adaptive control of non linear continuous time systems using neural networks general relative degree and mimo cases multilayer neural networks are used in a non linear adaptive control problem the plant is an unknown feedback linearizable continuous time system with relative degree 1 the single input single output system is studied first and then the methodology is extended to control square multi input multi output systems the control objective is for the plant to track a reference trajectory and the control law is defined in terms of the outputs of the neural networks the parameters of the networks are updated on line according to an augmented tracking error and the network derivatives a local convergence theorem is given on the convergence of the tracking error this control algorithm is applied to control a two input two output relative degree two system

quantitative phase field modeling of dendritic growth in two and three dimensions we report the results of quantitative phase field simulations of the dendritic crystallization of a pure melt in two and three dimensions these simulations exploit a recently developed thin interface limit of the phase field model a karma and w j rappel phys rev e 53 r3017 1996 which is given here a detailed exposition this limit makes it possible to perform efficient computations with a smaller ratio of capillary length to interface thickness and with an arbitrary interface kinetic coefficient simulations in one and two dimensions are first carried out to test the accuracy of phase field computations performed within this limit dendrite tip velocities and tip shapes are found to be in excellent quantitative agreement with exact numerical benchmarks of solvability theory obtained by a boundary integral method both with and without interface kinetics simulations in three dimensions exploit in addition to the asymptotics a methodology to calculate grid corrections due to the surface tension and kinetic anisotropies they are used to test basic aspects of dendritic growth theory that pertain to the selection of the operating state of the tip and to the three dimensional morphology of needle crystals without sidebranches for small crystalline anisotropy simulated values of ensuremath sigma are slightly larger than solvability theory predictions computed by the boundary integral method assuming an axisymmetric shape and agree relatively well with experiments for succinonitrile given the uncertainty in the measured anisotropy in contrast for large anisotropy simulated ensuremath sigma values are significantly larger than the predicted values this disagreement however does not signal a breakdown of solvability theory it is consistent with the finding that the amplitude of the mathrm cos 4 ensuremath varphi mode which measures the departure of the tip morphology from a shape of revolution increases with anisotropy this departure can therefore influence the tip selection in a way that is not accurately captured by the axisymmetric approximation for large anisotropy finally the tail shape at a distance behind the tip that is large compared to the diffusion length is described by a linear law r ensuremath sim z with a slope dr dz that is nearly equal to the ratio of the two dimensional and three dimensional steady state tip velocities furthermore the evolution of the cross section of a three dimensional needle crystal with increasing distance behind the tip is nearly identical to the evolution of a two dimensional growth shape in time in accord with the current theory of the three dimensional needle crystal shape

fuzzy learning control for a flexible link robot there are two main drawbacks in fuzzy control 1 the design of fuzzy controllers is usually performed in an ad hoc manner where it is often difficult to choose some of the controller parameters and 2 the fuzzy controller constructed for the nominal plant may later perform inadequately if significant and unpredictable plant parameter variations occur in this paper we illustrate these two problems on a two link flexible robot testbed by 1 developing implementing and evaluating a fuzzy controller for the robotic mechanism and 2 illustrating that payload variations can have negative effects on the performance of a well designed fuzzy control system next we show how to develop and implement a fuzzy model reference learning controller for the flexible robot and illustrate that it can automatically synthesize a rule base for a fuzzy controller that will achieve comparable performance to the case where it was manually constructed and automatically tune the fuzzy controller so that it can adapt to variations in the payload

diagnosability of discrete event systems subject to permanent sensor failures this paper considers a failure diagnosis problem for discrete event systems subject to permanent sensor failures a notion of diagnosability subject to permanent sensor failures is introduced with respect to a certain nondeterministic observation mask for its verification an aggregated mealy automaton with a deterministic and state dependent observation mask is defined it is shown that the diagnosability of the aggregated mealy automaton is equivalent to the diagnosability of the original system subject to permanent sensor failures then a method for verifying the diagnosability of the aggregated mealy automaton is presented moreover the delay bound within which the occurrence of any failure string can be detected subject to permanent sensor failures is computed

robustifying nonlinear systems using high order neural network controllers a robust control methodology for affine control of nonlinear dynamical systems is developed in this paper a correction control signal is added to a nominal controller designed to guarantee a desired performance for the corresponding nominal system to render the actual system uniformly and ultimately bounded the control signal is smooth and does not require a priori knowledge of an upper bound on the modeling error and or optimal weight values simulations performed on a simple nonlinear system illustrate the approach

a polynomial algorithm for testing diagnosability of discrete event systems failure diagnosis in large and complex systems is a critical task in the realm of discrete event systems sampath et al 1995 proposed a language based failure diagnosis approach they introduced the diagnosability for discrete event systems and gave a method for testing the diagnosability by first constructing a diagnoser for the system the complexity of this method of testing diagnosability is exponential in the number of states of the system and doubly exponential in the number of failure types we give an algorithm for testing diagnosability that does not construct a diagnoser for the system and its complexity is of fourth order in the number of states of the system and linear in the number of the failure types

polynomial time verification of diagnosability of partially observed discrete event systems the problem of verifying the properties of diagnosability and i diagnosability is considered we present new polynomial time algorithms for deciding diagnosability and i diagnosability these algorithms are based on the construction of a nondeterministic automaton called a verifier

a survey of adaptive fuzzy controllers nonlinearities and classifications adaptive fuzzy controllers afcs i e fuzzy controllers using heuristic expert knowledge and equipped with adaption ability are widely used in the industry in the present days as they are capable of dealing with ill formulated nonlinear systems where exact mathematical formulas are not known or partially described nonlinear systems afcs have been widely deployed to control many nonlinear systems with different types of critical nonlinearities over the last two decades many different approaches toward adaptive fuzzy control have been reported in this paper we recapitulate the latest research works related to afcs and provide an up to date survey on the latest development made in adaptive fuzzy control theory and applications based on different types of fuzzy systems considered and nonlinearities associated with the nonlinear system to be controlled we categorize the different approaches based on different types of nonlinearities and consider basic nonlinear systems nonlinear systems with external disturbances nonlinear systems with some special type of nonlinearities nonaffine nonlinear systems and strict feedback nonlinear systems it turns out that many existing methods are subject to various limitations and none of them is capable of controlling a general nonlinear systems hence it is still an open problem to design and develop a universal afc for a general class of nonlinear systems

