decentralized and adaptive nonlinear tracking of large scale systems via output feedback presents a solution to the problem of decentralized adaptive asymptotic tracking for a class of large scale systems using nonlinear output feedback the proposed constructive approach does not require any matching conditions on the parametric uncertainties nor growth conditions of any kind on the subsystem and interacting output nonlinearities any decentralized system in the family may have an unknown nonzero equilibrium point partially decentralized reduced order filters are presented to recover the unmeasured states the recursive decentralized output feedback design procedure is illustrated in a practical example of two inverted pendulums on carts without velocity measurements the effectiveness of the decentralized algorithm is supported by simulation results

decentralized filtered dynamic inversion for uncertain minimum phase systems decentralized filtered dynamic inversion is a control method for uncertain linear time invariant systems that are minimum phase have multi input multi output decentralized subsystems and are potentially subject to unknown disturbances this controller requires limited model information specifically knowledge of the relative degree and an estimate of the first nonzero markov parameter for each local subsystem decentralized filtered dynamic inversion is effective for command following and rejection of unknown disturbances we derive the decentralized filtered dynamic inversion controller and analyzes the closed loop stability and performance i e command following error we show that for sufficiently large choice of a single control parameter the closed loop system is asymptotically stable and the average power of the performance is arbitrarily small

the geometry of the universal teichmuller space and the euler weil petersson equation on the identity component of the universal teichmuller space endowed with the takhtajan teo topology the geodesics of the weil petersson metric are shown to exist for all time this component is naturally a subgroup of the quasisymmetric homeomorphisms of the circle viewed this way the regularity of its elements is shown to be h3 2 epsilon for all epsilon 0 the evolutionary pde associated to the spatial representation of the geodesics of the weil petersson metric is derived using multiplication and composition below the critical sobolev index 3 2 geodesic completeness is used to introduce special classes of solutions of this pde analogous to peakons our setting is used to prove that there exists a unique geodesic between each two shapes in the plane in the context of the application of the weil petersson metric in imaging c 2015 elsevier inc all rights reserved

brief decentralized control and disturbance attenuation for large scale nonlinear systems in generalized output feedback canonical form a global decentralized robust adaptive output feedback dynamic compensator is proposed for stabilization tracking and disturbance attenuation of the decentralized generalized output feedback canonical form this represents the largest class for which decentralized robust adaptive output feedback tracking and disturbance attenuation results are currently available the system is allowed to contain unknown parameters multiplying output dependent nonlinearities and also unknown nonlinearities satisfying certain bounds under the assumption that a constant matrix can be found for each subsystem to achieve a certain property it is shown that reduced order observers and backstepping controllers can be designed to achieve practical stabilization of the tracking error in each subsystem in the presence of bounded disturbance inputs sufficient conditions under which asymptotic tracking and stabilization can be achieved are also obtained signal gains from disturbance inputs to tracking errors are presented in the input to output practical stability and integral input to output practical stability frameworks a particular case in which the standard l 2 gain disturbance attenuation is achieved is also provided

how well does the owa operator represent real preferences we present the results of an empirical study in which we analyze the ability of the ordered weighted average owa operator to model actual preferences in a multi attribute ranking task we compare the owa to a competing model simple additive weighting saw and we also study whether its characteristic feature the ability to represent different attitudes toward compensation among attributes is reflected in the preferences provided by subjects we find that in general the owa model fits slightly less well to empirical data subjects whose preferences are better explained by the saw model are also more consistent in their choice behavior our results furthermore indicate that preferences of most subjects are not fully compensatory thus the ability of the owa operator to represent different attitudes toward compensation can be a useful feature in modeling actual preferences the structure of the weights estimated for the owa operator also suggests that it might provide a good approximation to certain types of decision heuristics

on the destabilizing effect of cross coupling in decentralized adaptive control abstract the stability of square multivariable linear time invariant lti systems coupled with an adaptive controller for which the process cross coupling terms have been neglected is studied in this paper our aim is to find conditions over the reference signals richness and the process transfer matrix frequency response such that for sufficiently small adaptation rates the stability of the adaptive system is insured it is shown that if the adaptive system without interconnections is stable then stability of the overall system is preserved if either 1 the frequency bands of the reference signals are non overlapping 2 when there is a spectrum overlap each output of the lti system to input signals in this spectrum has an average energy where the contribution from its corresponding input is larger than the one due to the other inputs global results are obtained for a simple single parameter adaptation scheme the extension to general adaptive controllers is straightforward in a local context 5

bi matching a new preference assessment method to reduce compatibility effects preference models and utility functions are often assessed by eliciting value trade offs among attributes prior research has shown that trade off judgments can be biased in systematic ways for example the attribute which is used as response receives more relative subjective weight i e the so called scale compatibility effects tversky et al tversky a s sattath p slovic 1988 contingent weighting in judgment and choice psych rev 95 371 384 this paper proposes a new procedure to elicit value trade offs called bidimensional matching or bi matching designed to alleviate this effect bi matching differs from traditional trade off judgments in that both attributes are adjusted simultaneously to reach indifference judgments bi matching is compared with simple matching and choice in four experimental studies to measure preferences for lotteries and riskless multiattribute alternatives the main results are 1 bi matching produces trade offs intermediate between those derived from matching on the more important attribute and matching on the less important attribute although closer to the former 2 the trade offs derived from choice reflect more relative weight on the more important dimension than those from bi matching 3 bi matching appears to reduce response error compared to standard matching these results are generally consistent with theoretical predictions we discuss the normative question of which preference assessment method is preferable the current results as a whole and the built in features of the bi matching procedure already position this elicitation method as a worthwhile alternative to traditional methods for helping decision makers introspect and construct their value trade offs

lottery equivalents reduction of the certainty effect problem in utility assessment this note describes a simple procedure for assessing utility functions which avoids many difficulties of the standard techniques the conventional methods suffer from at least three drawbacks they 1 generate utility functions that depend on the probability levels used 2 chain responses from one question to the next so that any bias is propagated and even magnified and 3 change ranges and reference points constantly introducing range effects and other distortions noting the evidence linking the dependence of utility functions on the certainty effect our method 1 compares lotteries with other lotteries rather than certain amounts 2 does not chain responses and 3 consistently uses elementary lotteries which control for range and reference points experimental work supports the proposed procedure

decentralized control design for large scale systems with strong interconnections using neural networks we propose a decentralized neural network nn controller for a class of large scale nonlinear systems with the strong interconnections the nns are used to approximate the unknown subsystems and interconnections due to the functional approximation capabilities of nns the additional precautions are not required to be made for avoiding the possible control singularity problems semiglobal asymptotic stability results are obtained and the tracking error converges to zero furthermore the issue of transient performance of the subsystems is also addressed under an analytical framework

