a new nonlinear robust disturbance observer abstract this paper presents a new nonlinear robust disturbance observer by using only the input output information for minimum phase dynamical systems with arbitrarily relative degrees the model uncertainties the nonlinear parts of the system are merged into the disturbance term and are regarded as a part of the disturbance the disturbance is assumed bounded however the upper and lower bounds are assumed unknown the new disturbance observer is inspired by the vss control theory whereas the upper and lower bounds of the disturbance are adaptively updated the estimation error of the disturbance can be made as small as necessary by choosing the design parameters the attraction of the proposed method lies in its robustness to disturbance and easiness to be implemented example and simulation results show the effectiveness of the proposed algorithm

enumerating solutions to p a q b r c s d let p q r s be polynomials with integer coefficients this paper presents a fast method using very little temporary storage to find all small integers a b c d satisfying p a q b r c s d numerical results include all small solutions to a 4 b 4 c 4 d 4 all small solutions to a 4 b 4 c 4 d 4 and the smallest positive integer that can be written in 5 ways as a sum of two coprime cubes

a new design for model reference robust control using state space techniques the authors propose a model reference control mrc structure that is different from existing mrc structures the new approach that we discuss is based on state space techniques however it is not simply an alternative form of the input output transfer function approach the method we use to achieve our result is obtained through a concept often called filtered transformation the filtered transformation has the effect of transforming the plant into a big system that is composed of two subsystems one subsystem satisfies the standard matching condition which is not enjoyed by the original plant while all the unmatched and unmodelled dynamics are drawn into the other unmatched subsystem the control objective for the original plant is transferred into the control of the matched subsystem while also ensuring that the unmatched subsystem remains uniformly bounded a robust control approach and the backstepping method are used to guarantee that the overall states are globally uniformly bounded and that

characteristic based treatment of source terms in euler equations for roe scheme the modifications required to apply roe s riemann solver to the euler equations with source terms are developed and demonstrated the generalized quasi one dimensional flow including the effects of friction secondary mass addition and energy addition has been considered the modifications require extensions of the expressions for the strengths of the characteristic waves the modified expressions for the wave strengths in roe s riemann solver are obtained from the theory of characteristics using the compatibility relations that depend on the specific source terms present appropriate discretization of the source terms is required to obtain the correct solution it is demonstrated that the compatibility relations in the presence of source terms can be used to modify not only roe s riemann solver but also characteristic based boundary conditions the validity of the proposed approach is illustrated by comparing the exact analytical solutions and the numerical solutions with and without the proposed corrections for two examples involving steady flow and one involving unsteady flow

gas kinetic schemes for compressible flow of real gases abstract this paper extends gas kinetic schemes to the euler equations for real gases in the current scheme the maxwell boltzmann gas distribution function is modified to recover macroscopic flow equations more specifically the internal degree of freedom of the gas distribution function becomes a function of flow variables according to the general equation of state the numerical results confirm the accuracy and robustness of the gas kinetic approach

an evaluation of roe s scheme generalizations for equilibrium real gas flows the extension of roe s approximate riemann solver to equilibrium real gas is analyzed by means of a general formulation allowing us to clarify the inherent nonuniqueness of the average state and the influence of the functional form of the equation of state several generalizations of roe s scheme are then reviewed and their numerical performances are discussed by computing some 2d steady hypersonic flows the flow solvers are coupled with a newly developed efficient and robust procedure for thermochemical air properties evaluation all of the tested equilibrium solvers achieve very similar results they are found of comparable numerical efficiency the higher performances being associated with vinokur s and liou s solvers it is concluded that equilibrium simulations in 2d are by no means less robust than the perfect gas ones when coupled with the proposed procedure for properties evaluation

on the minimum gap between sums of square roots of small integers let k and n be positive integers n k define r n k to be the minimum positive value of a1 ak b1 bk where a1 a2 ak b1 b2 bk are positive integers no larger than n define r n k to be logr n k it is important to find tight bounds for r n k and r n k in connection to the sum of square roots problem a famous open problem in computational geometry the current best lower bound and upper bound are far apart in this paper we prove an upper bound of 2o n logn for r n k which is better than the best known result o 22klogn whenever n cklogk for some constant c in particular our result implies an algorithm subexponential in k i e with time complexity 2o k logn o 1 to compare two sums of k square roots of integers of value o klogk we then present an algorithm to find r n k exactly in nk o k time and in n k 2 o k space as an example we are able to compute r 100 7 exactly in a few hours on a single pc the numerical data indicate that the root separation bound is very far away from the true value of r n k