fuzzy adaptive control of a certain class of siso discrete time processes in this manuscript we address the problem of the stability of a certain class of siso discrete time processes controlled by an adaptive fuzzy controller by using lyapunov stability theory these results were recently obtained for adaptive neural controllers and are extended here to adaptive fuzzy controllers of sugeno s type in order to achieve tracking of a reference signal with this kind of fuzzy system we allow both the membership functions and the consequent part of the rules to be adjusted by a parameter adaptation law we first present the gradient based steepest descent adaptation law and we argue that this gradient based adaptation law can be simplified dramatically thereafter we show the asymptotic stability of the overall system the convergence of the tracking error to zero when using this simplified parameters adjustment law unfortunately this result can only be proved when the outputs of the fuzzy controller can be expanded to the first order around the optimal parameter values that allow perfect tracking that is when the parameters are initialized not too far from their optimal values local stability however when the set of tunable parameters is restricted to the set appearing in the linear consequent part of the rules i e the membership functions of the premises are not modified and when the reference signal is the delayed desired output the stability result is strictly valid the parameters do not have to be initialized around the perfectly tuned values in this case the algorithm can be simplified further by only considering the sign of the derivative of the output of the process in terms of its last influential input

successive identification of a fuzzy model and its applications to prediction of a complex system abstract a successive identification method of a fuzzy model is suggested the identification mechanism consists of two levels one is the supervisor level and the other is the adjustment level the supervisor level determines a policy of parameter adjustment using a set of fuzzy adjustment rules the adjustment rules are derived from the fuzzy implications of a fuzzy model and are extended to fuzzy adjustment rules by using an extended concept of zadeh s contrast intensification the adjustment level executes the policy of parameter adjustment determined with the fuzzy adjustment rules the parameter adjustment consists of premise parameter adjustment and consequent parameter adjustment both of them are realized by the weighted recursive least square algorithm finally it is shown from two examples that the method is very useful for modeling complex systems

a lyapunov like characterization of asymptotic controllability it is shown that a control system in bf r n is asymptotically controllable to the origin if and only if there exists a positive definite continuous functional of the states whose derivative can be made negative by appropriate choices of controls

adaptive neural network tracking control with disturbance attenuation for multiple input nonlinear systems a switching adaptive neural network controller for multiple input nonlinear affine in the control dynamical systems with unknown nonlinearities is designed capable of arbitrarily attenuating l 2 or l infin external disturbances in the absence of disturbances a uniform ultimate boundedness property of the tracking error with respect to an arbitrarily small set around the origin is guaranteed as well as the uniform boundedness of all the signals in the closed loop the proposed switching adaptive controller effectively avoids possible division by zero while guaranteeing the continuity of switching in this way problems connected to existence of solutions and chattering phenomena are alleviated simulations illustrate the approach

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

fuzzy model based control stability robustness and performance issues a nonlinear controller based on a fuzzy model of mimo dynamical systems is described and analyzed the fuzzy model is based on a set of arx models that are combined using a fuzzy inference mechanism the controller is a discrete time nonlinear decoupler which is analyzed both for the adaptive and the fixed parameter cases a detailed stability analysis is carried out and the main result is that the closed loop is globally stable and robust with respect to unstructured uncertainty which may include modeling error and disturbances in addition bounds on the asymptotic and transient performance are given the main assumptions on the system and model are that they must not have strong nonminimum phase effects except time delay and the unstructured uncertainty must not be too large a simulation example illustrates some of the properties of the modeling method and model based control structure

diagnosability of stochastic discrete event systems we investigate diagnosability of stochastic discrete event systems we define the notions of a and aa diagnosability for stochastic automata these notions are weaker than the corresponding notion of diagnosability for logical automata introduced by sampath et al through the construction of a stochastic diagnoser we determine offline conditions necessary and sufficient to guarantee a diagnosability and sufficient to guarantee aa diagnosability we also show how the stochastic diagnoser can be used for on line diagnosis of failure events we illustrate the results through two examples from hvac systems

mixed feedforward feedback based adaptive fuzzy control for a class of mimo nonlinear systems this paper proposes a mixed feedforward feedback ffb based adaptive fuzzy controller design for a class of multiple input multiple output mimo uncertain nonlinear systems by integrating both feedforward and feedback compensation we introduce the ffb based fuzzy controller composed of a feedforward fuzzy compensator and a robust error feedback compensator to achieve a forward compensation of uncertainties the feedforward fuzzy compensator takes the desired commands as premise variables of fuzzy rules and adaptively adjusts the consequent part from an error measure meanwhile the feedback controller part is constructed based on hinfin control techniques and nonlinear damping design then the attenuation of both disturbances and estimated fuzzy parametric errors is guaranteed from a linear matrix inequality lmi based gain design the main advantages are i a simpler architecture for implementation is provided and ii the typical boundedness of assumption on fuzzy universal approximation errors is not required finally an inverted pendulum system and a two link robot are taken as application examples to show the expected performance

brief paper an adaptive neuro fuzzy tracking control for multi input nonlinear dynamic systems an adaptive neuro fuzzy control design is suggested in this paper for tracking of nonlinear affine in the control dynamic systems with unknown nonlinearities the plant is described by a takagi sugeno t s fuzzy model where the local submodels are realized through nonlinear dynamical input output mappings our approach relies upon the effective approximation of certain terms that involve the derivative of the lyapunov function and the unknown system nonlinearities the above task is achieved locally using linear in the weights neural networks a novel resetting scheme is proposed that assures validity of the control input stability analysis provides the control law and the adaptation rules for the network weights assuring uniform ultimate boundedness of the tracking and the signals appearing in the closed loop configuration illustrative simulations highlight the approach

