sums more importantly we prove that the kernel of each convolution sum decays in the spatial domain at a rate proportional to the inverse of the corresponding coupling function of the optimization problem

numerical relationships between neural networks continuous functions and fuzzy systems abstract in this survey paper we first discuss computational equivalence between continuous functions regular neural nets fuzzy controllers and discrete fuzzy expert systems we also discuss how to build hybrid neural nets numerically identical to a fuzzy controller or a discrete fuzzy expert system we then discuss computational equivalence between continuous fuzzy functions regular fuzzy neural nets and fuzzy systems we also discuss how to construct hybrid fuzzy neural nets to approximate continuous fuzzy functions

centralized and decentralized solutions of the linear exponential gaussian problem a particular class of stochastic control problems constrained to different information patterns is considered this class consists of minimizing the expectation of an exponential cost criterion with quadratic argument subject to a discrete time gauss markov dynamic system i e the linear exponential gaussian leg control problem besides the one step delayed information pattern previously considered the classical and the one step delayed information sharing osdis patterns are assumed after determining the centralized controller based upon the classical information pattern the optimal decentralized controller based upon the osdis pattern and the solution to a static team problem is found to be affine a unifying approach to determine controllers based upon these three information patterns is obtained by noting that the value of a quadratic exponent of an exponential function is independent of the information structure both necessary and sufficient conditions for the controllers to be minimizing are obtained regardless of the exponential form the negative exponential form is included which is unimodal but not convex

affine controller parameterization for decentralized control over banach spaces we cast the problem of optimal decentralized control as one of minimizing a closed loop norm subject to a subspace constraint on the controller in this note we consider continuous linear operators on banach spaces and show that a simple property called quadratic invariance is necessary and sufficient for the constraint set to be preserved under feedback and thus allows optimal synthesis to be recast as a convex optimization problem these results hold for any norm and any banach space

harmonicity of the inverse of a harmonic diffeomorphism abstract in this paper we obtain a necessary and sufficient condition for the harmonicity of the inverse of a harmonic diffeomorphism as an application we give explicit representations of reversible logharmonic diffeomorphisms as another application we connect the harmonicity of the inverse of a hyperbolic harmonic quasiconformal diffeomorphism with the schoen conjecture

solving systems of linear fuzzy equations abstract in this paper we wish to construct solutions for x to the fuzzy matrix equation ax b when the elements in a and b are triangular fuzzy numbers a is square and always non singular we argue that the previous method of solving for x based on the extension principle and regular fuzzy arithmetic should be abandoned since it too often fails to produce a solution we present six new solutions of which we show that five are identical we then adopt the common value x of these five new solutions as our solution to ax b we show that x is a fuzzy vector which is the generalization to rn of real fuzzy numbers we also show how these results pertain to and extend previous research on this problem within the area of interval analysis

sparsity promoting optimal control of systems with symmetries consensus and synchronization networks abstract optimal control problems in systems with symmetries and consensus synchronization networks are characterized by structural constraints that arise either from the underlying group structure or the lack of absolute measurements for part of the state vector our objective is to design controller structures and resulting control strategies that utilize limited information exchange between subsystems in large scale networks to obtain controllers with low communication requirements we seek solutions to regularized versions of the h 2 optimal control problem non smooth regularization terms are introduced to tradeoff network performance with sparsity of the feedback gain matrix in contrast to earlier results our framework allows the state space representations that are used to quantify the system s performance and sparsity of the static output feedback controller to be expressed in different sets of coordinates we show how alternating direction method of multipliers can be leveraged to exploit the underlying structure and compute sparsity promoting controllers in particular for spatially invariant systems the computational complexity of our algorithm scales linearly with the number of subsystems we also identify a class of optimal control problems that can be cast as semidefinite programs and provide an example to illustrate our developments

an architecture of neural networks with interval weights and its application to fuzzy regression analysis abstract in this paper we first propose an architecture of neural networks that have interval weights and interval biases a neural network with the proposed architecture maps an input vector of real numbers to an output interval the target output is also given as an interval next we define a cost function using the interval output from the neural network and the corresponding target output a learning algorithm is derived from the cost function in a similar manner as the bp back propagation algorithm we also show two variations of the learning algorithm for the proposed architecture which lead to the inclusion relation between the interval output and the interval target last we apply the learning algorithms to fuzzy regression analysis where target outputs are given as fuzzy numbers

