optimal estimation from limited noisy data abstract we discuss the following problem let a b f j dy f j e j 1 j n g3 j e p c jp given f j e j 1 j n estimate f x the idea is as follows the estimate is sought in the form a b f j dy f j j 1 j n j p c jp given f j j 1 j n estimate f x the idea is as follows the estimate is sought in the form f n x j 1 n j x f j j the problem is to find j x such that 1 e j 0 then tf n f 0 n 2 if g3 j e p c jp then d f n f 2 where 0 is a certain number we find j 1 j n optimal in a certain sense namely if e j 0 then j are found from the requirements a j 1 n j x a b j dy 1 a b l 1 n j x j y 2 x y 2 dy min note that a j 1 n j x j y n x y in an optimal way if e j 0 then j are found from a and c 2 if this problem is soluble and if not one increases 2 so that this problem becomes soluble

an algorithm for simplex tableau reduction the push to pull solution strategy the simplex algorithm requires artificial variables for solving linear programs which lack primal feasibility at the origin point we present a new general purpose solution algorithm called push to pull which obviates the use of artificial variables the algorithm consists of preliminaries for setting up the initialization followed by two main phases the push phase develops a basic variable set bvs which may or may not be feasible unlike simplex and dual simplex this approach starts with an incomplete bvs initially and then variables are brought into the basis one by one if the bvs is complete but the optimality condition is not satisfied then push phase pushes until this condition is satisfied using the rules similar to the ordinary simplex since the proposed strategic solution process pushes towards an optimal solution it may generate an infeasible bvs the pull phase pulls the solution back to feasibility using pivoting rules similar to the dual simplex method all phases use the usual gauss pivoting row operation and it is shown to terminate successfully or indicates unboundedness or infeasibility of the problem a computer implementation which further reduces the size of simplex tableau to the dimensions of the original decision variables is provided this enhances considerably the storage space and the computational complexity of the proposed solution algorithm illustrative numerical examples are also presented

on continuous dependence for an inverse initial boundary value problem for the wave equation abstract we show that the bounded coefficient q x of the wave equation u tt u qu x t 0 t u x 0 u t x 0 0 x u v x x x t 0 t can be continuously determined by its neumann to dirichlet map in certain function spaces

direct model reference takagi sugeno fuzzy control of siso nonlinear systems this study presents a novel direct model reference fuzzy controller it relaxes the special conditions on the reference model that is required by some of the approaches described in the literature as well as covering a more general class of takagi sugeno t s systems the stability of the proposed method is proved using a proper lyapunov function in addition the effects of modeling errors on the proposed controller are considered and a robust modification algorithm to alleviate this problem is introduced and analyzed the proposed method is then simulated on a flexible joint robot in a feedback linearization form and on chua s chaotic electrical circuit finally it is implemented and tested on a nonlinear dc motor with nonlinear state dependent disturbance

determining conductivity by boundary measurements ii interior results abstract in a recent paper the authors showed that an unknown real analytic conductivity gamma may be determined from static boundary measurements in this document they extend this analysis by demonstrating that a similar result holds for piecewise real analytic conductivities in addition for the special case of a layered structure it is shown that a three times continuously differentiable conductivity is identifiable by boundary measurements originator supplied keywords include inversion convergence algorithms estimates coefficients

observer based indirect adaptive fuzzy sliding mode control with state variable filters for unknown nonlinear dynamical systems this paper proposes an observer based indirect adaptive fuzzy sliding mode controller with state variable filters for a certain class of unknown nonlinear dynamic systems in which not all the states are available for measurement to design the proposed controller we first construct the fuzzy models to describe the input output behavior of the nonlinear dynamic system then an observer is employed to estimate the tracking error vector based on the observer a fuzzy sliding model controller is developed to achieve the tracking performance then a filtered observation error vector is obtained by passing the observation error vector to a set of state variable filters finally on the basis of the filtered observation error vector the adaptive laws are proposed to adjust the free parameters of the fuzzy models the stability of the overall control system is analyzed based on the lyapunov method simulation results illustrate the design procedures and demonstrate the tracking performance of the proposed controller