observability and diagnosability of finite state systems a unifying framework abstract in this paper a general framework is proposed for the analysis and characterization of observability and diagnosability of finite state systems observability corresponds to the reconstruction of the system s discrete state while diagnosability corresponds to the possibility of determining the past occurrence of some particular states for example faulty states a unifying framework is proposed where observability and diagnosability properties are defined with respect to a critical set i e a set of discrete states representing a set of faults or more generally a set of interest these properties are characterized and the involved conditions provide an estimation of the delay required for the detection of a critical state of the precision of the delay estimation and of the duration of a possible initial transient where the diagnosis is not possible or not required our framework makes it possible to precisely compare some of the observability and diagnosability notions existing in the literature with the ones introduced in our paper and this comparison is presented

solving the regularized strongly anisotropic cahn hilliard equation by an adaptive nonlinear multigrid method abstract we present efficient second order accurate and adaptive finite difference methods to solve the regularized strongly anisotropic cahn hilliard equation in 2d and 3d when the surface energy anisotropy is sufficiently strong there are missing orientations in the equilibrium level curves of the diffuse interface solutions corresponding to those missing from the sharp interface wulff shape and the anisotropic cahn hilliard equation becomes ill posed to regularize the equation a higher order derivative term is added to the energy this leads to a sixth order nonlinear parabolic equation for the order parameter an implicit time discretization is used to remove the high order time step stability constraints dynamic block structured cartesian mesh refinement is used to highly resolve narrow interfacial layers a multilevel nonlinear multigrid method is used to solve the nonlinear equations at the implicit time level one of the keys to the success of the method is the treatment of the anisotropic term this term is discretized in conservation form in space and is discretized fully implicitly in time numerical simulations are presented that confirm the accuracy efficiency and stability of the scheme we study the dynamics of interfaces under strong anisotropy and compare near equilibrium diffuse interface solutions to the sharp interface wulff shapes in 2d and 3d we also simulate large scale coarsening of a corrugated surface in 3d evolving by anisotropic surface diffusion we show the emergence of long range order during coarsening and an interesting mechanism of ordered coarsening

adaptive neural output feedback controller design with reduced order observer for a class of uncertain nonlinear siso systems an adaptive output feedback control is studied for uncertain nonlinear single input single output systems with partial unmeasured states in the scheme a reduced order observer roo is designed to estimate those unmeasured states by employing radial basis function neural networks and incorporating the roo into a new backstepping design an adaptive output feedback controller is constructively developed a prominent advantage is its ability to balance the control action between the state feedback and the output feedback in addition the scheme can be still implemented when all the states are not available the stability of the closed loop system is guaranteed in the sense that all the signals are semiglobal uniformly ultimately bounded and the system output tracks the reference signal to a bounded compact set a simulation example is given to validate the effectiveness of the proposed scheme

an adaptive meshfree method for phase field models of biomembranes part i we present an adaptive meshfree method for phase field models of biomembranes max ent smooth approximants can deal with the high order phase field equations the method resolves adaptively the models at an affordable computational cost convergence to sharp interface limit is shown with small regularization parameters we present an adaptive meshfree method to approximate phase field models of biomembranes in such models the helfrich curvature elastic energy the surface area and the enclosed volume of a vesicle are written as functionals of a continuous phase field which describes the interface in a smeared manner such functionals involve up to second order spatial derivatives of the phase field leading to fourth order euler lagrange partial differential equations pde the solutions develop sharp internal layers in the vicinity of the putative interface and are nearly constant elsewhere thanks to the smoothness of the local maximum entropy max ent meshfree basis functions we approximate numerically this high order phase field model with a direct ritz galerkin method the flexibility of the meshfree method allows us to easily adapt the grid to resolve the sharp features of the solutions thus the proposed approach is more efficient than common tensor product methods e g finite differences or spectral methods and simpler than unstructured c 0 finite element methods applicable by reformulating the model as a system of second order pde the proposed method implemented here under the assumption of axisymmetry allows us to show numerical evidence of convergence of the phase field solutions to the sharp interface limit as the regularization parameter approaches zero in a companion paper we present a lagrangian method based on the approximants analyzed here to study the dynamics of vesicles embedded in a viscous fluid

neural network control of a rotating elastic manipulator abstract nonminimum phase property of a rotating elastic manipulator causes difficulties for both classical and neural network inverse model control while most of the neural network methods for control of elastic manipulators do not appear to converge to a solution when the system is lightly damped in this paper an appropriate cost function for a neural controller is proposed in the designed neural control system there are only three layer feedforward networks consisting of an input layer with two nodes one hidden layer and output layer with one node the number of units in the hidden layer and the value of the learning rate are robust to this designed network algorithm in order to simulate the transient response of the rotating elastic manipulator system a single input single output state space representation is presented for the system nonlinear model it can be seen from the simulation results the designed neural controller can not only achieve very good tracking performance zero steady state errors and strong robustness to system parameter uncertainty but also reject the effects of the input torque disturbance

comparison of phase field models for surface diffusion the description of surface diffusion controlled dynamics via the phase field method is less trivial than it appears at first sight a seemingly straightforward approach from the literature is shown to fail to produce the correct asymptotics albeit in a subtle manner two models are constructed that approximate known sharp interface equations without adding undesired constraints numerical simulations of the standard and a more sophisticated model from the literature as well as of our two models are performed to assess the relative merits of each approach the results suggest superior performance of the models in at least some situations

adaptive control of nonlinear systems using neural networks layered networks are used in a nonlinear adaptive control problem the plant is an unknown feedback linearizable discrete time system represented by an input output model a state space model of the plant is obtained to define the zero dynamics which are assumed to be stable a linearizing feedback control is derived in terms of some unknown nonlinear functions to identify these functions it is assumed that they can be modelled by layered neural networks the weights of the networks are updated and used to generate the control a local convergence result is given computer simulations verify the theoretical result

a self organizing fuzzy control approach for bank to turn missiles abstract in this paper an adaptive fuzzy autopilot is developed for bank to turn btt missiles we propose a self organizing rotated fuzzy basis function control system that is more flexible than fuzzy basis function expansion in that not only the output weights but also the shapes of fuzzy basis functions can be tuned another characteristic of this autopilot is to incorporate the terminal attractor controller into the autopilot to speed up the convergence rate the global stability analysis established in the lyapunov sense shows that the states and tracking errors of the btt missile are uniformly bounded finally there are two simulation examples to demonstrate the effectiveness of the proposed autopilot the purpose of the first example is to indicate the better performance including faster convergence speed and lower steady state error obtained by autopilots with terminal attractors as compared with that autopilot without terminal attractor another simulation result proves that btt missile can manipulate under various flight conditions in our scenarios and shows the superior tracking performance