decentralized nonlinear output feedback stabilization with disturbance attenuation as a continuation of our recent work 1999 this paper addresses the problem of decentralized robust output feedback stabilization with disturbance attenuation for large scale systems with strong nonlinear interconnections we focuses on a constructive solution to this decentralized control problem without requiring common matching and growth conditions appearing in the past literature the decentralized output feedback laws proposed achieve internal global asymptotic stability in the sense of lyapunov and external stability in the sense of sontag 1995 1998

analytic dependence of riemann mappings for bounded domains and minimal surfaces in this paper we prove that the functional which takes a closed lavrentiev curve to the corresponding riemann mapping is locally lipl on the set of all closed lavrentiev curves this set is a subset of bmo t it is however not open in bmo t we also prove that the previous functional is analytic for certain classes of closed lavrentiev curves including the class of curves which have some symmetry with respect to the unit circle these classes of curves are submanifolds of bmo t finally we consider the functional which takes a lavrentiev curve closed or not in n dimensional euclidean space to the corresponding minimal surface and we study the differentiability and analyticity of this functional on certain function spaces 1993 john wiley sons inc

decentralized dynamic output feedback control of nonlinear interconnected systems the problem of robust stabilization is considered for a class of nonlinear interconnected systems which consist of linear subsystems coupled by nonlinear interconnections that are unknown and quadratically bounded a decentralized dynamic output feedback based linear controller is proposed where the feedback gain matrices of local controllers are obtained by solving an optimization problem subject to linear matrix inequalities local sliding mode observers are employed to asymptotically estimate the subsystems states and at the same time to reconstruct the unknown nonlinear interconnections the closed loop system driven by the proposed decentralized dynamic output feedback controller is guaranteed to be connectively stable with maximized interconnection bounds

a parameter free elicitation of the probability weighting function in medical decision analysis an important reason why people violate expected utility theory is probability weighting previous studies on the probability weighting function typically assume a specific parametric form exclude heterogeneity in individual preferences and exclusively consider monetary decision making this study presents a method to elicit the probability weighting function in rank dependent expected utility theory that makes no prior assumptions about the functional form of the probability weighting function we use both aggregate and individual subject data thereby allowing for heterogeneity of individual preferences and we examine probability weighting in a new domain medical decision making there is significant evidence of probability weighting both at the aggregate and at the individual subject level the modal probability weighting function is inverse s shaped displaying both lower subadditivity and upper subadditivity probability weighting is in particular relevant at the boundaries of the unit interval compared to studies involving monetary outcomes we generally find more elevation of the probability weighting function the robustness of the empirical findings on probability weighting indicates its importance ignoring probability weighting in modeling decision under risk and in utility measurement is likely to lead to descriptively invalid theories and distorted elicitations

weil petersson teichmuller space revisited abstract in our previous paper 23 it was proved that a sense preserving homeomorphism g on the unit circle s 1 belongs to the weil petersson class wp s 1 namely g can be extended to a quasiconformal mapping to the unit disk whose beltrami coefficient is square integrable in the poincare metric if and only if g is absolutely continuous such that log g belongs to the sobolev class h 1 2 in this sequel to 23 we show that the smooth hilbert manifold structure on wp s 1 inherited from h 1 2 by the pullback g log g is compatible with the standard hilbert manifold structure introduced by takhtajan teo 27 this enables us to give a fast approach to some results in our previous papers 23 and 24

robust redesign of adaptive control effects of unmodeled high frequency dynamics on stability and performance of adaptive control schemes are analyzed in the regulation problem global stability properties are no longer guaranteed but a region of attraction exists for exact adaptive regulation the dependence of the region of attraction on unmodeled parasitics is examined first then the general case of model reference adaptive control is considered in which parasitics can destroy stability and boundedness properties a modified adaptive law is proposed guaranteeing the existence of a region of attraction from which all signals converge to a residual set which contains the equilibrium for exact tracking the size of this set depends on design parameters the frequency range of parasitics and the reference input signal characteristics

on stability l2 gain and h control for switched systems this paper addresses the issues of stability l 2 gain analysis and h control for switched systems via multiple lyapunov function methods a concept of general lyapunov like functions is presented a necessary and sufficient condition for stability of switched systems is given in terms of multiple generalized lyapunov like functions which enables derivation of improved stability tests an l 2 gain characterization and a design method for stabilizing switching laws a solution to the h control problem for switched systems is also provided

indirect adaptive control for interconnected systems an indirect adaptive controller for interconnected systems is introduced each subsystem is subject to bounded disturbances and to possibly unbounded interconnections with other subsystems a variable dead zone is incorporated into a gradient estimation scheme to limit the effects of the interconnections and disturbances an adaptive state feedback control law is described which stabilizes the interconnected system forcing the input and output signals of each subsystem to remain bounded

weil petersson teichmuller space iii dependence of riemann mappings for weil petersson curves the classical riemann mapping theorem implies that there exists a so called riemann mapping which takes the upper half plane onto the left domain bounded by a jordan curve in the extended complex plane the primary purpose of the paper is to study the basic problem how does a riemann mapping depend on the corresponding jordan curve we are mainly concerned with those jordan curves in the weil petersson class namely the corresponding riemann mappings can be quasiconformally extended to the whole plane with beltrami coefficients being square integrable under the poincare metric after giving a geometric characterization of a weil petersson curve we endow the space of all normalized weil petersson curves with a new real hilbert manifold structure in a geometric manner and show that this new structure is topologically equivalent to the standard complex hilbert manifold structure which implies that an appropriately chosen riemann mapping depends continuously on a weil petersson curve and vice versa this can be considered as the first result about the continuous dependence of riemann mappings on non smooth jordan curves

optimal complexity reduction of polyhedral piecewise affine systems this paper focuses on the np hard problem of reducing the complexity of piecewise polyhedral systems e g polyhedral piecewise affine pwa systems the results are fourfold firstly the paper presents two computationally attractive algorithms for optimal complexity reduction that under the assumption that the system is defined over the cells of a hyperplane arrangement derive an equivalent polyhedral piecewise system that is minimal in the number of polyhedra the algorithms are based on the cells and the markings of the hyperplane arrangement in particular the first algorithm yields a set of disjoint non overlapping merged polyhedra by executing a branch and bound search on the markings of the cells the second approach leads to non disjoint overlapping polyhedra by formulating and solving an equivalent and well studied logic minimization problem secondly the results are extended to systems defined on general polyhedral partitions and not on cells of hyperplane arrangements thirdly the paper proposes a technique to further reduce the complexity of piecewise polyhedral systems if the introduction of an adjustable degree of error is acceptable fourthly the paper shows that based on the notion of the hyperplane arrangement pwa state feedback control laws can be implemented efficiently three examples including a challenging industrial problem illustrate the algorithms and show their computational effectiveness in reducing the complexity by up to one order of magnitude

