comprehensive analysis of a new fuzzy rule interpolation method the first published result in fuzzy rule interpolation was the spl alpha cut based fuzzy rule interpolation termed as kh fuzzy rule interpolation originally devoted for complexity reduction a modified version of the kh approach has been presented by yam et al 1999 which eliminates the subnormality problem while at the same time intending to maintain the advantageous computational properties of the original method this paper presents a comprehensive analysis of the new method which includes detailed comparison with the original kh fuzzy rule interpolation method concerning the explicit functions of the methods preservation of piecewise linearity and stability the fuzziness of the conclusion with respect to the fuzziness of the observation is also investigated in comparison with several interpolation techniques all these comparisons shows that the new method preserves the advantageous properties of the kh method and alleviates its most significant disadvantage the problem of subnormality

nonlinear control of feedforward systems with bounded signals the stabilization problem for a class of nonlinear feedforward systems is solved using bounded control it is shown that when the lower subsystem of the cascade is input to state stable and the upper subsystem not exponentially unstable global asymptotic stability can be achieved via a simple static feedback having bounded amplitude that requires knowledge of the upper part of the state only this is made possible by invoking the bounded real lemma and a generalization of the small gain theorem thus stabilization is achieved with typical saturation functions saturations of constant sign or quantized control moreover the problem of asymptotic stabilization of a stable linear system with bounded outputs is solved by means of dynamic feedback finally a new class of stabilizing control laws for a chain of integrators with input saturation is proposed some robustness issues are also addressed and the theory is illustrated with examples on the stabilization of physical systems

stabilization of linear systems in the presence of output measurement saturation this note considers siso nonlinear systems which have a linear controllable and observable part followed by a measurement saturation nonlinearity a controller is presented which feeds back only the saturating output measurements and nevertheless globally asymptotically stabilizes the system the equilibrium is actually reached in finite time i e the controller is dead beat

identifying codes and covering problems the identifying code problem for a given graph involves finding a minimum set of vertices whose neighborhoods uniquely overlap at any given graph vertex initially introduced in 1998 this problem has demonstrated its fundamental nature through a wide variety of applications such as fault diagnosis location detection and environmental monitoring in addition to deep connections to information theory superimposed and covering codes and tilings this work establishes efficient reductions between the identifying code problem and the well known set covering problem resulting in a tight hardness of approximation result and novel provably tight polynomial time approximations the main results are also extended to r robust identifying codes and analogous set 2r 1 multicover problems finally empirical support is provided for the effectiveness of the proposed approximations including good constructions for well known topologies such as infinite two dimensional grids

semi global stabilization of linear systems subject to output saturation abstract it is established that a siso linear stabilizable and detectable system subject to output saturation can be semi globally stabilized by linear output feedback if all its invariant zeros are in the closed left half plane no matter where the open loop poles are this result complements a recent result that such systems can always be globally stabilized by discontinuous nonlinear feedback laws and can be viewed as dual to a well known result a linear stabilizable and detectable system subject to input saturation can be semi globally stabilized by linear output feedback if all its poles are in the open left half plane no matter where the invariant zeros are

input to state stabilization of linear systems with positive outputs this paper considers the problem of stabilization of linear systems for which only the magnitudes of outputs are measured it is shown that if a system is controllable and observable then one can find a stabilizing controller which is robust with respect to observation noise in the iss sense

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

stabilization of linear controllable systems by means of bounded continuous nonlinear feedback control abstract using an inner ellipsoidal approximation to the controllable set of controllable linear systems a bounded continuous nonlinear stabilizing feedback control is designed the resulting control is a smooth local approximation to the time optimal control in particular this design approach is used to globally stabilize the n th order integrator system

on the hardness of approximating minimization problems we prove results indicating that it is hard to compute efficiently good approximate solutions to the graph coloring set covering and other related minimization problems specifically there is an e 0 such that graph coloring cannot be approximated with ratio n e unless p np set covering cannot be approximated with ratio c log n for any c 1 4 unless np is contained in dtime n poly log n similar results follow for related problems such as clique cover fractional chromatic number dominating set and others