max min fuzzy hopfield neural networks and an efficient learning algorithm abstract we set up a dynamical fuzzy neural network system i e the so called max min fuzzy hopfield network in the paper and prove the lyapunov stability of the equilibrium points attractor of the system also we discuss the uniform stability of the system and show some sufficient conditions with which the given fuzzy pattern is the attractor of the system moreover we obtain a nontrivially attractive basin of the attractor therefore our models have good fault tolerance with an analytic method we design an efficient learning algorithm for connected weights of the networks finally simulation examples demonstrate our conclusions

fuzzy nonlinear regression analysis of dose response relationships abstract a general methodology for fuzzy regression is developed and illustrated by analyzing a dose response relationship fuzzy regression is used as an alternative to statistical regression analysis because the relationship between variables is imprecise data are uncertain and sample sizes are insufficient three goodness of fit criteria are used namely the maximum the average vagueness and the prediction vagueness criterion in the case of a nonlinear relationship the calculation of fuzzy regression parameters leads to a nonlinear programming problem this technique is illustrated by the relationship between the dose of a n nitroso compound and the probability of tumor development in rats this relationship is nonlinear imprecise and based on only six data points in the present case three common dose response models are fitted using nonlinear fuzzy regression techniques with the six data points regression parameters have been obtained by minimizing a nonlinear objective function under a set of specific nonlinear constraints the methodology is relatively simple and offers a viable alternative to statistical regression techniques

univalent functions in h _ h d etude des fonctions univalentes dans h h d solutions d une equation aux derivees partielles non lineaire elliptique

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

fuzzy functional analysis i basic concepts properties of continuous functions from the set of fuzzy numbers with support in a closed interval to the set of all fuzzy numbers are investigated associated to the metrics on the set of all fuzzy numbers we give two metrics on the set of all continuous functions and prove that the algebraic operations are continuous

optimal decentralized state feedback control with sparsity and delays this work presents the solution to a class of decentralized linear quadratic state feedback control problems in which the plant and controller must satisfy the same combination of delay and sparsity constraints using a novel decomposition of the noise history the control problem is split into independent subproblems that are solved using dynamic programming the approach presented herein both unifies and generalizes many existing results

analyses of regular fuzzy neural networks for approximation capabilities abstract by introducing a trapezoidal fuzzy function and using the properties of the function we set up a continuously increasing fuzzy function that cannot be arbitrarily closely approximated on a compact set of f 0 r by the regular fuzzy neural network rfnn thus the conclusions in buckley and hayashi fuzzy sets and systems 61 1994 43 51 are improved and the problem if the rfnn is the universal approximator to the class of continuously increasing fuzzy functions is solved finally we obtain the universal approximation to the extended fuzzy functions by rfnn

non stretch mappings for a sharp estimate of the beurling ahlfors operator abstract in this paper we identify certain classes of non stretch mappings that enjoy a sharp estimate of the beurling ahlfors operator we first make use of a property of subharmonic functions to prove that the banuelos wang conjecture and the iwaniec conjecture are true for a class of mappings that satisfy a quasilinear conjugate beltrami equation by utilizing the principal solutions of beltrami equations we further explicitly construct some classes of non stretch mappings for which the banuelos wang conjecture and the iwaniec conjecture are true

the cal h _ 2 control problem for quadratically invariant systems with delays this technical note gives a new solution to the output feedback cal h 2 problem for quadratically invariant communication delay patterns a characterization of all stabilizing controllers satisfying the delay constraints is given and the decentralized cal h 2 problem is cast as a convex model matching problem the main result shows that the model matching problem can be reduced to a finite dimensional quadratic program a recursive state space method for computing the optimal controller based on vectorization is given

stabilization of networked control systems with sparse observer controller networks in this technical note we provide a set of stability conditions for linear time invariant networked control systems with arbitrary topology using a lyapunov direct approach we then use these stability conditions to provide a novel low complexity algorithm for the design of a sparse observer based control network we employ distributed observers by employing the output of other nodes to improve the stability of each observer dynamics to avoid unbounded growth of controller and observer gains we impose bounds on their norms the effects of relaxation of these bounds is discussed when trying to find the complete decentralization conditions

convexity of decentralized controller synthesis in decentralized control problems a standard approach is to specify the set of allowable decentralized controllers as a closed subspace of linear operators this then induces a corresponding set of youla kucera parameters previous work has shown that quadratic invariance of the controller set implies that the set of youla kucera parameters is convex in this technical note we prove the converse we thereby show that the only decentralized control problems for which the set of youla kucera parameters is convex are those which are quadratically invariant we further show that under additional assumptions quadratic invariance is necessary and sufficient for the set of achievable closed loop maps to be convex we give two versions of our results the first applies to bounded linear operators on a banach space and the second applies to possibly unstable causal lti systems in discrete or continuous time