brief paper tracking and synchronisation for a class of pwa systems in this paper the tracking problem for a class of discontinuous piecewise affine pwa systems is addressed we propose an observer based output feedback control design consisting of a feedforward a piecewise affine feedback law and a model based observer solving the tracking problem these synthesis results can also be employed to tackle the master slave synchronisation problem for pwa systems it is shown that for certain classes of pwa systems the design is characterised in terms of linear matrix inequalities the results are illustrated by application to mechanical systems with discontinuous friction characteristics

chord arc curves and the beurling transform we study the relation between the geometric properties of a quasicircle gamma and the complex dilatation mu of a quasiconformal mapping that maps the real line onto gamma denoting by s the beurling transform we characterize bishop jones quasicircles in terms of the boundedness of the operator i mu s on a particular weighted l 2 space and chord arc curves in terms of its invertibility as an application we recover the l 2 boundedness of the cauchy integral on chord arc curves

dissipativity theory for switched systems a framework of dissipativity theory for switched systems using multiple storage functions and multiple supply rates is set up each subsystem of a switched system is associated with a storage function to describe the energy stored in the subsystem and is associated with a supply rate that represents energy coming from outside the subsystem when the subsystem is active the exchange of energy between the active subsystem and an inactive subsystem is characterized by cross supply rates stability is reached when all supply rates can be made negative as long as the total exchanged energy between the active subsystem and any inactive subsystems is finite in some sense two special forms of dissipativity passivity and l 2 gain are addressed for both cases asymptotic stability is guaranteed under certain negative output feedback plus asymptotic zero state detectability switched passivity conditions and switched l 2 gain inequalities are respectively derived which are generalizations of classical ones feedback invariance of passivity and a small gain theorem are also given

locally univalent functions vmoa and the dirichlet space we study geometric properties of the image of the unit circle under a bounded locally univalent function g such that log g belongs either to the dirichlet space d vmoa or the little bloch space b 0 concerning vmoa and b 0 our findings generalize the corresponding results for conformal maps shown by pommerenke in the late 1970s in the case of d we give a strictly geometric necessary condition for g to satisfy log g is an element of d and also offer two different semi geometric characterizations of when log g is an element of d

fuzzy adaptive decentralized output feedback control for large scale nonlinear systems with dynamical uncertainties in this paper an adaptive fuzzy decentralized robust output feedback control approach is proposed for a class of large scale strict feedback nonlinear systems with the unmeasured states the large scale nonlinear systems in this paper are assumed to possess the unstructured uncertainties unmodeled dynamics and unknown high frequency gain sign fuzzy logic systems are used to approximate the unstructured uncertainties k filters are designed to estimate the unmeasured states and a dynamical signal and a special nussbaum gain function are introduced into the control design to solve the problem of unknown high frequency gain sign and dominate unmodeled uncertainties respectively based on the backstepping design and adaptive fuzzy control methods an adaptive fuzzy decentralized robust output feedback control scheme is developed it is proved that the proposed adaptive fuzzy control approach can guarantee that all the signals in the closed loop system are uniformly and ultimately bounded and the tracking errors converge to a small neighborhood of the origin the effectiveness of the proposed approach is illustrated by using simulation results

modified error decentralized control with observer backstepping in this paper an output feedback version of the modified error method is presented for linear coupled plants the novelty lies in the combination of a modified control function of lyapunov with the observer backstepping technique to obtain a totally decentralized output feedback scheme furthermore the design algorithm is presented in a new recursive form that goes beyond the general expressions yielded by the backstepping the decentralization i e the elimination of the cross terms from the obtained multivariable controller is rendered possible by a new choice of the regulated errors in the backstepping procedure the internal stability and the tracking performances of the closed loop system are still preserved as long as the observer convergence is guaranteed and the h x norm of the plant interaction quotient is less than one the developed scheme is successfully applied to the control of a rougher flotation phenomenological simulator

parameter free elicitation of utility and probability weighting functions this paper proposes a two step method to successively elicit utility functions and decision weights under rank dependent expected utility theory and its more descriptive version cumulative prospect theory the novelty of the method is that it is parameter free and thus elicits the whole individual preference functional without imposing any prior restriction this method is used in an experimental study to elicit individual utility and probability weighting functions for monetary outcomes in the gain and loss domains concave utility functions are obtained for gains and convex utility functions for losses the elicited weighting functions satisfy upper and lower subadditivity and are consistent with previous parametric estimations the data also show that the probability weighting function for losses is more elevated than for gains

decentralized adaptive output feedback control for a class of nonlinear large scale systems with unknown time varying delayed interactions in this paper the authors investigate a decentralized adaptive output feedback controller design for large scale nonlinear systems with input saturations and time delayed interconnections unmatched in control inputs the interaction terms with unknown time varying delays are bounded by unknown nonlinear bounding functions including all states of subsystems this point is a main contribution of this paper compared with previous output feedback control approaches which assume that the time delayed bounding functions only depend on measurable output variables the bounding functions are compensated by using appropriate lyapunov krasovskii functionals and the function approximation technique based on neural networks the observer dynamic surface design technique is employed to design the proposed memoryless local controller for each subsystem in addition we prove that all signals in the closed loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin finally an example is provided to illustrate the effectiveness of the proposed control system

direct and indirect model reference adaptive control for multivariable piecewise affine systems this article proposes direct and indirect model reference adaptive control strategies for multivariable piecewise affine systems which constitute a popular tool to model hybrid systems and approximate nonlinear systems a chosen reference model which can be linear or also piecewise affine describes the desired closed loop system behavior that is to be achieved by the adaptive controllers for unknown system dynamics each subsystem acquires its own set of control gains which is tuned under careful consideration of the switching behavior in the indirect approach the use of dynamic gain adjustment avoids singularities in the certainty equivalence principle it is shown for both algorithms that the state of the reference model is tracked asymptotically given a common lyapunov function for the switched reference model is available furthermore parameter convergence in both the direct and indirect approach is proven for sufficiently rich reference signals finally both algorithms are evaluated in numerical simulations and their advantages and disadvantages are discussed