three dimensional earth conductivity inversion abstract we have constructed two inverse algorithms using tikhonov regularization one follows the well known method of solving the linearized data model relation subject to some regularizing operator which forces the solution to satisfy some desirable features we refer to the other more novel approach as the inverse scattering currents method this procedure uses the linear relation between data and scattering currents induced in an inhomogeneous structure and the relation between the scattering currents and the unknown conductivity the inverse problem is solved iteratively using these two relations

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

variable structure adaptive fuzzy control for a class of nonlinear time delay systems abstract in this paper the problem of variable structure adaptive fuzzy control for a class of nonlinear time delay systems is investigated sliding surface dependent of the time delay is constructed based on the lyapunov krasovskii method two adaptive fuzzy logic systems are proposed to approximate two unknown continuous nonlinear functions containing the current state and the delayed state respectively the corresponding reaching law is designed which can drive the state trajectory of the closed system onto the sliding surface within limited time simulation investigation verifies the effect of the main results of the paper

relative degrees and adaptive feedback linearization control of t s fuzzy systems this paper presents a new study on the relative degrees of single input and single output t s fuzzy systems in general noncanonical forms and proposes a feedback linearization based control design method for such systems the study extends the system relative degree concepts commonly used for the control of nonlinear systems to general t s fuzzy systems derives various relative degree conditions for general t s fuzzy systems and establishes the relative degree dependent normal forms a feedback linearization based control design framework is developed for general t s fuzzy systems using its normal form to achieve closed loop stability and asymptotic output tracking under relaxed design conditions a new adaptive feedback linearization based control scheme for t s fuzzy systems in general noncanonical forms with parameter uncertainties is designed and analyzed some extensions of relative degrees and their possible application to robust adaptive control for noncanonical form t s fuzzy systems are also demonstrated an illustrative example is presented with simulation results to demonstrate the control system design procedure and to show the effectiveness of the proposed control scheme

the inverse scattering problem for time harmonic acoustic waves in an inhomogeneous medium with complex refraction index abstract the inverse scattering problem of determining the complex refraction index of a compact inhomogeneous medium from a knowledge of the far field patterns of the scattered fields corresponding to many incident time harmonic plane acoustic waves is solved by using the colton monk method again by using the same method the analogue of karp s theorem for the scattering of acoustic waves through an inhomogeneous medium with compact support is proven

pieri homotopies for problems in enumerative geometry applied to pole placement in linear systems control huber sottile and sturmfels j symbolic comput 26 1998 pp 767 788 proposed pieri homotopies to enumerate all p planes in c m p mathbb c m p that meet n given m 1 ki planes in general position with k1 k2 kn mp as a condition to have a finite number of solution p planes pieri homotopies turn the deformation arguments of classical schubert calculus into effective numerical methods by expressing the deformations algebraically and applying numerical path following techniques we describe the pieri homotopy algorithm in terms of a poset of simpler problems this approach is more intuitive and more suitable for computer implementation than the original chain oriented description and provides also a self contained proof of correctness we extend the pieri homotopies to the quantum schubert calculus problem of enumerating all polynomial maps of degree q into the grassmannian of p planes in mathbb c m p that meet mp q m p given m planes in general position sampled at mp q m p interpolation points our approach mirrors existing counting methods for this problem and yields a numerical implementation for the dynamic pole placement problem in the control of linear systems

inversion of limited angle tomographic data abstract a new method is given for analytical inversion of the radon transform given limited angle data numerical aspects of this inversion problem are discussed