roe matrices for ideal mhd and systematic construction of roe matrices for systems of conservation laws in this paper the construction of a roe s scheme for the conservative system of ideal magnetohydrodynamics mhd is presented as this method relies on the computation of a roe matrix the problem is to find a matrixa ul ur which satisfies the following properties it is required to be consistent with the jacobian of the fluxf to have real eigenvalues a complete set of eigenvectors and to satisfy the relation f a ul ur u whereulandurare two admissible states and utheir difference for the ideal mhd system using eulerian coordinates a roe matrix is obtained without any hypothesis on the specific heat ratio especially its construction relies on an original expression of the magnetic pressure jump moreover a roe matrix is computed for lagrangian ideal mhd by extending the results of munz who obtained such a matrix for the system of lagrangian gas dynamics so this second matrix involves arithmetic averages unlike the eulerian one which contains classical roe averages like in eulerian gas dynamics in this paper a systematic construction of lagrangian roe matrices in terms of eulerian roe matrices for a general system of conservation laws is also presented this result applied to the above eulerian and lagrangian matrices for ideal mhd gives two new matrices for this system in the same way by applying this construction to the gas dynamics equations new roe matrices are also obtained all these matrices allow the construction of roe type schemes some numerical examples on the shock tube problem show the applicability of this method

on a4 b4 c4 d4 on utilise les courbes elliptiques pour determiner une infinite de solutions de l equation a 4 b 4 c 4 d 4 en entiers copremiers a partir de 2682440 4 153656639 4 18796760 4 20615673 4 on donne ainsi un contre exemple de la conjecture d euler concernant la generalisation du grand theoreme de fermat

exact and approximate riemann solvers for real gases a procedure is developed for solving the riemann problem rp for the flow of gases obeying an equation of state eos of the form p p a first method is introduced producing solutions of the exact rp the algorithm is validated by applying it to the classical test case of the shock tube for a perfect gas thereafter the method is applied to gases having eos of the van der waals or virial types with very good resulting accuracy however the procedure is somewhat demanding in computer time therefore some simplifying assumptions are introduced into the computation of simple waves leading to an approximate solution of the rp in most circumstances excellent results are obtained and the computer time is much more competitive however under certain extreme flow conditions it is recommended that a combination of the exact and approximate solvers for the rp be employed

on the development of discontinuous observers abstract a framework is proposed for the development and analysis of robust observers for uncertain dynamical systems a variable structure systems approach is used emphasis is placed upon the numerical tractability of the associated synthesis procedure a selected numerical example is used to illustrate the proposed algorithm

a t o 2 n 2 s o 2 n 4 algorithm for certain np complete problems in this paper we develop a general purpose algorithm that can solve a number of np complete problems in time t o 2 n 2 and space s o 2 n 4 the algorithm can be generalized to a fam

entropy flux splittings for hyperbolic conservation laws part i general framework a general framework is proposed for the derivation and analysis of flux splittings and the corresponding flux splitting schemes for systems of conservation laws endowed with a strictly convex entropy the approach leads to several new properties of the existing flux splittings and to a method for the construction of entropy flux splittings for general situations a large family of genuine entropy flux splittings is derived for several significant examples the scalar conservation laws the p system and the euler system of isentropic gas dynamics in particular for the isentropic euler system we obtain a family of splittings that satisfy the entropy inequality associated with the mechanical energy for this system it is proved that there exists a unique genuine entropy flux splitting that satisfies all of the entropy inequalities which is also the unique diagonalizable splitting this splitting can be also derived by the so called kinetic formulation simple and useful difference schemes are derived from the flux splittings for hyperbolic systems such entropy flux splitting schemes are shown to satisfy a discrete cell entropy inequality for the diagonalizable splitting schemes an a priori l estimate is provided by applying the principle of bounded invariant regions the convergence of entropy flux splitting schemes is proved for the 2 2 systems of conservation laws and the isentropic euler system 1995 john wiley sons inc

interpolating sliding mode observer for a ball and beam system abstracta principle of interpolating sliding mode observer is introduced in this paper the observer incorporates multiple linear observers through interpolation of multiple estimates which is treated as a type of adaptation the principle is then applied to the ball and beam system for observation of the slope of the beam from the measurement of the ball position the linearised model of the ball and beam system using multiple linearisation points is developed the observer dynamics implemented in matlab simulink real time workshop environment experiments conducted on the ball and beam experimental setup demonstrate excellent performance of the designed novel interpolating adaptive observer