technical communique an efficient algorithm for optimal control of pwa systems with polyhedral performance indices we present an algorithm for the computation of explicit optimal control laws for piecewise affine pwa systems with polyhedral performance indices the algorithm is based on dynamic programming dp and represents an extension of ideas initially proposed in kerrigan and mayne 2003 optimal control of constrained piecewise affine systems with bounded disturbances in proceedings of the 41st ieee conference on decision and control las vegas nevada usa december and baotic et al 2003 a new algorithm for constrained finite time optimal control of hybrid systems with a linear performance index in proceedings of european control conference cambridge uk september specifically we show how to exploit the underlying geometric structure of the optimization problem in order to significantly improve the efficiency of the off line computations an extensive case study is provided which clearly indicates that the algorithm proposed in this paper may be preferable to other schemes published in the literature

on adaptive state regulation an indirect adaptive state regulator consisting of an adaptive observer and an asymptotic feedback matrix synthesis is discussed in a rigorous analysis lyapunov stability of the resulting closed loop system without the need for external excitation possible global instabilities as well as global convergence subject to sufficient excitation are shown moreover the behavior of the closed loop system is analyzed for cases in which the true plant differs from the assumed linear time invariant model in that it is of higher order contains slight nonlinearities and time variation effects and is subject to plant and measurement disturbances

technical communique a robust decentralized model reference adaptive control for non minimum phase interconnected systems in this paper we present a decentralized model reference adaptive control for interconnected subsystems in the sense that no information exchange occurs between the subsystems the approach is based on the interconnection output estimation using the polynomial series which offers a general solution for interconnected subsystems the parameter estimation scheme is a combined adaptive data filtering with a recursive least squares algorithm with parameter projection and normalization the problem of minimum phased subsystems is handled by an adaptive input output data filtering hence the zeros of each subsystem estimated model are relocated inside the unit circle this estimated model which is minimum phased is then used for the control synthesis it is shown that the stability conditions based on weak interconnections are relaxed also the robustness of the proposed adaptive control against unmodeled dynamics is stated finally the results are illustrated by numerical examples

decentralized adaptive output feedback design for large scale nonlinear systems in this paper we present a global decentralized adaptive design procedure for a class of large scale nonlinear systems which utilizes only local output feedback the advocated scheme guarantees robustness to parametric and dynamic uncertainties in the interconnections and also rejects any bounded disturbances entering the system the systems belonging to this class are those which can be transformed using a global diffeomorphism to the output feedback canonical form where the interconnections are a function of subsystem outputs only the uncertainties are assumed to be bounded by an unknown pth order polynomial in the outputs the resulting controller maintains global robustness and disturbance rejection properties the output tracking error is shown to be bounded within a compact set the size of which can be made arbitrarily small by appropriate choice of the control gains for the case where the objective is regulation global asymptotic regulation of all the states of the closed loop system is achieved

universal teichmuller space and bmo abstract we first give some new characterizations on bmoa teichmuller space and various characterizations on vmoa teichmuller space as well in particular we prove that a quasisymmetric conformal welding h corresponds to an asymptotically smooth curve in the sense of pommerenke 1978 32 precisely when h is absolutely continuous with log h vmo we then show that these bmo teichmuller spaces have natural complex structures

parameter space methods for robust control design a guided tour the results obtained in studies of robust stability and stabilizability of control systems with parametric structured uncertainties are reviewed both the algebraic methods based upon characteristic equations and the methods using lyapunov functions and riccati equations are discussed and compared in the context of algebraic methods most promising are the kharitonov type approach and the optimization procedure of embedding a geometric figure of some kind inside the stability regions of the parameter space maximizing its size using minimax or some other mathematical programming technique in the framework of lyapunov s direct method the dominant approach has been a quadratic function estimation of stability regions in the parameter space in large sale systems the concept of vector lyapunov functions has been used with the possibility of choosing quadratic forms norm like functions and their combinations

technical communique decentralized adaptive control of linear interconnected systems based on laguerre series representation this paper investigates the problem of completely decentralized adaptive control of large scale systems when the subsystems are stable a new approach which eliminates the assumptions about the interconnection terms the time delay the order etc is proposed each subsystem is modeled by an orthonormal laguerre network put in state space form a simple decentralized predictive control law is proposed the potential of such a scheme is illustrated by simulation results

passivity based analysis of the minimal control synthesis algorithm the adaptive minimal control synthesis mcs algorithm and its extensions have been the subject of a number of analytical and implementation investigations since 1990 the purpose of this paper is to improve upon the original stability and robustness proofs for mcs using the concept of passivity in particular we present a formal stability proof for the basic centralized algorithm together with robustness proofs in the cases of plant parameter variations and external disturbances

weil petersson teichmuller space ii smoothness of flow curves of h32 vector fields abstract given a continuous vector field t of sobolev class h 3 2 on the unit circle s 1 the flow maps g t of the differential equation d d t t 0 are known to be quasisymmetric homeomorphisms very recently gay balmaz ratiu 15 conjectured that the flow curve g t is in the weil petersson class wp s 1 and is continuously differentiable with respect to the hilbert manifold structure of wp s 1 introduced by takhtajan teo 40 the first assertion had already been demonstrated in our previous paper 36 in this sequel to 36 we will continue to deal with the weil petersson class wp s 1 and completely solve this conjecture in the affirmative

quasiconformal mappings and chord arc curves given a quasiconformal mapping p on the plane what conditions on its dilatation guarantee that p r is rectifiable and pir is locally abso lutely continuous we show in this paper that if satisfies certain quadratic carleson measure conditions with small norm then p r is a chord arc curve with small constant and p x p 0 g0 ea t dt for x e r with a e bmo having small norm conversely given any such map from r c we show that it has an extension to c with the right kind of dilatation similar results hold with r replaced by a chord arc curve examples are given that show that it would be hard to improve these results applications are given to conformal welding and the theorem of coifman and meyer on the real analyticity of the riemann mapping on the manifold of chord arc curves let p be a quasiconformal map of the plane onto itself thus p is a homeomorphism with locally integrable distributional derivatives and ps upz where u e l c il ul100 1 here we use the notations fz af azf 2 z id f fz 2 aa ida f this function u is called the complex dilatation of p the mapping theorem for q c maps states that for each u e l c il ul100 1 there is a q c map p on c with dilatation u and p is unique up to normalization a basic problem is to understand how geometric properties of p are reflected in u for example one would like to have natural conditions on u which imply that p r is rectifiable and p ir is absolutely continuous this question arises naturally when considering problems in conformal mappings and conformal welding in this paper we obtain such estimates for the mapping theorem and we also give some applications our results involve bmo aoo weights chord arc curves and carleson measures and so we first review the appropriate definitions a locally integrable function f on r lies in bmo if llfil sup lil if x fil dx received by the editors june 1 1986 1980 mathematics subject classification 1985 revision primary 30g60 secondary 42b20 30e20