multidimensional inverse problems and completeness of the products of solutions to pde a method is given for proving uniqueness theorems for some inverse problems the method is based on a result on completeness of the products of solutions to pde as an example the following uniqueness theorems are proved 1 the scattering amplitude a k known for all s2 and a fixed k 0 determines the compactly supported q x l2 d uniquely 2 the surface data u x y k known for all x y p x x3 0 and a fixed k 0 determine the compactly supported x l2 d d r 3 x x3 0 is arbitrarily small determine aj x j 1 2 uniquely here 2u k2u k2a1x a2 x u x y in r3 a1 l2 d a2 h2 d the same conclusion holds if the surface data are known at two distinct frequencies 4 the surface data u x y k known for all x y p and all k 0 determine v x and h k uniquely here 2 k2 k2 x u x y h k x l2 d h k is fourier transform of a wavelet of compact support 5 the conductivity x w2 2 d x c 0 is uniquely determined by the measurements of u and un on d here n is the outward normal to d d r3 is a bounded domain with a smooth boundary d x u 0 in d 6 necessary and sufficient conditions are given for a function a k s2 k 0 is fixed to be the scattering amplitude corresponding to a local potential from a certain class

numerical solution of some inverse scattering problems of geophysics some results are reported of the numerical solution of the inverse problem which consists of finding an inhomogeneity v x in the 3d region r 3 x x3 0 under the surface of the earth from the knowledge of the acoustic field u x y k at low frequencies k for all positions of the source y and the receiver x on the surface p x x3 0 of the earth the inhomogeneity v x in the refraction coefficient is related to the data of u x y k on p by an integral equation of the first kind this inverse problem is extremely ill conditioned the numerical computations in this paper show how to successfully obtain v x which was a priori assumed to be a known constant in an a priori unknown region b and zero outside b an ad hoc b searching procedure together with a regularization method have been used to solve the resulting ill condioned linear system for the discretized problem a subsequent direct comparison finds b more accurately this type of computation can be used to detect piecewise constant inhomogeneity in a medium for example to detect a hole or a crack in a rock or in a construction element

balancing the lifting values to improve the numerical stability of polyhedral homotopy continuation methods polyhedral homotopy continuation methods exploit the sparsity of polynomial systems so that the number of solution curves to reach all isolated solutions is optimal for generic systems the numerical stability of tracing solution curves of polyhedral homotopies is mainly determined by the height of the powers of the continuation parameter to reduce this height we propose a procedure that operates as an intermediate stage between the mixed volume computation and the tracing of solution curves this procedure computes new lifting values of the support of a polynomial system these values preserve the structure of the mixed cell configuration obtained from the mixed volume computation and produce better balanced powers of the continuation parameter in the polyhedral homotopies

adaptive parameter estimator based on t s fuzzy models and its applications to indirect adaptive fuzzy control design in this paper a new on line parameter estimation methodology for the general continuous time takagi sugeno t s fuzzy model whose parameters are poorly known or uncertain is presented an estimator with an appropriate adaptive law for updating the parameters is designed and analyzed based on the lyapunov theory the adaptive law is designed so that the estimation model follows the parameterized plant model by the proposed estimator the parameters of the t s fuzzy model can be estimated by observing the behavior of the system and it can be a basis for indirect adaptive fuzzy control in order to show the applicability of the proposed estimator indirect adaptive fuzzy control design examples with the proposed estimator are presented

homotopies exploiting newton polytopes for solving sparse polynomial systems this paper is concerned with the problem of finding all isolated solutions of a polynomial system the bkk bound defined as the mixed volume of the newton polytopes of the polynomials in the system is a sharp upper bound for the number of isolated solutions in mathbb c 0 n mathbb c 0 mathbb c backslash 0 of a polynomial system with a sparse monomial structure first an algorithm is described for computing the bkk bound following the lines of bernshtei n s proof the algorithmic construction of the cheater s homotopy or the coefficient homotopy is obtained the mixed homotopy methods can be combined with the random product start systems based on a generalized bezout number applications illustrate the effectiveness of the new approach