sharp interface limits of the cahn hilliard equation with degenerate mobility in this work sharp interface limits for the degenerate cahn hilliard equation with a polynomial double well free energy and a mobility that vanishes at the minima of the double well are derived for the choice of a quadratic mobility the leading order sharp interface motion is not governed by pure surface diffusion as has been previously claimed in the literature but contains a contribution from nonlinear porous medium type bulk diffusion at the same order our analysis reveals that there are two subcases one where the solution for the order parameter is bounded between the minima proven to exist for the first mobility by elliott and garcke siam j math anal 27 1996 pp 404 423 and one where it converges to the classical stationary solution of the cahn hilliard equation consistent treatment of the bulk diffusion requires the matching of exponentially large and small terms in combination with multiple inner layers moreover the leading order sharp interface motion depends sensitively on the choice of mobility the asymptotic analysis shows that for example with a biquadratic mobility the leading order sharp interface motion is driven only by surface diffusion the sharp interface models are corroborated by comparing relaxation rates of perturbations to a radially symmetric stationary state with those obtained by the phase field model

on the design of a nonlinear adaptive variable structure derivative estimator develops a derivative estimator using variable structure system vss and adaptive techniques the proposed nonlinear adaptive variable structure derivative estimator requires little knowledge about the observed signal source and is able to handle the observed signals that are the outputs of either linear or nonlinear dynamic systems with uncertainties in the absence of system noise the uniform boundedness of the proposed derivative estimation is guaranteed by means of the adaptive control approach by virtue of vss the new derivative estimator is capable of adapting itself to the noise environment especially the unpredictable changes in system noise

numerical simulation of anisotropic surface diffusion with curvature dependent energy the aim of this paper is the numerical simulation of surface diffusion processes in the presence of a strong anisotropy and curvature dependence in the surface energy we derive semi implicit finite element discretizations based on a splitting into three second order equations the discretization we use yields indefinite linear systems for the nodal values of the height function the curvature concentration and the chemical potential we provide several numerical examples and parametric studies with respect to some of the parameters in the surface energy and with respect to the coverage the results to our knowledge the first that have been obtained for this model confirm theoretical predictions namely partial faceting of the surfaces with rounded corners

a new phase field model for strongly anisotropic systems we present a new phase field model for strongly anisotropic crystal and epitaxial growth using regularized anisotropic cahn hilliard type equations such problems arise during the growth and coarsening of thin films when the anisotropic surface energy is sufficiently strong sharp corners form and unregularized anisotropic cahn hilliard equations become ill posed our models contain a high order willmore regularization where the square of the mean curvature is added to the energy to remove the ill posedness the regularized equations are sixth order in space a key feature of our approach is the development of a new formulation in which the interface thickness is independent of crystallographic orientation using the method of matched asymptotic expansions we show the convergence of our phase field model to the general sharp interface model we present two and three dimensional numerical results using an adaptive nonlinear multigrid finite difference method we find excellent agreement between the dynamics of the new phase field model and the sharp interface model the computed equilibrium shapes using the new model also match a recently developed analytical sharp interface theory that describes the rounding of the sharp corners by the willmore regularization

phase field theory of edges in an anisotropic crystal in the presence of sufficiently strong surface energy anisotropy the equilibrium shape of an isothermal crystal may include corners or edges models of edges have to date involved the regularization of the corresponding free boundary problem resulting in equilibrium shapes with smoothed out edges in this paper we take a new approach and consider how a phase field model which provides a diffuse description of an interface can be extended to the consideration of edges by an appropriate regularization of the underlying mathematical model using the method of matched asymptotic expansions we develop an approximate solution which corresponds to a smoothed out edge from which we are able to determine the associated edge energy

two mode adaptive fuzzy control with approximation error estimator in this paper we propose a two mode adaptive fuzzy controller with approximation error estimator in the learning mode the controller employs some modified adaptive laws to tune the fuzzy system parameters and an approximation error estimator to compensate for the inherent approximation error in the operating mode the fuzzy system parameters are fixed only the estimator is updated online mathematically we show that the closed loop system is stable in the sense that all the variables are bounded in both modes we also establish mathematical bounds on the tracking error state vector control signal and the rms error using these bounds we show that controller s design parameters can be chosen to achieve desired control performance after that an algorithm to automatically switch the controller between two modes is presented finally simulation studies of an inverted pendulum system and a chua s chaotic circuit demonstrate the usefulness of the proposed controller

stable fuzzy neural tracking control of a class of unknown nonlinear systems based on fuzzy hierarchy error approach in this paper a stable fuzzy neural tracking control of a class of unknown nonlinear systems based on the fuzzy hierarchy approach is proposed the adaptive fuzzy neural controller is constructed from the fuzzy neural network with a set of fuzzy rules the corresponding network parameters are adjusted online according to the control law and update law for the purpose of controlling the plant to track a given trajectory a stability analysis of the unknown nonlinear system is discussed based on the lyapunov principle in order to improve the convergence of the nonlinear dynamical systems a fuzzy hierarchy error approach fhea algorithm is incorporated into the adaptive update and control scheme the simulation results for an unstable nonlinear plant demonstrate the control effectiveness of the proposed adaptive fuzzy neural controller and are consistent with the theoretical analysis

stable adaptive fuzzy control for mimo nonlinear systems in this paper an indirect adaptive fuzzy control scheme is presented for a class of multi input and multi output mimo nonlinear systems whose dynamics are poorly understood within this scheme fuzzy systems are employed to approximate the plant s unknown dynamics in order to overcome the controller singularity problem the estimated gain matrix is decomposed into the product of one diagonal matrix and two orthogonal matrices a robustifying control term is used to compensate for the lumped errors and all parameter adaptive laws and robustifying control term are derived based on lyapunov stability analysis the proposed scheme guarantees that all the signals in the resulting closed loop system are uniformly ultimately bounded uub moreover the tracking errors can be made small enough if the designed parameter is chosen to be sufficiently large a simulation example is used to demonstrate the effectiveness of the proposed control scheme

practical identification of narmax models using radial basis functions a wide class of discrete time non linear systems can be represented by the nonlinear autoregressive moving average narmax model with exogenous inputs this paper develops a practical algorithm for identifying narmax models based on radial basis functions from noise corrupted data the algorithm consists of an iterative orthogonal forward regression routine coupled with model validity tests the orthogonal forward regression routine selects parsimonious radial basistunc tion models while the model validity tests measure the quality of fit the modelling of a liquid level system and an automotive diesel engine are included to demonstrate the effectiveness of the identification procedure