decentralized adaptive control of interconnected systems the adaptive control of a class of large scale systems formed of an arbitrary interconnection of subsystems with unknown parameters nonlinearities and bounded disturbances is investigated it is first shown that no matter how weak the interconnections are a decentralized adaptive control scheme can become unstable approaches are then developed for stabilization and tracking using new decentralized adaptive controllers in the case where the relative degree n of the transfer function of each decoupled subsystem is less than or equal to two sufficient conditions are established which guarantee boundedness and exponential convergence of the state and parameter errors to bounded residual sets in the absence of disturbances and interconnections the decentralized adaptive control schemes guarantee exact convergence of the tracking errors to zero the effectiveness of the proposed adaptive schemes is demonstrated using a simple example

on decentralised control of non linear interconnected systems the asymptotic stabilisation problem of a class of large scale interconnected systems is considered where the non linear interconnections between subsystems satisfy quadratic constraints that are functions of the whole system s state vector a decentralised combined observer controller compensator is proposed and analysed where the subsystems state vectors are estimated using local sliding mode observers the closed loop system driven by the proposed decentralised compensator is guaranteed to be asymptotically stable subject to two conditions that are easily verifiable simulation results illustrate the effectiveness of the proposed decentralised combined observer controller compensator

making descriptive use of prospect theory to improve the prescriptive use of expected utility this paper proposes a quantitative modification of standard utility elicitation procedures such as the probability and certainty equivalence methods to correct for commonly observed violations of expected utility traditionally decision analysis assumes expected utility not only for the prescriptive purpose of calculating optimal decisions but also for the descriptive purpose of eliciting utilities however descriptive violations of expected utility bias utility elicitations that such biases are effective became clear when systematic discrepancies were found between different utility elicitation methods that under expected utility should have yielded identical utilities as it is not clear how to correct for these biases without further knowledge of their size or nature most utility elicitations still calculate utilities by means of the expected utility formula this paper speculates on the biases and their sizes by using the quantitative assessments of probability transformation and loss aversion suggested by prospect theory it presents quantitative corrections for the probability and certainty equivalence methods if interactive sessions to correct for biases are not possible then the authors propose to use the corrected utilities rather than the uncorrected ones in prescriptions of optimal decisions in an experiment the discrepancies between the probability and certainty equivalence methods are removed by the authors proposal

decentralized adaptive stabilization in the presence of unknown backlash like hysteresis due to the difficulty of handling both hysteresis and interactions between subsystems there is still no result available on decentralized stabilization of unknown interconnected systems with hysteresis even though the problem is practical and important in this paper we provide solutions to this challenging problem by proposing two new schemes to design decentralized output feedback adaptive controllers using backstepping approach for each subsystem a general transfer function with arbitrary relative degree is considered the interactions between subsystems are allowed to satisfy a nonlinear bound with certain structural conditions in the first scheme no knowledge is assumed on the bounds of unknown system parameters in case that the uncertain parameters are inside known compact sets we propose an alternative scheme where a projection operation is employed in the adaptive laws in both schemes the effects of the hysteresis and the effects due to interactions are taken into consideration in devising local control laws it is shown that the designed local adaptive controllers can ensure all the signals in the closed loop system bounded a root mean square type of bound is obtained for the system states as a function of design parameters this implies that the transient system performance can be adjusted by choosing suitable design parameters with scheme ii the proposed control laws allow arbitrarily strong interactions provided their upper bounds are available in the absence of hysteresis perfect stabilization is ensured and the l 2 norm of the system states is also shown to be bounded by a function of design parameters when the second scheme is applied

periodic and chaotic responses of an sdf system with piecewise linear stiffness subjected to combined harmonic and flow induced excitations the response of a single degree of freedom sdf vibrating system with unsymmetrical piecewise linear stiffness subjected to combined harmonic and flow induced excitations is investigated motion limiting stops different tension and compression behavior etc may introduce an unsymmetrical piecewise linear stiffness characteristic a multi harmonic balance cum newton raphson procedure in conjunction with an fft algorithm is adopted to determine the stable and unstable periodic solutions the stability of the periodic solutions is investigated by using floquet theory digital simulation results reveal periodic quasi periodic and chaotic motions of the system in a range of flow velocities mode locked oscillations with period 5 motions are found to occur in certain range of flow velocities bifurcation diagrams and lyapunov exponents are also presented

probability versus certainty equivalence methods in utility measurement are they equivalent certainty equivalence ce and probability equivalence pe methods are the two most frequently used procedures for constructing von neumann morgenstern utility functions in this paper we compare these methods experimentally using a two stage within subject design by asking subjects first for a ce judgment and later for a related pe judgment or vice versa a consistency test is devised which any deterministic expectation model including those allowing probability transformations should meet using four related experiments this consistency test is applied separately to gain and loss questions and to the two sequences of linked equivalence judgments namely ce pe and pe ce the empirical results reveal serious inconsistencies between the ce and pe responses for each of the four experiments the extent of discrepancy depends strongly on the subject s initial risk attitude and whether the gain or loss domain is examined to explain the complex pattern of results the second part of the paper explores several plausible hypotheses the first of these concerns the role of random error in either the responses or the utility function itself it is shown that both can lead to bias although not of a type that could explain our results thereafter shifts in reference points are examined a particular reframing of the pe response mode is postulated in which a pure gamble is psychologically translated into a mixed one leading to increased risk aversion this hypothesis which is also supported by other evidence offers a complete and simple explanation of the results finally several other behavioral hypotheses are examined after developing a weighted average model to simulate them they concern anchoring effects differences in salience between the probability and outcome dimensions strategic misrepresentation regret or rejoice influences and endowment effects although each hypothesis predicts some type of bias none of these five could singly explain the particular pattern of bias observed in general the study demonstrates 1 that serious discrepancies exist between the ce and pe methods of utility measurement 2 that the particular results are incompatible with traditional deterministic choice models 3 how random response errors through propagation can induce systematic biases in the utility function 4 that reframing of the pe mode offers a simple reference shift explanation of the complex findings and 5 how various heuristics and biases can be operationalized and simulated to assess their effects on utility measurement as such this study represents a further step toward a systematic investigation of response mode biases in utility measurement