adaptive control of weiner type nonlinear systems abstract this study is concerned with the problem of adaptive control of a wiener type nonlinear process it is assumed that the linear dynamic part of the process can be represented by a pulse transfer function of known order with stable inverse followed by a known time delay the memoryless nonlinearity is one to one on a compact set and belongs to one of two classes 1 piecewise linear with known breakpoints or 2 smooth function in which case an approximation is made it is represented by linear splines the output signal from the linear part is not available for measurement the global stability of the proposed model reference adaptive control scheme is established subject to the assumption that the nonlinearity can be represented exactly by the linear spline function with a given set of breakpoints otherwise there will be a residual tracking error which depends on the nonlinearity approximation error but the boundedness of all signals can be assured the proposed scheme is used for adaptive control of the ph process in a continuous flow reactor

stabilization of nonlinear discrete time systems using state detection some recent results concerning stabilization of continuous time systems using state detection are extended to the case of discrete time nonlinear systems it is shown that if a discrete time locally detectable system can be stabilized by a state feedback law then it can also be stabilized by a feedback law that depends on the output of a weak detector

geometric compatibility modification abstract compatibility modification is a rule based inference strategy that uses the similarity of the input with the antecedent of a rule to modify the consequent existing compatibility modification inference techniques have employed a set theoretic assessment of compatibility in this paper a distance based compatibility measure is derived from a generalization of the dissemblance index for fuzzy sets this measure is then used to develop an inference technique based on geometric compatibility this geometric approach is compared with two other distance based inference techniques linear rule interpolation and bound dependent linear revision

alarm placement in systems with fault propagation abstract in this paper we consider systems that can be modeled as directed acyclic graphs such that nodes represent components of the system and directed edges represent fault propagation between components some components can be equipped with alarms that ring when they detect faulty abnormal behavior we study algorithms that attempt to minimize the number of alarms to be placed so that a fault at any single component can be detected and uniquely diagnosed we first show that the minimization problem is intractable i e np hard even when restricted to three level graphs in which all nodes have outdegree two or less we present optimal algorithms for three special classes of graphs tree structured graphs single entry single exit series parallel graphs and two level graphs we then present a polynomial time approximation algorithm for the general case which guarantees that the ratio of the number of alarms placed to the optimum required is within a factor that is logarithmic in the number of nodes in the graph moreover by showing a reduction from the minimum dominating set problem to the minimum alarm set problem we argue that this performance guarantee is tight to within a constant factor finally we demonstrate the connection between the minimum alarm set problem and the minimum test collection problem and prove similar results

model recovery anti windup for output saturated siso linear closed loops we define model recovery anti windup for siso linear control systems with output saturation we address the problem by relying on a hybrid modification of the linear closed loop which employs a suitable logic variable to activate deactivate various components of a control scheme the scheme relies on a finite time observation law an open loop observer and an open loop input generator which is capable of driving the plant output within the saturation limits then the control scheme is based on suitable hybrid resetting laws allowing the controller to operate on the artificial output signal generated by the open loop observer when the actual plant output is outside the saturation limits unlike existing results not only we prove uniform global asymptotic stability of the closed loop but we also prove the local preservation and global recovery properties typical of model recovery anti windup paradigms we also illustrate the proposed technique on an example study

semiglobal regulation of linear systems in presence of measurement constraint in this note we consider the problem of output regulation for linear single input single output systems in presence of time varying measurement constraint it is shown how an internal model based regulator processing a saturated uncertain function of the regulated error can be designed in order to secure asymptotic tracking rejection of exosystem generated references disturbances the design is semiglobal in the initial state of the plant and of the exosystem and requires the zero dynamics of the controlled system to be weakly minimum phase

a similarity measure for fuzzy rulebases based on linguistic gradients fuzzy rulebases are an approximate representation of some interesting system as such they could potentially be used for indexing and searching candidate solutions in case based reasoning cbr systems in a variety of application areas however there is currently no method for directly and efficiently determining the similarity between two rulebases which is a necessary element of their use in any cbr system we propose a method for measuring similarity between two linguistic fuzzy rulebases based on the granular computing technique of linguistic gradients the proposed similarity measure is based on comparing the linguistic structure of two rulebases using the linguistic gradient operator to reveal that structure our algorithm operates at the level of linguistic rulebases rather than a defuzzified reasoning surface and thus belongs to the computing with words paradigm in a validation experiment we compare our new method with the root mean square difference between reasoning surfaces for 603 pairs of fuzzy rulebases drawn from the literature a spearman correlation analysis shows that our new linguistic method is consistent with the numerical rms results while being theoretically and empirically faster than computing an accurate rms difference

output feedback stabilization of a class of wiener systems a globally stabilizing output feedback controller is designed for a class of continuous time wiener systems the wiener systems we consider consist of a linear dynamical block and an output polynomial nonlinearity connected in series the hybrid controller consists of three modes of operation which are periodically applied to the system the controller achieves a dead beat response of the closed loop system