observer matrix gain optimization for stochastic continuous time nonlinear systems it is shown that for a class of stationary stochastic nonlinear systems satisfying a global lipschitz condition the high gain observer with a constant gain matrix may guarantee an upper bound for the averaged quadratic error of state estimation the nonlinearity is assumed to be a priory known the main contribution of this paper consists in designing of a numerical procedure for the optimal gain matrix minimizing this upper bound the convergence analysis of this procedure is presented as well as an example illustrating its finite steps workability it is shown that within a neighborhood of the optimal matrix gain the others provide lower estimation performance

comparative study of high resolution shock capturing schemes for a real gas recently developed second order explicit shock capturing methods in conjunction with generalized flux vector splittings and a generalized approximate riemann solver for a real gas are studied the comparisons are made on different one dimensional riemann shock tube problems for equilibrium air with various ranges of mach numbers densities and pressures six different riemann problems are considered these tests provide a check on the validity of the generalized formulas since theoretical prediction of their properties appears to be difficult because of the non analytical form of the state equation the numerical results in the supersonic and low hypersonic regimes indicate that these produce good shock capturing capability and that the shock resolution is only slightly affected by the state equation of equilibrium air the difference in shock resolution between the various methods varies slightly from one riemann problem to the other but the overall accuracy is very similar for the one dimensional case the relative efficiency in terms of operation count for the different methods is within 30 percent the main difference between the methods lies in their versatility in being extended to multidimensional problems with efficient implicit solution procedures

an approximate inverse system for nonminimum phase systems and its application to disturbance observer this paper proposes an approximate inverse system for nonminimum phase dynamical systems based on the least square approximation method the nonminimum phase systems are approximated by minimum phase systems the proposed formulation is applied to the disturbance observation problems for multivariable nonminimum phase systems with arbitrary relative degrees the disturbances which are assumed bounded are the combination of the external disturbances the nonlinearities and the model uncertainties of the system the estimation error of the disturbances is controlled by the design parameters furthermore the accuracy of the estimation also depends on the frequencies of the disturbances simulation results show the effectiveness of the proposed method

output feedback stabilization of uncertain dynamical systems given an uncertain dynamical system with a linear nominal part matched uncertainties and a measured output a sufficient condition is given for the existence of an output feedback stabilizing controller for the general multiinput multioutput case checking the sufficient condition involves the selection of a matrix f for the special class of single input single output systems f is a positive or negative scalar and it is shown that if the nominal system transfer function is strictly positive real then an output feedback stabilizing controller does indeed exist

a novel estimation algorithm based on data and low order models for virtual unmodeled dynamics in this paper the challenging issue of estimating virtual unmodeled dynamics is addressed a novel estimation algorithm based on historical data and the output of low order approximation models for virtual un modeled dynamics is presented in particular the virtual un modeled dynamics are decomposed into known and unknown parts where only the unknown part is to be estimated the method effectively avoids the need to use the unknown control input directly and enables the estimation of the un modeled dynamics with a relatively simple algorithm moreover it is shown that the proposed algorithm overcomes the difficulty in obtaining the control solutions caused by the fact that the controller input is embedded in un modeled dynamics finally simulation studies are presented to demonstrate the effectiveness of the proposed method

a novel sliding mode observer for state and fault estimation in systems not satisfying matching and minimum phase conditions abstract in this paper a novel sliding mode observer is proposed for systems that do not satisfy common conditions required for fault estimation in particular the so called matching condition and minimum phase condition other works attempt to circumvent the matching condition by using multiple observers in cascade or higher order sliding modes whilst the minimum phase condition can be relaxed at the cost of some faults and the states being not estimated or the fault estimation being corrupted by the fault time derivative or other dynamics for the proposed scheme in this paper only one observer is required the minimum phase condition is relaxed to detectability and the matching condition is greatly simplified to a condition related to the system dimensions which makes the scheme also applicable to the case where there are less outputs than faults finally a simulation example is conducted to verify the effectiveness of the proposed observer

generalized flux vector splitting and roe average for an equilibrium real gas abstract the flux vector splittings of steger warming and van leer and roe s approximate riemann solver are generalized to arbitrary equilibrium gas laws comparisons with other formulations are made

a sliding mode observer for infinitely unobservable descriptor systems in existing work of sliding mode observers smos for descriptor systems a necessary condition is that the system must be infinitely observable this paper presents a scheme that circumvents that condition by reformulating the system as a reduced order system where certain structures in the system matrix are manipulated and certain states are treated as unknown inputs following that an smo is implemented on the reduced order system where state and fault estimation can be achieved necessary and sufficient conditions of this scheme are also presented finally a simulation example shows the effectiveness of the proposed scheme