technical communique stabilizing decentralized model predictive control of nonlinear systems this note presents a stabilizing decentralized model predictive control mpc algorithm for nonlinear discrete time systems no information is assumed to be exchanged between local control laws the stability proof relies on the inclusion of a contractive constraint in the formulation of the mpc problem

trajectory tracking control of bimodal piecewise affine systems this paper deals with a trajectory tracking problem for a class of bimodal piecewise affine systems which is inherently difficult because of the discontinuous changes of their vector fields first we introduce an error variable and an error system as a generalization of the tracking error and its system as an error variable a function switched by the mode of a piecewise affine system is adopted to overcome the inherent difficulty in trajectory tracking control of piecewise affine systems next we design a tracking controller which stabilizes the error system using a lyapunov like function which can be applied to systems including state jumps furthermore the feasibility condition of tracking for siso piecewise linear systems is simplified finally a numerical example is given to illustrate the effectiveness of the proposed method

piecewise affine state feedback for piecewise affine slab systems using convex optimization abstract this paper shows that lyapunov based state feedback controller synthesis for piecewise affine pwa slab systems can be cast as an optimization problem subject to a set of linear matrix inequalities lmis analytically parameterized by a vector furthermore it is shown that continuity of the control inputs at the switchings can be guaranteed by adding equality constraints to the problem without affecting its parameterization structure finally it is shown that piecewise affine state feedback controller synthesis for piecewise affine slab systems to maximize the decay rate of a quadratic control lyapunov function can be cast as a set of quasi concave optimization problems analytically parameterized by a vector before casting the synthesis in the format presented in this paper lyapunov based piecewise affine state feedback controller synthesis could only be formulated as a bi convex optimization program which is very expensive to solve globally thus the fundamental importance of the contributions of the paper relies on the fact that for the first time the piecewise affine state feedback synthesis problem has been formulated as a convex problem with a parameterized set of lmis that can be relaxed to a finite set of lmis and solved efficiently to a point near the global optimum using available software furthermore it is shown for the first time that in some situations the global can be exactly found by solving only one concave problem

on flows of h 3 2 vector fields on the circle in this paper we study the regularity of flow maps of h 3 2 vector fields on the circle in terms of fractional sobolev spaces this problem is motivated by the understanding of the geometry of bers s universal teichmuller space

some notes on quasisymmetric flows of zygmund vector fields abstract in an important paper 24 reimann showed that the flow mappings of a continuous vector field of zygmund class are quasisymmetric homeomorphisms in this paper we will discuss the flow mappings when the vector field belongs to the smooth zygmund class or the sobolev class h 3 2

canonical forms of generic piecewise linear continuous systems this technical note reports a simple but effective strategy to derive a single coordinate transformation of a generic n dimensional piecewise linear continuous vector field that puts both of its subsystems into the same observer or control canonical form the only hypothesis required is that both subsystems are either observable or controllable to derive the result the structure of the system is used in order to prove that it suffices to consider the same transformation for both subsystems the theoretical results are illustrated by means of the colpitts oscillator as a practical case of study

adaptive tracking control for discrete time switched nonlinear systems with dead zone inputs abstract this paper studies the adaptive tracking control problem of a discrete time switched nonlinear system with dead zone input under a class of switching signals with average dwell time due to the complicated structure of the discrete time switched nonlinear systems and the existence of the dead zone it makes a great obstacle for controlling such a class of systems the fuzzy logic systems are employed to approximate the unknown terms of each subsystem in addition both stable subsystems and unstable subsystems are considered the controllers of subsystems update laws and switching signals are designed such that the closed loop system is stable and all the signals are bounded finally a simulation example is employed to illustrate the effectiveness of the proposed method

a cross coupled bistage fuzzy controller for biaxis servomechanism control this paper presents a methodology to design a cross coupled bistage fuzzy controller for cross coupled servomechanisms in the bistage fuzzy inference the consequence in the first stage is passed to the second stage as fact and the consequence of the second stage is used as the control input the proposed approach is used to reduce the complexity of the fuzzy system a more systematic method which is based on a performance index of the fuzzy control system is developed to generate bistage fuzzy rule sets to show the effectiveness the proposed approach is applied to control a cross coupled biaxial servomechanism system which is difficult to obtain by an accurate nonlinear mathematical model in the case of a circular trajectory simulation results have shown that the desired contouring the accuracy can be achieved and the proposed approach outperforms the uncoupled approaches

semi global decentralised output feedback stabilisation for a class of uncertain nonlinear systems this paper discusses the problem of semi global decentralised output feedback control for a class of uncertain nonlinear systems based on the ideas of the homogeneous systems theory and the adding a power integrator technique we first design a homogeneous observer and an output feedback control law for each nominal subsystem without the nonlinearities then using the homogeneous domination approach we relax the linear growth condition to a polynomial one and construct decentralised stabilisers to render the nonlinear system semi globally asymptotically stable two simulation examples are provided to show the effectiveness of the control scheme

observer based control of piecewise affine systems this paper presents a new synthesis method for both state and dynamic output feedback control of a class of hybrid systems called piecewise affine pwa systems the synthesis procedure delivers stabilizing controllers that can be proven to give either asymptotic or exponential convergence rates the synthesis method builds on existing pwa stability analysis tools by transforming the design into a closed loop analysis problem wherein the controller parameters are unknown more specifically the proposed technique formulates the search for a piecewise quadratic control lyapunov function and a piecewise affine control law as an optimization problem subject to linear constraints and a bilinear matrix inequality the linear constraints in the synthesis guarantee that sliding modes are not generated at the switching the resulting optimization problem is known to be hard but suboptimal solutions can be obtained using the three iterative algorithms presented in the paper the new synthesis technique allows con

reduced order observer based decentralised control of non linear interconnected systems the output feedback based asymptotic stabilisation problem for a class of non linear interconnected systems is considered where the non linear interconnections between subsystems satisfy quadratic constraints a novel decentralised dynamic output feedback control strategy involving local projection operator based reduced order observers is proposed this decentralised controller is characterised by the separation property two easily verifiable conditions that guarantee the asymptotic stability of the closed loop system driven by the proposed decentralised controller are given the effectiveness of the developed decentralised control strategy is illustrated with a numerical example and simulations

a solution to the decentralized adaptive stabilization problem in this paper we present for the first time a solution to the problem of designing a globally convergent truly decentralized adaptive controller for systems of arbitrary relative degree without any matching assumptions specifically we prove that using morse s new dynamic certainty equivalent adaptive controller we can determine a class of unmodelled interconnections in the face of which regulation of the plant utput to zero with internal stability is still possible furthermore we prove that the output regulation happens with some guaranteed transient performance bounds namely we show that the l2 norm of the output is uniformly bounded by the initial parameter estimation error and that if the latter and the plant initial conditions are sufficiently small then we can ensure a bound for the l norm of the output