adaptive indirect fuzzy sliding mode controller for networked control systems subject to time varying network induced time delay two major challenges in networked control systems are the time varying networked induced delays and the packet losses to alleviate these problems this study presents a novel fuzzy sliding mode controller where a fuzzy system is used to estimate the nonlinear dynamical system online and the networked induced delay is handled by pade approximation the problem of packet losses is handled by viewing them as large time varying delays in the system the sliding mode based design procedure used ensures the stability and the robustness of the proposed controller in the presence of disturbances and time varying networked induced time delays using an appropriate lyapunov function it is proved that the tracking error converges to the neighborhood of zero asymptotically furthermore since the adaptation laws of the parameters are derived by using of the lyapunov function these laws are also found to be stable simulation results show that the proposed fuzzy sliding mode controller is capable of controlling nonlinear dynamical systems over a network which is subject to bounded external disturbances time varying network induced delays and packet losses with adequate performance

maxentropic reconstruction of fourier and laplace transforms in this note the first of a series we present a maxentropic procedure to recover a function from the knowledge of a finite number of values of a linear integral transform and apply it to the case of the fourier or the laplace transforms also we consider the case in which the values of the transform are known to be polluted by noise

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

decentralized adaptive fuzzy control for large scale nonlinear systems abstract a decentralized adaptive fuzzy control scheme for a class of large scale nonlinear systems is proposed in this paper the design is based on the principle of sliding mode control and the approximation capability of fuzzy systems the control architecture employs decentralized fuzzy systems to adaptively compensate for plant uncertainties by using the lyapunov function method the control algorithm is proved to be globally stable with tracking errors converging to a neighborhood of zero

numerical recovery of the layered medium from the surface data abstract in this paper an inverse problem is formulated and its numerical solution is given the problem is of interest for example in geophysics numerical results show that the algorithm is efficient for noisy data practical recommendations are given the problem consists of finding n z the refraction coefficient of the medium given the surface data u x k x p x x3 0 and all k 0 k0 where k0 0 is an arbitrary small wave number the governing equation is 2 k2n z u x x x1 x2 z analytical solution to this inverse problem is given a numerical implementation is suggested and the results of the numerical experiments are reported

formal solutions of inverse scattering problems iv error estimates the formal solutions of certain three dimensional inverse scattering problems presented in papers i iii in this series j math phys 10 1819 1969 17 1175 1976 21 2648 1980 are employed here to obtain quantitative estimates on the error resulting from the use of the born approximations in both direct and inverse potential scattering problems these estimates are uniformly valid at all energies and for all sufficiently weak potentials

adaptive fuzzy sliding mode control of nonlinear system in this paper the fuzzy approximator and sliding mode control smc scheme are considered we propose two methods of adaptive smc schemes that the fuzzy logic systems approximators are used to approximate the unknown system functions in designing the smc of nonlinear system in the first method a fuzzy logic system is utilized to approximate the unknown function f of the nonlinear system x sup n f x t b x t u and the robust adaptive law is proposed to reduce the approximation errors between the true nonlinear functions and fuzzy approximators in the second method two fuzzy logic systems are utilized to approximate the f and b respectively and the control law which is robust to approximation error is also designed the stabilities of proposed control schemes are proved and these schemes are applied to an inverted pendulum system the comparisons between the proposed control schemes are shown in simulations