an improved estimation method for unmodeled dynamics based on anfis and its application to controller design by representing nonlinear systems as a combination of linear part and unmodeled dynamics in this paper an improved estimation algorithm using an adaptive neuro fuzzy inference system anfis for unmodeled dynamics is presented at first the unmodeled dynamics is divided into two parts using the differential expansion of the control input at the last time instant then the two parts are estimated by the anfis it has been shown that the proposed algorithm overcomes the problem that the unknown control input is embedded in unmodeled dynamics which makes the true value of unmodeled dynamics difficult obtain moreover the method improves the precision of the estimation of unmodeled dynamics second under the assumption that the growth rate of unmodeled dynamics does not exceed its input vector the one to one mapping and regularization technique are adopted to deal with the input and output data and the unmodeled dynamics respectively as a result the data vector can be guaranteed to lie inside a compact set which ensures the use of the universal approximation property of the anfis on the other hand it has been shown that datum of a system can be fully used to obtain the parameters centers widths in membership functions and the network connection weights in the anfis by offline training these parameters are tuned online to improve the estimation convergence rate of the unmodeled dynamics the effectiveness of the proposed estimation method is illustrated by comparing it with the simulation results that are obtained from the other existing methods finally the proposed estimation method is applied to the nonlinear switching control design both simulation and theoretical analysis have confirmed that the nonlinear switching control which adopts the proposed estimation method cannot only guarantee the stability and convergence of the system but can exhibit a desired dynamic performance for the closed loop system as well

an lmi approach for designing sliding mode observers this paper presents a method to design sliding mode observers for a class of uncertain systems using linear matrix inequalities the objective is to exploit the degrees of freedom available in the design which have hitherto been ignored because of the lack of a tractable solution framework the relationship between the linear component of the sliding mode observer and a particular sub optimal observer arising from classical linear quadratic gaussian lqg theory is demonstrated this helps motivate how the design weighting matrices inherent in the method may be chosen in practice it will also be shown how the weighting matrices affect the dynamics of the sliding motion furthermore using pole placement and pole clustering methods the poles of the sliding motion can be forced to lie in a specified region in the complex plane so that the performance of the sliding motion can be tuned this paper will also present a more general solution where the eigenvalues of the linear part of the observer are forced

comparative study of non linear state observation techniques abstract this paper contains a comparative study of four techniques for observing the slates of non linear systems the first technique examined is inspired by bestle and zeitz and icrener and respondek in this method a non linear transformation is found that brings the system into a canonical form from where observer design is facilitated the second technique is attributable to thau in this method the error between the system s true state and the output of the observer is shown to be asymptotically convergent to zero provided that an additional assumption is valid the third technique is due to baumann and rugh in this method extended or pseudolinearization of the error differential equation about a family of equilibrium points results in an observer design such that the eigenvalues of the linearized error equation are locally invariant finally techniques from variable structure systems are utilized to design an observer that yields an exponentially decaying error like thau s observer but unl

accurate computation of contact discontinuities in flows with general equations of state abstract the evolution of a contact discontinuity in a real fluid flow is particularly difficult to compute with a conservative scheme indeed godunov type schemes involve an averaging step which may create an intermediate state with an incorrect pressure spurious acoustic waves are then generated these waves affect transient simulations as well as implicit time marching procedures for steady state computations however a formulation involving the pressure as a dependent variable can be used to restore a fast convergence for steady state computations

a new state observer for perspective systems in this note we consider the problem of estimating the state of a class of perspective systems the problem can be converted into the observation of a dynamical system with nonlinearities a new discontinuous state observer which is motivated by the sliding mode control method and adaptive techniques is proposed for the obtained dynamical system the assumptions are reasonable and the convergence conditions are intuitive and have apparently physical interpretations the attraction of the new method is that the algorithm is very simple and easy to be implemented and it is robust to measurement noises further minor a priori knowledge of the system is required in the new formulation simulation results show the superiority of the new method to the traditional ones

a simple extension of roe s scheme for real gases abstract the purpose of this paper is to develop a highly accurate numerical algorithm to model real gas flows in local thermodynamic equilibrium lte the euler equations are solved using a finite volume method based on roe s flux difference splitting scheme including real gas effects a novel algorithm is proposed to calculate the jacobian matrix which satisfies the flux difference splitting exactly in the average state for a general equation of state this algorithm increases the robustness and accuracy of the method especially around the contact discontinuities and shock waves where the gas properties jump appreciably the results are compared with an exact solution of the riemann problem for the shock tube which considers the real gas effects in addition the method is applied to a blunt cone to illustrate the capability of the proposed extension in solving two dimensional flows