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

surface evolution of elastically stressed films under deposition by a diffuse interface model we consider the heteroepitaxial growth of thin films by numerical simulations within a diffuse interface model the model is applicable to describe the self organization of nanostructures the influence of strain surface energies and kinetics on the surface evolution is considered a matched asymptotic analysis shows the formal convergence of an anisotropic viscous cahn hilliard model to a general surface evolution equation the system is solved by adaptive finite elements in three dimensions and in special cases compared with sharp interface models

prescribed performance adaptive control for multi input multi output affine in the control nonlinear systems we consider the tracking problem of unknown robustly stabilizable multi input multi output mimo affine in the control nonlinear systems with guaranteed prescribed performance by prescribed performance we mean that the tracking error converges to a predefined arbitrarily small residual set with convergence rate no less than a prespecified value exhibiting maximum overshoot as well as undershoot less than some sufficiently small preassigned constants utilizing an output error transformation we obtain a transformed system whose robust stabilization is proven necessary and sufficient to achieve prescribed performance guarantees for the output tracking error of the original system provided that initially the transformed system is well defined consequently a switching robust control lyapunov function rclf based adaptive state feedback controller is designed to solve the stated problem the proposed controller is continuous and successfully overcomes the problem of computing the control law when the approximation model becomes uncontrollable simulations illustrate the approach

a universal construction of artstein s theorem on nonlinear stabilization abstract this note presents an explicit proof of the theorem due to artstein which states that the existence of a smooth control lyapunov function implies smooth stabilizability moreover the result is extended to the real analytic and rational cases as well the proof uses a universal formula given by an algebraic function of lie derivatives this formula originates in the solution of a simple riccati equation

stable adaptive control for nonlinear multivariable systems with a triangular control structure a stable adaptive controller is developed for a class of nonlinear multivariable systems using nonlinearly parametrized function approximators by utilizing the system triangular property integral type lyapunov functions are introduced for deriving the control structure and adaptive laws without the need of estimating the decoupling matrix of the multivariable nonlinear system it is shown that stability of the adaptive closed loop system is guaranteed and transient performance is analytically quantized by mean square and l sub spl infin tracking error bound criteria

stable neural network based adaptive control for sampled data nonlinear systems for a class of mimo sampled data nonlinear systems with unknown dynamic nonlinearities a stable neural network nn based adaptive control approach which is an integration of an nn approach and the adaptive implementation of the variable structure control with a sector is developed the sampled data nonlinear system is assumed to be controllable and its state vector is available for measurement the variable structure control with a sector serves two purposes one is to force the system state to be within the state region in which the nn s are used when the system goes out of neural control and the other is to provide an additional control until the system tracking error metric is controlled inside the sector within the network approximation region the proof of a complete stability and a tracking error convergence is given and the setting of the sector and the nn parameters is discussed it is demonstrated that the asymptotic error of the system can be made dependent only on inherent network approximation errors and the frequency range of unmodeled dynamics simulation studies of a two link manipulator show the effectiveness of the proposed control approach

multiphase thermomechanics with interfacial structure 2 evolution of an isothermal interface paper 1 1988 g 1 of this series began an investigation whose goal is a thermomechanics of two phase continua based on gibbs s notion of a sharp phase interface endowed with thermomechanical structure in that paper a balance law balance of capillary forces was introduced and then applied in conjunction with suitable statements of the first two laws of thermodynamics the chief results are thermodynamic restrictions on constitutive equations exact and approximate free boundary conditions at the interface and a hierarchy of free boundary problems the simplest versions of these problems the mullins sekerka problems are essentially the classical stefan problem with the free boundary condition u 0 for the temperature replaced by the condition u h k where k is the curvature of the free boundary and h 0 is a material constant this dependence on curvature renders the problem difficult and apart from numerical studies involving linearization stability there are almost no supporting theoretical results

initial state detectability of stochastic discrete event systems with probabilistic sensor failures abstract initial state estimation is an important problem in discrete event systems in this problem the initial state of the system is unknown and one wants to determine the initial state of the system based on its observation in this paper we investigate the problem of initial state detection of partially observed discrete event systems in the stochastic setting we consider two sources of randomness in this problem stochastic dynamic of the system and probabilistic sensor failures specifically we model a stochastic discrete event system by a probabilistic finite state automaton and we use a probabilistic projection function as the observation model the notion of stochastic initial state detectability si detectability is introduced in order to capture whether or not the probability of detecting the initial state converges to one even in the presence of potential sensor failures an approach for the verification of si detectability is proposed we also investigate the complexity of the si detectability verification problem and we show that this problem is pspace complete

linking anisotropic sharp and diffuse surface motion laws via gradient flows we compare four surface motion laws for sharp surfaces with their diffuse interface counterparts by means of gradient flows on corresponding energy functionals the energy functionals can be defined to give the same dependence on normal direction for the energy of sharp plane surfaces as for their diffuse counterparts the anisotropy of the kinetics can be incorporated into the inner product without affecting the energy functional

the stone weierstrass theorem and its application to neural networks the stone weierstrass theorem and its terminology are reviewed and neural network architectures based on this theorem are presented specifically exponential functions polynomials partial fractions and boolean functions are used to create networks capable of approximating arbitrary bounded measurable functions a modified logistic network satisfying the theorem is proposed as an alternative to commonly used networks based on logistic squashing functions