a computer implementation of the push and pull algorithm and its computational comparison with lp simplex method the simplex algorithm requires artificial variables for solving linear programs which lack primal feasibility at the origin point we present a new general purpose solution algorithm called push and pull which obviates the use of artificial variables the algorithm consists of preliminaries for setting up the initialization followed by two main phases the push phase develops a basic variable set bvs which may or may not be feasible unlike simplex and dual simplex this approach starts with an incomplete bvs initially and then variables are brought into the basis one by one if the bvs is complete but the optimality condition is not satisfied then push phase pushes until this condition is satisfied using the rules similar to the ordinary simplex since the proposed strategic solution process pushes towards an optimal solution it may generate an infeasible bvs the pull phase pulls the solution back to feasibility using pivoting rules similar to the dual simplex method all phases use the usual gauss pivoting row operation and it is shown to terminate successfully or indicates unboundedness or infeasibility of the problem a computer implementation which enables the user to run either push and pull or ordinary simplex algorithms is provided the fully coded version of the algorithm is available from the authors upon request a comparison analysis to test the efficiency of push and pull algorithm comparing to ordinary simplex is accomplished illustrative numerical examples are also presented

an inverse problem of the wave equation this paper is organized as follows in sect 1 the statement of the inverse problem is formulated the basic results are formulated and proved in sect 2 some auxiliary material on the x ray transform is given in a self contained way for convenience of the reader this material is used in section one

second order sliding fuzzy interval type 2 control for an uncertain system with real application a new second order sliding mode type 2 fuzzy controller for nonlinear uncertain perturbed systems is developed in this paper to overcome the constraint on the knowledge of the system model we have used local models that are related to some operating points to synthesize a type 2 nominal fuzzy global model the control is based on the super twisting algorithm which is among second order sliding mode controls smcs moreover two adaptive fuzzy type 2 systems have been introduced to generate the two super twisting signals to avoid both the chattering and the constraint on the knowledge of disturbances and uncertainties upper bounds these adaptive fuzzy type 2 systems are adjusted online by two adaptation laws that are deduced from the stability analysis in the lyapunov sense it has only one input i e the sliding surface and one output i e the optimal values of the gains control which are hard to compute with the original algorithm many results of the one link manipulator are obtained first by the simulation in order to compare the performances of the proposed method with that given by levant and then in a real time application in order to confirm the efficiency of the proposed approach the experimentation and simulation are done for the tracking control problem

observer based adaptive fuzzy control for siso nonlinear systems abstract the observer based indirect and direct adaptive fuzzy controllers are developed for a class of siso uncertain nonlinear systems the proposed approaches do not need the availability of the state variables by designing the state observer the adaptive fuzzy systems which are used to model the unknown functions can be constructed using the state estimations thus a new hybrid adaptive fuzzy control method is proposed by combining the above adaptive fuzzy system with the h control technique based on lyapunov stability theorem the proposed adaptive fuzzy control system can guarantee the stability of the whole closed loop systems and obtain good tracking performance as well the proposed methods are applied to an inverted pendulum system and a chaotic system and achieve satisfactory simulation results

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

behavior of the solutions to exterior boundary value problems at low frequencies abstract a simple method is given to study the low frequency behavior of the solutions to exterior boundary value problems for elliptic equations of second order

nonlinear control via approximate input output linearization the ball and beam example approximate input output linearization of nonlinear systems which fail to have a well defined relative degree is studied for such systems a method for constructing approximate systems that are input output linearizable is provided the analysis presented is motivated through its application to a common undergraduate control laboratory experiment the ball and beam where it is shown to be more effective for trajectory tracking than the standard jacobian linearization

indirect adaptive fuzzy sliding mode control part i fuzzy switching in this paper by using the concept of sliding mode control design and lyapunov synthesis approach we propose an indirect adaptive fuzzy sliding mode control iafsmc scheme for a class of nonlinear systems in contrast to the existing sliding mode fuzzy control system designs where the sliding mode control law is directly substituted by a fuzzy controller in our approach both the equivalent control term and switching type control term in the sliding mode control law are approximated by fuzzy systems respectively an on line adaptive tuning algorithm for the consequent parameters in the fuzzy rules is also designed the sliding mode based design procedure ensures the stability and robustness of the proposed iafsmc we prove that the proposed adaptive scheme can achieve asymptotically stable tracking of a reference input with a guarantee of the bounded system signals the chattering phenomena in the sliding mode control is attenuated and the steady error is also alleviated simulation studies have shown that the presented adaptive design of fuzzy sliding mode controller performs very well in the presence of an unknown disturbance