minimal control synthesis adaptive control of continuous bimodal piecewise affine systems this paper is concerned with the derivation of a model reference adaptive control mrac scheme for bimodal piecewise affine pwa continuous systems the algorithm is based on an extension of the minimal control synthesis algorithm originally developed as an mrac for smooth systems the resulting adaptive algorithm is a switched feedback controller able to cope with uncertain continuous pwa systems the proof of stability based on the newly developed passivity theory for hybrid systems is provided and the effectiveness of the new proposed control is shown on a representative example

paper instability analysis and improvement of robustness of adaptive control the effects of unmodeled high frequency dynamics and bounded disturbances on stability and performance of adaptive control schemes are analyzed five possible types of instability mechanisms parameter drift linear instability fast adaptation instability high frequency instability and throughput instability are analyzed using simple examples a procedure is used to construct lyapunov like functions for a modified adaptive controller applied to a dominant plant of relative degree one in the presence of parasitics and disturbances and obtain sufficient conditions under which none of the five types of instability can occur the modified scheme is robust in the sense that it guarantees the existence of a large region of attraction from which all the trajectories remain bounded and the state errors converge exponentially to a much smaller residual set the size of the region of attraction depends on the speed of parasitics in such a way that as the parasitics become infinitely fast the region of attraction becomes the whole space

decentralized adaptive fuzzy output feedback control of switched large scale nonlinear systems in this paper a decentralized adaptive fuzzy output feedback control problem is discussed for a class of switched large scale nonlinear systems without the measurements of the system states fuzzy logic systems are used to approximate the unknown nonlinear functions and a switched observer is designed to avoid the conservativeness caused by adoption of a common observer for all subsystems a common coordinate transformation of all subsystems is constructed to get rid of individual coordinate transformations for subsystems that are required when applying the backstepping recursive design scheme meanwhile since the exponential decline property of lyapunov functions for individual subsystems is no longer satisfied in this paper the classical average dwell time method cannot be directly applied based on this a switched observer based decentralized adaptive fuzzy output feedback control technique is set up by exploiting the average dwell time method and backstepping it is proved that all the signals of the resulting closed loop system are semiglobally uniformly ultimately bounded under a class of switching signals with average dwell time while the tracking errors converge to a small neighborhood of the origin the effectiveness of the proposed control scheme is illustrated by its applications to a two inverted pendulum system and a quadruple tank process system

control of frictional dynamics of a one dimensional particle array control of frictional forces is required in many applications of tribology while the problem is approached by chemical means traditionally a recent approach was proposed to control the system mechanically to tune frictional responses we design feedback control laws for a one dimensional particle array sliding on a surface subject to friction the frenkel kontorova model describing the dynamics is a nonlinear interconnected system and the accessible control elements are average quantities only we prove local stability of equilibrium points of the un controlled system in the presence of linear and nonlinear particle interactions respectively we then formulate a tracking control problem whose control objective is for the average system to reach a designated targeted velocity using accessible elements sufficient stabilization conditions are explicitly derived for the closed loop error systems using the lyapunov theory based methods simulation results show satisfactory performances the results can be applied to other physical systems whose dynamics is described by the frenkel kontorova model

the predictive utility of generalized expected utility theories many alternative theories have been proposed to explain violations of expected utility eu theory observed in experiments several recent studies test some of these alternative theories against each other formal tests used to judge the theories usually count the number of responses consistent with the theory ignoring systematic variation in responses that are inconsistent we develop a maximum likelihood estimation method which uses all the information in the data creates test statistics that can be aggregated across studies and enables one to judge the predictive utility the fit and parsimony of utility theories analyses of 23 data sets using several thousand choices suggest a menu of theories which sacrifice the least parsimony for the biggest improvement in fit the menu is mixed fanning prospect theory eu and expected value which theories are best is highly sensitive to whether gambles in a pair have the same support eu fits better or not eu fits poorly our method may have application to other domains in which various theories predict different subsets of choices e g refinements of nash equilibrium in noncooperative games

resolving inconsistencies in utility measurement under risk tests of generalizations of expected utility this paper explores inconsistencies that occur in utility measurement under risk when expected utility theory is assumed and the contribution that prospect theory and some other generalizations of expected utility can make to the resolution of these inconsistencies we used five methods to measure utilities under risk and found clear violations of expected utility of the theories studied prospect theory was the most consistent with our data the main improvement of prospect theory over expected utility was in comparisons between a riskless and a risky prospect riskless risk methods we observed no improvement over expected utility in comparisons between two risky prospects risk risk methods an explanation for the latter observation may be that there was less distortion in probability weighting in the interval 0 10 0 20 than has commonly been observed

hybrid model reference adaptive control of piecewise affine systems this paper is concerned with the derivation of a model reference adaptive control mrac scheme for multimodal piecewise affine pwa and piecewise linear systems the control allows the plant to track asymptotically the states of a multimodal piecewise affine or smooth reference model the reference model can be characterized by a number and geometry of phase space regions that can be entirely different from those of the plant numerical simulations on a set of representative examples confirm the theoretical derivation and proof of stability

global boundedness of discrete time adaptive control just using estimator projection in this paper we study a discrete time indirect adaptive control algorithm which contains a constrained gradient parameter estimator and a pole assignment control law synthesis module this adaptive control algorithm does not involve modifications like data normalization use of deadzones or injection of persistently excited signals also it requires no a priori knowledge of system modelling errors it is shown that global robustness properties still hold when this simple algorithm is applied to systems with bounded disturbances and arbitrarily small fast parasitic dynamics the problem of indirect decentralized adaptive control of interconnected systems is also considered we use the above adaptive algorithm to design completely decentralized local adaptive controllers for each isolated subsystem by ignoring interactions between subsystems we show that the local controllers designed in this way are robust in the sense that all signals in the closed loop adaptive system are bounded for bounded initial conditions reference inputs disturbances and an arbitrarily small amount of interaction between subsystems and unmodelled dynamics of each subsystem

decentralized quantized control for ncss under periodic protocol this paper is concerned with the problem of designing decentralized quantized controller for networked control systems ncss that are subject to time varying transmission intervals packet dropout communication constraints and limited bandwidth the convex overapproximation method proposed in donkers and heemels 2011 is used to handle with time varying transmission intervals packet dropout process in this paper is modeled as both independent identically distributed process and homogeneous markov jumping process the uniform quantizer is adopted here to deal with limited bandwidth in quantization strategy which switches between zooming out and zooming in modes a variable called proportionality coefficient of saturation value is used to handle with the complex coupling relationship between system states and quantized variables periodic protocol is used here to deal with communication constraints under which only one node can access the network and send its information per transmission within this setup we derive stability results in terms of linear matrix inequalities lmis an illustrative example is given to show the usefulness of the proposed framework for the stability analysis of some classes of ncss