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

adaptive control of a class of nonlinear systems with fuzzy logic an adaptive tracking control architecture is proposed for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture employs fuzzy systems which are expressed as a series expansion of basis functions to adaptively compensate for the plant nonlinearities global asymptotic stability of the algorithm is established in the lyapunov sense with tracking errors converging to a neighborhood of zero simulation results for an unstable nonlinear plant are included to demonstrate that incorporating the linguistic fuzzy information from human experts results in superior tracking performance

observer based fuzzy adaptive control for strict feedback nonlinear systems in this paper a new fuzzy adaptive control approach is developed for a class of siso strict feedback nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is introduced for state estimation as well as system identification under the framework of the backstepping design fuzzy adaptive output feedback control is constructed recursively it is proven that the proposed fuzzy adaptive control approach guarantees the semi global boundedness property for all the signals and the tracking error to a small neighborhood of the origin simulation studies are included to illustrate the effectiveness of the proposed approach

stable adaptive control using fuzzy systems and neural networks stable direct and indirect adaptive controllers are presented which use takagi sugeno fuzzy systems conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal for a class of continuous time nonlinear plants with poorly understood dynamics the indirect adaptive scheme allows for the inclusion of a priori knowledge about the plant dynamics in terms of exact mathematical equations or linguistics while the direct adaptive scheme allows for the incorporation of such a priori knowledge in specifying the controller we prove that with or without such knowledge both adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of a reference input in addition for the direct adaptive scheme a technique is presented in which linguistic knowledge of the inverse dynamics of the plant may be used to accelerate adaptation the performance of the indirect and direct adaptive schemes is demonstrated through the longitudinal control of an automobile within an automated lane

a regularized equation for anisotropic motion by curvature for realistic interfacial energies the equations of anisotropic motion by curvature exhibit backward parabolic behavior over portions of their domain thereby inducing phenomena such as the formation of facets and wrinkles in this paper a physically consistent regularized equation that may be used to analyze such phenomena is derived

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

perspectives of fuzzy systems and control although fuzzy control was initially introduced as a model free control design method based on the knowledge of a human operator current research is almost exclusively devoted to model based fuzzy control methods that can guarantee stability and robustness of the closed loop system state of the art techniques for identifying fuzzy models and designing model based controllers are reviewed in this article attention is also paid to the role of fuzzy systems in higher levels of the control hierarchy such as expert control supervision and diagnostic systems open issues are highlighted and an attempt is made to give some directions for future research

sampled data adaptive nn tracking control of uncertain nonlinear systems in this paper for a class of single input single output siso uncertain nonlinear systems adaptive neural tracking controllers designed for digital computer implementation are proposed the overall scheme can be considered as a sampled data adaptive neural control system as an intermediate result it is proven that for a sufficiently small sampling period the emulated adaptive neural controller i e the discrete implementation of the continuous time adaptive neural network controller ensures semiglobal uniformly ultimate boundedness of the closed loop system then based on the exact discrete time model a controller redesign is proposed that performs efficiently for sampling periods for which the emulation controller fails the redesigned controller consists of two terms the emulated control law and an extra robustness term designed to increase the order of the perturbation with respect to the sampling period in the lyapunov difference in all cases high order neural networks are employed to approximate the unknown nonlinearities using lyapunov techniques it is proven that for a sufficiently small sampling period the proposed redesigned controller ensures the semiglobal boundedness of all the signals in the closed loop while the output of the system converges to a small neighborhood of the desired trajectory simulation results illustrate the superiority of the proposed scheme with respect to the emulation controller and verify the theoretical analysis

feedback linearization using neural networks abstract for a class of single input single output continuous time nonlinear systems a multilayer neural network based controller that feedback linearizes the system is presented control action is used to achieve tracking performance for a state feedback linearizable but unknown nonlinear system the control structure consists of a feedback linearization portion provided by two neural networks plus a robustifying portion that keeps the control magniture bounded a stability proof is given in the sense of lyapunov it is shown that all the signals in the closed loop system are uniformly ultimately bounded no off line learning phase is needed initialization of the network weights is straightforward

verification of codiagnosability for discrete event systems modeled by mealy automata with nondeterministic output functions in the conventional framework for failure diagnosis of partially observed discrete event systems it is assumed that for each event the corresponding output symbol is determined uniquely however this assumption does not hold in discrete event systems such as a mobile system where an output symbol depends on not only an event but also a state at which the event occurs in this technical note we model such discrete event systems by mealy automata with nondeterministic output functions and consider a decentralized failure diagnosis problem that requires any occurrence of a failure should be detected by at least one local diagnoser within a uniformly bounded number of steps we introduce an extended version of codiagnosability as a condition for the existence of a decentralized diagnoser we then present an algorithm for verifying the extended codiagnosability condition

stable multi input multi output adaptive fuzzy neural control in this letter stable direct and indirect adaptive controllers are presented that use takagi sugeno t s fuzzy systems 1985 conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal vector for a class of continuous time multi input multi output mimo square nonlinear plants with poorly understood dynamics the direct adaptive scheme allows for the inclusion of a priori knowledge about the control input in terms of exact mathematical equations or linguistics while the indirect adaptive controller permits the explicit use of equations to represent portions of the plant dynamics we prove that with or without such knowledge the adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of the reference inputs we do not impose any initialization conditions on the controllers and guarantee convergence of the tracking error to zero

interface evolution in three dimensions with curvature dependent energy and surface diffusion interface controlled evolution phase transitions epitaxial growth of elastic films when the interfacial energy is a nonconvex function of orientation the anisotropic curvature flow equation becomes backward parabolic to overcome the instability thus generated a regularization of the equation that governs the evolution of the interface is needed in this paper we develop a regularized theory of curvature flow in three dimensions that incorporates surface diffusion and bulk surface interactions the theory is based on a superficial mass balance configurational forces and couples consistent with superficial force and moment balances a mechanical version of the second law that includes via the configurational moments work that accompanies changes in the curvature of the interface a constitutive theory whose main ingredient is a positive definite isotropic quadratic dependence of the interfacial energy on the curvature tensor two special cases are investigated i the interface is a boundary between bulk phases or grains and ii the interface separates an elastic thin film bonded to a rigid substrate from a vapor phase whose sole action is the deposition of atoms on the surface