uniqueness theorems for multidimensional inverse problems with unbounded coefficients abstract in a g ramm inverse problems 3 1987 l77 l82 a method to prove uniqueness theorems is given the method uses an estimate of the solution to a partial differential equation with l d coefficients here the estimate is established for l2 d coefficients and the resulting uniqueness theorems are formulated

a novel takagi sugeno based robust adaptive fuzzy sliding mode controller in this paper a nonlinear dynamic system is first approximated by n fuzzy based linear state space subsystems to track a trajectory dominant by a specific frequency the reference models with desired amplitude and phase features are established by the same fuzzy sets of the system rule similarly the same fuzzy sets of the system rule are employed to design robust fuzzy sliding mode control rfsmc and adaptive fuzzy sliding mode control afsmc the difference between rfsmc and afsmc is that afsmc contains an updating law to learn system uncertainties and then an extra compensation is designed it is different from the most previous papers to learn the whole nonlinear functions as the norm of the sliding surface is inside of a defined set the updating law starts simultaneously as it is outside of the other set the updating law stops for the purpose of smoothing the possibility of discontinuous control input a transition between rfsmc and afsmc is also assigned under the circumstances the proposed control robust adaptive fuzzy sliding mode control rafsmc can automatically tune as a rfsmc or an afsmc then the advantages coming from the rfsmc and afsmc are obtained finally the stabilities of the overall system of rfsmc afsmc and rafsmc are verified by lyapunov stability theory the compared simulations among rfsmc afsmc and rafsmc are also carried out to confirm the usefulness of the proposed control scheme

design of interval type 2 fuzzy sliding mode controller in this paper an interval type 2 fuzzy sliding mode controller it2fsmc is proposed for linear and nonlinear systems the proposed it2fsmc is a combination of the interval type 2 fuzzy logic control it2flc and the sliding mode control smc which inherits the benefits of these two methods the objective of the controller is to allow the system to move to the sliding surface and remain in on it so as to ensure the asymptotic stability of the closed loop system the lyapunov stability method is adopted to verify the stability of the interval type 2 fuzzy sliding mode controller system the design procedure of the it2fsmc is explored in detail a typical second order linear interval system with 50 parameter variations an inverted pendulum with variation of pole characteristics and a duffing forced oscillation with uncertainty and disturbance are adopted to illustrate the validity of the proposed method the simulation results show that the it2fsmc achieves the best tracking performance in comparison with the type 1 fuzzy logic controller t1flc the it2flc and the type 1 fuzzy sliding mode controller t1fsmc

a polyhedral method for solving sparse polynomial systems a continuation method is presented for computing all isolated roots of a semimixed sparse system of polynomial equations we introduce mixed subdivisions of newton polytopes and we apply them to give a new proof and algorithm for bernstein s theorem on the expected number of roots this results in a numerical homotopy with the optimal number of paths to be followed in this homotopy there is one starting system for each cell of the mixed subdivision and the roots of these starting systems are obtained by an easy combinatorial construction

symmetry properties of scattering amplitudes and applications to inverse problems abstract for the transformations of the potential q q l where l is one of the following transformations rotation scaling or translation the corresponding transformation of the scattering amplitude is given a necessary and sufficient condition on the scattering amplitude for the scatterer to be spherically symmetric is derived as an application of the above results

on uniqueness of an inverse problem for a 1 d wave equation from transmission data this paper concerns the uniqueness of a coefficient inverse problem for a one dimensional wave equation we allow the unknown coefficient under consideration to be discontinuous this type of inverse problem arises in seismology corresponding to the case in which the medium to be detected has discontinuous interfaces by virtue of spectra theory of the sturm liouville problem and asymptotics of the green function we prove that the discontinuous coefficient can be uniquely recovered from the source function f in l 1 0 infty and the response function g furthermore lemma 6 in this paper corrects some mistakes in t kimura and t suzuki siam j appl math 53 1993 pp 1747 1761 about the asymptotics of the green function this correction means that some related parts in the aforementioned article also need to be rectified correspondingly