curvature of the probability weighting function when individuals choose among risky alternatives the psychological weight attached to an outcome may not correspond to the probability of that outcome in rank dependent utility theories including prospect theory the probability weighting function permits probabilities to be weighted nonlinearly previous empirical studies of the weighting function have suggested an inverse s shaped function first concave and then convex however these studies suffer from a methodological shortcoming estimation procedures have required assumptions about the functional form of the value and or weighting functions we propose two preference conditions that are necessary and sufficient for concavity and convexity of the weighting function empirical tests of these conditions are independent of the form of the value function we test these conditions using preference ladders a series of questions that differ only by a common consequence the concavity convexity ladders validate previous findings of an s shaped weighting function concave up to p 0 40 and convex beyond that probability the tests also show significant nonlinearity away from the boundaries 0 and 1 finally we fit the ladder data with weighting functions proposed by tversky and kahneman tversky amos daniel kahneman 1992 advances in prospect theory cumulative representation of uncertainty j risk and uncertainty5 297 323 and prelec prelec dra en 1995 the probability weighting function unpublished paper

an energy amplification condition for decentralized adaptive stabilization the author is interested here in the problem of global decentralized adaptive regulation of the plant output to zero of square multivariable linear time invariant systems without any restrictions on relative degrees or matching assumptions the first solution to this problem was recently reported by the author using morse s new dynamic certainty equivalent adaptive controller to prove that global stabilization is possible if the unmodeled interconnections do not induce amplification of the energy of the signals in all channels in this paper the author shows that to preserve global convergence it is actually enough to have only one nonamplifying channel instrumental for the establishment of the authors result is the fundamental s procedure losslessness theorem of megretsky and treil together with some basic loop transformations and d scalings

switched adaptive control of switched nonlinearly parameterized systems with unstable subsystems this paper investigates the problem of adaptive stabilization for a class of switched nonlinearly parameterized systems where the solvability of the adaptive stabilization problem for subsystems is unnecessary a new switched adaptive control technique for the problem studied is set up by exploiting the generalized multiple lyapunov functions method and the parameter separation technique different update laws are designed to reduce the conservativeness caused by adoption of a common update law for all subsystems also the proposed technique permits removal of a common restriction in which the parameterization in the switched systems is restricted to a linear parameterization as an application of the proposed design technique stabilization for a class of non triangular switched systems with nonlinear parameterization is achieved by design of adaptive controllers since no subsystem of such a switched system is assumed to be adaptively stabilizable the problem under study cannot be handled by the existing methods a two inverted pendulums as a practical example is also provided to demonstrate the effectiveness of the proposed design method

non affine nonlinear adaptive control of decentralized large scale systems using neural networks this paper introduces a new decentralized adaptive neural network controller for a class of large scale nonlinear systems with unknown non affine subsystems and unknown interconnections represented by nonlinear functions a radial basis function neural network is used to represent the controller s structure the stability of the closed loop system is guaranteed through lyapunov stability analysis the effectiveness of the proposed decentralized adaptive controller is illustrated by considering two nonlinear systems a two inverted pendulum and a turbo generator the simulation results verify the merits of the proposed controller

adaptive asymptotic tracking control of uncertain time driven switched linear systems this technical note establishes a novel result for adaptive asymptotic tracking control of uncertain switched linear systems the result exploits a recently proposed stability condition for switched systems in particular a time varying positive definite lyapunov function is used to develop a novel piecewise continuous model reference adaptive law and a dwell time switching law in contrast with previous research where asymptotic tracking was possible only in the presence of a common lyapunov function for the reference models in this work asymptotic tracking is shown in a more general setting additionally in the presence of persistence of excitation the controller parameter estimation errors will converge to zero asymptotically the main contribution of this work consists in establishing a symmetry between adaptive control of classical non switched linear systems and adaptive control of switched linear systems a practical example with an electro hydraulic system is adopted to illustrate the results

application of the minimal control synthesis algorithm to the control and synchronization of chaotic systems the paper addresses the problem of controlling and synchronizing chaos using the minimal control synthesis algorithm stoten and benchoubane 1990b after unifying the synchronization and control problems within the same theoretical framework the scope of the original mcs algorithm is extended firstly by removing the assumption that both the plant and the reference model are in phase canonical form and secondly by including the case of vanishing nonlinear disturbances acting on the system finally the application to two common chaotic systems the control of a duffing oscillator and the synchronization of two chua circuits is investigated

adaptive tracking games for coupled stochastic linear multi agent systems stability optimality and robustness distributed adaptive tracking type games are investigated for a class of coupled stochastic linear multi agent systems with uncertainties of unknown structure parameters external stochastic disturbances unmodeled dynamics and unknown agents interactions the control goal is to make the states of all the agents converge to a desired function of the population state average psa due to the fact that only local information is available for each agent the control is distributed for the time invariant parameter case the extended least squares algorithm nash certainty equivalence nce principle and certainty equivalence ce principle are used to estimate the unknown parameters and the psa term and to design adaptive control respectively under some mild conditions it is shown that the closed loop system is almost surely uniformly stable with respect to the population number n the estimate for the psa term is strongly consistent the adaptive control is almost surely an asymptotic nash equilibrium when the dynamics of each agent contains time varying parameters and unmodeled dynamics the projected least mean square lms algorithm nce principle and ce principle are adopted to estimate the unknown time varying parameters and the unknown psa term and to design robust adaptive control respectively in addition to stability of the closed loop system and consistency of the psa estimate the control law is shown to be robust nash equilibrium with respect to the unmodeled dynamics the variation of the unknown parameters and the external disturbances two numerical examples are given to illustrate the methods and results of this paper

decentralized h_ infty filter design for discrete time interconnected fuzzy systems this paper describes a decentralized h infin filter design for discrete time interconnected fuzzy systems based on piecewise quadratic lyapunov functions the systems consist of j discrete time interconnected takagi sugeno t s fuzzy subsystems and a decentralized h infin filter is designed for each subsystem it is shown that the stability of the overall filtering error system with h infin performance can be established if a piecewise quadratic lyapunov function can be constructed moreover the parameters of filters can be obtained by solving a set of linear matrix inequalities that are numerically feasible two simulation examples are given to show the effectiveness of the proposed approach