functional equivalence between radial basis function networks and fuzzy inference systems it is shown that under some minor restrictions the functional behavior of radial basis function networks rbfns and that of fuzzy inference systems are actually equivalent this functional equivalence makes it possible to apply what has been discovered learning rule representational power etc for one of the models to the other and vice versa it is of interest to observe that two models stemming from different origins turn out to be functionally equivalent

observer based fuzzy adaptive control for multi input multi output nonlinear systems with a nonsymmetric control gain matrix and unknown control direction in this study we present an observer based fuzzy adaptive control scheme for a class of uncertain multi input multi output nonlinear systems with a nonsymmetric control gain matrix unknown control direction and unmeasured states in this scheme fuzzy systems are used to approximate the unknown nonlinear functions and an adaptive fuzzy state observer is designed to estimate the unmeasured states the parameter adaptive laws are designed by fuzzy basis functions rather than by its filtering and a robust control term is used to compensate for the lumped errors the proposed method solves the problem of the nonsymmetric control gain matrix and it requires no a priori knowledge of the control direction for the states that are unmeasured we prove that all of the signals in the resulting closed loop systems are bounded and that the tracking errors converge asymptotically to zero two simulation examples are used to demonstrate the effectiveness of the proposed scheme

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

robust neuro fuzzy control of multivariable systems by tuning consequent membership functions a robust neuro fuzzy controller with tuning mechanism of membership functions and neural weights to achieve the tracking control of composite multivariable systems is proposed the control strategy is developed to facilitate robust property by self tuning the consequent membership functions of the fuzzy controllers by an on line tuning mechanism the fuzzy system can effectively deal with the equivalent uncertainties that may appear in the subsystems due to plant uncertainty function approximation error or external disturbance by using lyapunov stability theory the overall system with the proposed controller has been proved to be uniform ultimate bounded simulation results of a two link robot control demonstrate the effectiveness and robustness of the design

stable adaptive neuro control design via lyapunov function derivative estimation a new approach to the tracking problem for affine in the control nonlinear dynamical systems whose nonlinearities are assumed to be unknown is presented in this paper the philosophy of the developed technique is based on estimating the derivative of an unknown lyapunov function exploiting the approximation capabilities of the linear in the weights neural network structures a novel resetting strategy guarantees the boundedness away from zero of certain signals the uniform ultimate boundedness of the tracking error to an arbitrarily small set plus the boundedness of all other signals in the closed loop is guaranteed

a level set approach to anisotropic flows with curvature regularization modeling and simulation of faceting effects on surfaces are topics of growing importance in modern nanotechnology such effects pose various theoretical and computational challenges since they are caused by non convex surface energies which lead to ill posed evolution equations for the surfaces in order to overcome the ill posedness regularization of the energy by a curvature dependent term has become a standard approach which seems to be related to the actual physics too the use of curvature dependent energies yields higher order partial differential equations for surface variables whose numerical solution is a very challenging task in this paper we investigate the numerical simulation of anisotropic growth with curvature dependent energy by level set methods which yield flexible and robust surface representations we consider the two dominating growth modes namely attachment detachment kinetics and surface diffusion the level set formulations are given in terms of metric gradient flows which are discretized by finite element methods in space and in a semi implicit way as local variational problems in time finally the constructed level set methods are applied to the simulation of faceting of embedded surfaces and thin films

finite element method for epitaxial growth with attachment detachment kinetics an adaptive finite element method is developed for a class of free or moving boundary problems modeling island dynamics in epitaxial growth such problems consist of an adatom adsorbed atom diffusion equation on terraces of different height boundary conditions on terrace boundaries including the kinetic asymmetry in the adatom attachment and detachment and the normal velocity law for the motion of such boundaries determined by a two sided flux together with the one dimensional surface diffusion the problem is solved using two independent meshes a two dimensional mesh for the adatom diffusion and a one dimensional mesh for the boundary evolution the diffusion equation is discretized by the first order implicit scheme in time and the linear finite element method in space a technique of extension is used to avoid the complexity in the spatial discretization near boundaries all the elements are marked and the marking is updated in each time step to trace the terrace height the evolution of the terrace boundaries includes both the mean curvature flow and the surface diffusion its governing equation is solved by a semi implicit front tracking method using parametric finite elements simple adaptive techniques are employed in solving the adatom diffusion as well as the boundary motion problem numerical tests on pure geometrical motion mass balance and the stability of a growing circular island demonstrate that the method is stable efficient and accurate enough to simulate the growing of epitaxial islands over a sufficiently long time period

equilibria and dislocations in epitaxial growth abstract an overview of recent analytical developments in epitaxial growth is presented the energy release via the onset of dislocations is addressed regularity of quasistatic equilibria is studied both in the absence and in the presence of dislocations morphological evolution of anisotropic epitaxially strained films is considered under the assumption that the surface evolves by surface diffusion under the influence of a chemical potential

fuzzy adaptive observer backstepping control for mimo nonlinear systems in this paper a fuzzy adaptive backstepping output feedback control approach is developed for a class of multi input and multi output mimo nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is designed for state estimation as well as system identification combining with the backstepping design techniques a fuzzy adaptive output feedback control is constructed recursively it is proved that the proposed fuzzy adaptive control approach can guarantee the semi global uniform ultimate boundedness for all the signals and the tracking error to a small neighborhood of the origin simulation studies illustrate the effectiveness of the proposed approach

adaptive tuning of the fuzzy controller for robots an adaptive tuning algorithm of the fuzzy controller is developed for a class of serial link robot arms the algorithm can on line tune parameters of premise and consequence parts of fuzzy rules of the fuzzy basis function fbf controller the main part of the fuzzy controller is a fuzzy basis function network to approximate unknown rigid serial link robot dynamics under some mild assumptions a stability analysis guarantees that both tracking errors and parameter estimate errors are bounded moreover a robust technique is adopted to deal with uncertainties including approximation errors and external disturbances simulations of the proposed controller on the puma 560 robot arm demonstrate the effectiveness