computing all nonsingular solutions of cyclic n polynomial using polyhedral homotopy continuation methods all isolated solutions of the cyclic n polynomial equations are not known for larger dimensions than 11 we exploit two types of symmetric structures in the cyclic n polynomial to compute all isolated nonsingular solutions of the equations efficiently by the polyhedral homotopy continuation method and to verify the correctness of the generated approximate solutions numerical results on the cyclic 8 to the cyclic 12 polynomial equations including their solution information are given

a computed torque controller for uncertain robotic manipulator systems fuzzy approach computed torque control ctc is an effective motion control strategy for robotic manipulator systems which can ensure globally asymptotic stability however ctc scheme requires precise dynamical models of robotic manipulators to handle this impossibility in this paper a new approach combing ctc and fuzzy control fc is developed for trajectory tracking problems of robotic manipulators with structured uncertainty and or unstructured uncertainty fuzzy part with a set of tunable parameters is employed to approximate lumped uncertainty due to parameters variations unmodeled dynamics and so on in robotic manipulators based on lyapunov stability theorem it is shown that the proposed controller can guarantee stability of closed loop systems and satisfactory tracking performances the proposed approach indicates that ctc method is also valid for controlling uncertain robotic manipulators as long as compensative controller is appropriately designed finally computer simulation results on a two link elbow planar robotic manipulator are presented to show tracking capability and effectiveness of the proposed scheme

indirect adaptive fuzzy sliding mode control part ii parameter projection and supervisory control the objective of this paper is to show that the error dynamics of the lyapunov synthesis is similar to the sliding surface of sliding mode control smc we compare and evaluate the role and performance of sliding surface boundary layer and lyapunov synthesis finally the indirect adaptive fuzzy sliding mode control iafsmc is equipped with state boundedness supervisory controller and parameter projection simulation studies illustrate the application of the proposed method

fuzzy on line identification of siso nonlinear systems abstract a new fuzzy on line identification algorithm for a single input single output continuous time nonlinear dynamic system is presented this method combines the conventional on line identification with fuzzy logic system the nonlinear system is approximated by a set of fuzzy rules that describe the local linear dynamic in each subspace formed by fuzzifying the input and output space the continuous time fuzzy input output model is identified on line by using the input and output measurements a fuzzy identification algorithm has been developed and a convergence analysis is carried out simulation studies have demonstrated that this fuzzy on line identifier can match the time varying nonlinear system within 5 accuracy

a stability approach to fuzzy control design for nonlinear systems abstract by the application of fuzzy set theory a method for feedback control of nonlinear systems based on the principle of sliding mode control is developed called fuzzy sliding mode control the control method provides a simple way to achieve asymptotic stability of the systems other attractive features of the method include a minimal realization of the fuzzy controller and robustness against model uncertainties and external disturbances in addition the method is capable of handling the chattering problem inherent to sliding mode control simply and effectively a simulation study of an inverted pendulum system is presented to demonstrate these features of the method also it is indicated that the method is easy to use for practicing control engineers

a linearized inverse boundary value problem for maxwell s equations abstract in this paper we consider the problem of determining the electromagnetic state of a body from measurements made on the surface of the body we study the full set of maxwell s equations that govern time harmonic electric and magnetic fields we seek to reconstruct the magnetic permeability the electric permitivity and the electric conductivity in the interior of the body from measurements made on the surface we exhibit appropriate boundary measurements in the form of a boundary mapping specifically the mapping from the tangential components of the electric field to the tangential components of the magnetic field this data can be used to reconstruct and approximately provided they deviate only slightly from known constants we also estimate the reconstruction errors