a delay dependent approach to h filtering for stochastic delayed jumping systems with sensor non linearities in this paper a delay dependent approach is developed to deal with the stochastic h filtering problem for a class of ito type stochastic time delay jumping systems subject to both the sensor non linearities and the exogenous non linear disturbances the time delays enter into the system states the sensor non linearities and the external non linear disturbances the purpose of the addressed filtering problem is to seek an h filter such that in the simultaneous presence of non linear disturbances sensor non linearity as well as markovian jumping parameters the filtering error dynamics for the stochastic time delay system is stochastically stable with a guaranteed disturbance rejection attenuation level by using ito s differential formula and the lyapunov stability theory we develop a linear matrix inequality approach to derive sufficient conditions under which the desired filters exist these conditions are dependent on the length of the time delay we then characterize the expression of the fi

improvements and critique on sugeno s and yasukawa s qualitative modeling investigates sugeno s and yasukawa s 1993 qualitative fuzzy modeling approach we propose some easily implementable solutions for the unclear details of the original paper such as trapezoid approximation of membership functions rule creation from sample data points and selection of important variables we further suggest an improved parameter identification algorithm to be applied instead of the original one these details are crucial concerning the method s performance as it is shown in a comparative analysis and helps to improve the accuracy of the built up model finally we propose a possible further rule base reduction which can be applied successfully in certain cases this improvement reduces the time requirement of the method by up to 16 in our experiments

semiglobal stabilization of multi input linear systems with saturated linear state feedback abstract for multi input linear systems with eigenvalues in the closed left half comlex plane we address the problem of stabilization by a linear state feedback subject to saturation using an eigenvalue generalized eigenvector assignment technique we prove that such systems can be semiglobally stabilized with a saturated linear state feedback based on this result we propose an algorithm to calculate an e parametrized family of state feedback gain matrices that semiglobally stabilize the system two examples are used to illustrate the results

gradual inference rules in approximate reasoning abstract gradual inference rules of the form the more x is f the more y is g or of similar forms with the less instead of the more which express a progressive change of the degree to which the entity y satisfies the gradual property g when the degree to which the entity x satisfies the gradual property f is modified are often encountered in commonsense reasoning a representation of such rules by means of fuzzy sets is proposed and discussed this representation turns out to be based on a special implication function already considered in multiple valued logic patterns of reasoning involving gradual inference rules are formalized their links with interpolation mechanisms are pointed out

regranulation a granular algorithm enabling communication between granular worlds abstract in this paper we describe a granular algorithm for translating information between two granular worlds represented as fuzzy rulebases these granular worlds are defined on the same universe of discourse but employ different granulations of this universe in order to translate information from one granular world to the other we must regranulate the information so that it matches the information granularity of the target world this is accomplished through the use of a first order interpolation algorithm implemented using linguistic arithmetic a set of elementary granular computing operations we first demonstrate this algorithm by studying the common fuzzy pd rulebase at several different granularities and conclude that the 3 3 granulation may be too coarse for this objective we then examine the question of what the natural granularity of a system might be this is studied through a 10 fold cross validation experiment involving three different granulations of the same underlying mapping for the problem under consideration we find that a 7 7 granulation appears to be the minimum necessary precision

global stabilization by output feedback examples and counterexamples abstract we show by means of examples that global complete observability and global stabilizability by state feedback are not sufficient to guarantee global stabilizability by dynamic output feedback we show that a main obstruction is related to unboundedness unobservability this is that some unmeasured state components may escape in finite time whereas the measurements remain bounded

a comparison of similarity measures of fuzzy values abstract this paper extends the work of pappis and karacapilidis 1993 to present and compare the properities of several measures of similarity of fuzzy values the measures examined in this paper are based on the geometric model the set theoretic approach and the matching function s we presented in chen 1988 it is shown that several properties are common to all measures and some properties do not hold for all of them

semi global exponential stabilization of linear discrete time systems subject to input saturation via linear feedbacks abstract in this paper we show that a linear discrete time system subject to input saturation is semi globally exponentially stabilizable via linear state and or output feedback laws as long as the system in the absence of input saturation is stabilizable and detectable and has all its poles located inside or on the unit circle furthermore the semi globally stabilizing feedback laws are explicitly constructed the results presented here are parallel to our earlier results on the continuous time counterpart lin and saberi 1993