adaptive neural output feedback tracking control for a class of uncertain discrete time nonlinear systems this brief studies an adaptive neural output feedback tracking control of uncertain nonlinear multi input multi output mimo systems in the discrete time form the considered mimo systems are composed of n subsystems with the couplings of inputs and states among subsystems in order to solve the noncausal problem and decouple the couplings it needs to transform the systems into a predictor form the higher order neural networks are utilized to approximate the desired controllers by using lyapunov analysis it is proven that all the signals in the closed loop system is the semi globally uniformly ultimately bounded and the output errors converge to a compact set in contrast to the existing results the advantage of the scheme is that the number of the adjustable parameters is highly reduced the effectiveness of the scheme is verified by a simulation example

fuzzy adaptive controller for mimo nonlinear systems with known and unknown control direction this paper investigates fuzzy adaptive control schemes for a class of multi input multi output mimo unknown nonlinear systems with known and unknown sign of the control gain matrix three fuzzy adaptive control schemes are developed in the design of the second and third controller we will exploit a decomposition of the control gain matrix into a symmetric positive definite matrix a diagonal matrix with diagonal entries 1 or 1 and a unity upper triangular matrix the nussbaum type function is used to deal with the unknown control direction i e the unknown sign of the control gain matrix for updating the parameters of the fuzzy system an adaptation proportional integral pi law is proposed theoretical results are illustrated through two simulation examples

second order convex maximum entropy approximants with applications to high order pde we present a new approach for second order maximum entropy max ent meshfree approximants that produces positive and smooth basis functions of uniform aspect ratio even for non uniform node sets and prescribes robustly feasible constraints for the entropy maximization program defining the approximants we examine the performance of the proposed approximation scheme in the numerical solution by a direct galerkin method of a number of partial differential equations pdes including structural vibrations elliptic second order pdes and fourth order pdes for kirchhoff love thin shells and for a phase field model describing the mechanics of biomembranes the examples highlight the ability of the method to deal with non uniform node distributions and the high accuracy of the solutions surprisingly the first order meshfree max ent approximants with large supports are competitive when compared to the proposed second order approach in all the tested examples even in the higher order pdes

adaptive fuzzy control for mimo nonlinear systems with nonsymmetric control gain matrix and unknown control direction in this paper an indirect adaptive fuzzy control scheme is developed for a class of uncertain multi input multi output nonlinear systems with nonsymmetric control gain matrix and unknown control direction the nonsymmetric control gain matrix is expressed as the sum of a symmetric matrix and a skew symmetric matrix and the symmetric matrix as well as the skew symmetric matrix is approximated by fuzzy systems by using the symmetric matrix decomposition technique the estimated symmetric matrix is decomposed into the product of one diagonal matrix and two orthogonal matrixes based on the decomposition results the adaptive fuzzy controller is developed to avoid the possible singularity problem and the parameter initialization problem a robust control term is employed to compensate for the lumped errors and a nussbaum type function is incorporated in the robust control term to deal with the unknown control direction the proposed scheme guarantees that all the signals in the resulting closed loop system are bounded and that the tracking errors converge asymptotically to zero two simulation examples are used to demonstrate the effectiveness of the proposed scheme

surface diffusion of graphs variational formulation error analysis and simulation surface diffusion is a fourth order highly nonlinear geometric driven motion of a surface with normal velocity proportional to the surface laplacian of mean curvature we present a novel variational formulation for graphs and derive a priori error estimates for a time continuous finite element discretization we also introduce a semi implicit time discretization and a schur complement approach to solve the resulting fully discrete linear systems after computational verification of the orders of convergence for polynomial degrees 1 and 2 we show several simulations in one dimension and two dimensions with and without forcing which explore the smoothing effect of surface diffusion as well as the onset of singularities in finite time such as infinite slopes and cracks

motion of elastic thin films by anisotropic surface diffusion with curvature regularization in this paper we prove short time existence uniqueness and regularity for a surface diffusion evolution equation with curvature regularization in the context of epitaxially strained two dimensional films this is achieved by using the h 1 gradient flow structure of the evolution law via de giorgi s minimizing movements this seems to be the first short time existence result for a surface diffusion type geometric evolution equation in the presence of elasticity

on codiagnosability and coobservability with dynamic observations codiagnosability and coobservability in discrete event systems where observations are dynamic are considered instead of having a fixed set of observable events the observation of an event is dynamic trace dependent in this paper a procedure is developed to transform the problem of coobservability to the problem of codiagnosability in the context of dynamic observations this proves that problems of coobservability are transformable to problems of codiagnosability and enables us to leverage the large literature available for codiagnosability to solve problems of coobservability furthermore in the case of dynamic observations the known polynomial complexity tests for the property of codiagnosability based on verifier automata with fixed observable event set s are no longer directly applicable a new testing procedure is developed that can handle transition based dynamic observations and remains of polynomial complexity in the state space of the system this new testing procedure employs a covering of the state space of the system based on cluster automata which enhances its computational efficiency based on cluster automata a new type of verifier automaton is built called the c verifier for verification of codiagnosability as an application of the above mentioned transformation the c verifier becomes a unified method for verifying both codiagnosability and coobservability

coarsening dynamics of the convective cahn hilliard equation abstract we characterize the coarsening dynamics associated with a convective cahn hilliard equation cch in one space dimension first we derive a sharp interface theory through a matched asymptotic analysis two types of phase boundaries kink and anti kink arise due to the presence of convection and their motions are governed to leading order by a nearest neighbors interaction coarsening dynamical system cds theoretical predictions on cds include the characteristic length l m for coarsening exhibits the temporal power law scaling t1 2 provided l m is appropriately small with respect to the peclet length scale l p binary coalescence of phase boundaries is impossible ternary coalescence only occurs through the kink ternary interaction two kinks meet an anti kink resulting in a kink direct numerical simulations performed on both cds and cch confirm each of these predictions a linear stability analysis of cds identifies a pinching mechanism as the dominant instability which in turn leads to kink ternaries we propose a self similar period doubling pinch ansatz as a model for the coarsening process from which an analytical coarsening law for the characteristic length scale l m emerges it predicts both the scaling constant c of the t1 2 regime i e l m ct 1 2 as well as the crossover to logarithmically slow coarsening as l m crosses l p our analytical coarsening law stands in good qualitative agreement with large scale numerical simulations that have been performed on cch