on multistage fuzzy neural network modeling in the past couple of years there has been increasing interest in the fusion of neural networks and fuzzy logic most of the existing fuzzy neural network fnn models have been proposed to implement different types of single stage fuzzy reasoning mechanisms and inevitably they suffer from the dimensionality problem when dealing with complex real world problems to address the problem fnn modeling based on multistage fuzzy reasoning msfr is pursued here and two hierarchical network models namely incremental type and aggregated type are introduced the new models called multistage fnn msfnn model a hierarchical fuzzy rule set that allows the consequence of a rule passed to another as a fact through the intermediate variables from the stipulated input output data pairs they can generate an appropriate fuzzy rule set through structure and parameter learning procedures proposed in this paper in addition we have particularly addressed the input selection problem of these two types of multistage network models and proposed two efficient methods for them the effectiveness of the proposed msfnn models in handling high dimensional problems is demonstrated through various numerical simulations

lq control for coordinated linear systems coordinated linear systems are a special class of hierarchical linear systems with a strict top to bottom information structure the lq problem over all structure preserving static state feedbacks is discussed the overall control problem separates into conditionally independent subproblems a numerical approach to their solution is derived and the behavior and performance of the resulting control law are illustrated in examples

universal approximators for fuzzy functions abstract we show how to construct a large class of universal approximators for fuzzy functions which continuously map fuzzy numbers into fuzzy numbers and are the extension principle extensions of continuous real valued functions one important application is that layered feedforward neural nets with real weights and bias terms and fuzzy signals whose output is computed using the extension principle are universal approximators for these functions

optimal symmetric h sub 2 controllers for systems with collocated sensors and actuators this note addresses the problem of designing the optimal symmetric h 2 controller for a plant with collocated sensors and actuators but with possibly asymmetric disturbance injection and performance specification for such a control problem the generalized plant has a symmetric block representing the transfer matrix from the control input to the measured output a complete solution to the optimal h 2 control problem with the symmetric structural constraint is given in terms of the optimal solution to a standard h 2 model matching problem without the constraint

stabilization of bilinear sparse matrix control systems using periodic inputs abstract in this brief paper using results from the theory of averaging of bilinear systems we provide a graph theoretic characterization for the existence of periodic control inputs that stabilize a sparse matrix system to the origin in particular we introduce a class of extensions to the directed graph corresponding to a given sparse matrix system which when contains a stable sparse matrix system implies that the original system is stabilizable using periodic inputs when this condition holds we provide a systematic procedure for designing such controllers our technical approach combines ideas from the theory of bilinear control systems and averaging theory with graph theoretic results

optimal control of spatially distributed systems in this paper we study the structural properties of optimal control of spatially distributed systems such systems consist of an infinite collection of possibly heterogeneous linear control systems that are spatially interconnected via certain distant dependent coupling functions over arbitrary graphs we study the structural properties of optimal control problems with infinite horizon linear quadratic criteria by analyzing the spatial structure of the solution to the corresponding operator lyapunov and riccati equations the key idea of the paper is the introduction of a special class of operators called spatially decaying sd these operators are a generalization of translation invariant operators used in the study of spatially invariant systems we prove that given a control system with a state space representation consisting of sd operators the solution of operator lyapunov and riccati equations are sd furthermore we show that the kernel of the optimal state feedback for each subsystem decays in the spatial domain with the type of decay e g exponential polynomial or logarithmic depending on the type of coupling between subsystems

dynamic decentralized sequential detection under uniformly distributed observations decentralized sequential detection problems with communicating detectors are solved under the assumptions that the observations are independent and uniformly distributed and that decision errors are uniformly penalized for the cases of one step delayed sequential and nonsequential signaling explicit decision rules are proposed and exact conditions for their member by member optimality are derived these decision rules approximate high performance threshold rules with very strict thresholds when decision errors are heavily penalized

decentralized disturbance accommodation with limited plant model information the design of optimal disturbance accommodation and servomechanism controllers with limited plant model information is studied in this paper we consider discrete time linear time invariant systems that are fully actuated and composed of scalar subsystems each of which is controlled separately and influenced by a scalar disturbance each disturbance is assumed to be generated by a system with known dynamics and unknown initial conditions we restrict ourselves to control design methods that produce structured dynamic state feedback controllers where each subcontroller at least has access to the state measurements of those subsystems that can affect its corresponding subsystem the performance of such control design methods is compared using a metric called the competitive ratio which is the worst case ratio of the cost of a given control design strategy to the cost of the optimal control design with full model information we find an explicit minimizer of the competitive ratio and show that it is undo

sparsity promotion in state feedback controller design a globally convergent algorithm for synthesis of sparse optimal state feedback sosf control of linear time invariant lti systems is proposed this problem is known to be np hard due to its combinatorial nature a structured mathcal h 2 norm controller design problem is intrinsically non convex even if a fixed structure is known in advance the proposed algorithm minimizes the mathcal h 2 norm performance index and simultaneously regularizes the sparsity of the control structure using the l 1 norm it guarantees that the solution converges to a stationary point of the original problem the algorithm is implemented using linear matrix inequalities lmis which are efficient reliable and extendable to other control problems the performance of the proposed algorithm is illustrated with application to several examples the results are also compared with alternating direction method of multiplier admm for sparse lqr design as a special case of the mathcal h 2 norm problem in most instances the appropriate selection of the control structure leads to a near optimal performance index with a substantially reduced number of communication links

hybrid identification in fuzzy neural networks this paper introduces an identification method for nonlinear models in the form of fuzzy neural networks fnn in this model we use two forms of the fuzzy inference methods a simplified and linear fuzzy inference and exploit a standard error back propagation learning algorithm the fnn modeling and identification environment realizes parameter identification through a synergistic usage of clustering techniques genetic optimization and a complex search method we use a hard c means hcm clustering algorithm to determine initial apexes of the membership functions of the information granules used in this fuzzy model the parameters such as apexes of membership functions learning rates and momentum coefficients are then adjusted using hybrid algorithm the proposed hybrid identification algorithm is carried out by combining both genetic optimization genetic algorithm ga and the improved complex method an aggregate objective function performance index with a weighting factor is introduced to achieve a sound balance between approximation and generalization of the model according to the selection and adjustment of the weighting factor of this objective function we reveal how to design a model with sound approximation and generalization abilities the proposed model is experimented with using several time series data gas furnace sewage treatment process and nox emission process data of gas turbine power plant

fuzzy least squares abstract several models for simple least squares fitting of fuzzy valued data are developed criteria are given for when fuzzy data sets can be fitted to the models and analogues of the normal equations are derived

solving fuzzy equations we start in the next section 10 2 with looking at possible solutions to the simple fuzzy linear equation overline a cdot overline x overline b overline c we discuss three different types of solution which we have studied before in solving fuzzy equations then we present a fourth type of solution based on our fuzzy monte carlo method in section 10 2 2 this new solution is based on random fuzzy numbers in section 10 3 we look at only classical solutions to the fuzzy quadratic equation and apply our fuzzy monte carlo method to obtain new solutions then in section 10 4 we consider the fuzzy matrix equation overline a cdot overline x overline b and a number of solution types for overline x and then another solution based on fuzzy monte carlo techniques the last section contains a brief summary and our conclusions

robust stabilization of nonlinear interconnected systems by decentralized dynamic output feedback the objective of this note is to propose a dynamic output control scheme within the lmi framework for robust decentralized stabilization of systems composed of linear dynamic subsystems coupled by static nonlinear interconnections satisfying quadratic constraints the procedure utilizes the general linear dynamic feedback structure and consists of two steps the first giving a block diagonal lyapunov matrix together with the robustness degree and the second the controller parameters a numerical example illustrates the applicability of the method

univalent harmonic functions several families of complex valued univalent harmonic functions are studied from the point of view of geometric function theory one class consists of mappings of a simply connected domain onto an infinite horizontal strip with a normalization at the origin extreme points and support points are determined as well as sharp estimates for fourier coefficients and distortion theorems next mappings in izi 1 are considered that leave infinity fixed some coefficient estimates distortion theorems and covering properties are obtained for such mappings with real boundary values many extremal problems are solved explicitly

fuzzy neural networks a survey abstract in this paper a fuzzy neural network will be a layered feedforward neural net that has fuzzy signals and or fuzzy weights we survey recent results on learning algorithms and applications for fuzzy neural networks

from global finite time linear computations to local edge based interaction rules a network of locally interacting agents can be thought of as performing a distributed computation but not all computations can be faithfully distributed this technical note investigates which global linear transformations can be computed in finite time using local rules with time varying weights i e rules which rely solely on information from adjacent nodes in a network the main result states that a linear transformation is computable in finite time using local rules if and only if the transformation has positive determinant an optimal control problem is solved for finding the local interaction rules and simulations are performed to elucidate how optimal solutions can be obtained

can fuzzy neural nets approximate continuous fuzzy functions abstract we first argue that regular fuzzy neural nets based on standard fuzzy arithmetic and the extension principle cannot be universal approximators this negative result is surprising since regular neural nets are universal approximators we then argue that hybrid fuzzy neural nets not necessarily based on standard fuzzy arithmetic can be universal approximators