extended discrete time multivariable adaptive control using long term predictor an extended method for the design of discrete time multivariable adaptive control is presented unlike most adaptive control algorithms future control inputs are in this method predetermined by using the long term predictor with this concept applications of discrete time multivariable adaptive controls which have been applied to only a limited class of practical problems owing to the unboundedness of the control inputs can be extended to some types of non minimum phase process in addition it is shown that a more generalized control objective such as minimizing a sum of quadratic errors plus a penalty on control action can be easily adopted in the design of adaptive controllers by using the concept of a long term predictor

group similarity solutions of the lax pair for a generalized hirota satsuma equation a modified version of generalized hirota satsuma is here analytically solved using a two parameter group transformation method we here through a group symmetry transformation reduce its lax pair to a system of ordinary equations and find new solutions three similarity transformation variables are investigated for each case an analytical solution is obtained through a homogenous balance of terms in the reduced lax pair the obtained results are plotted and show a profile proper to deflagration processes well described by degasperis procesi equation

persistence properties for a family of nonlinear partial differential equations abstract we examine the persistence of decay properties for a family of dispersive nonlinear partial differential equations we show that certain decay properties of the initial data persist for as long as the solution exists on the other hand for a subset of the family certain decay rates are possible only for the trivial solution for example the only solution that remains with compact support for any further time is the trivial solution

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

separate bias estimation with reduced order kalman filters this paper presents the optimal two stage kalman filter for systems that involve noise free observations and constant but unknown bias like the full order separate bias kalman filter this new filter provides an alternative to state vector augmentation and offers the same potential for improved numerical accuracy and reduced computational burden when dealing with systems involving accurate essentially noise free measurements this new filter offers an additional advantage a reduction in filter order the optimal separate bias reduced order estimator involves a reduced order filter for estimating the state the order equalling the number of states less the number of observations

local error estimates for discontinuous solutions of nonlinear hyperbolic equations let u x t be the possibly discontinuous entropy solution of a nonlinear scalar conservation law with smooth initial data suppose u varepsilon x t is the solution of an approximate viscosity regularization where varepsilon 0 is the small viscosity amplitude it is shown that by post processing the small viscosity approximation u varepsilon pointwise values of u and its derivatives with an error as close to e as desired can be recovered the analysis relies on the adjoint problem of the forward error equation which in this case amounts to a backward linear transport equation with discontinuous coefficients the novelty of our approach is to use a generalized e condition of the forward problem in order to deduce a w 1 infty energy estimate for the discontinuous backward transport equation this in turn leads to e uniform estimate on moments of the error u varepsilon u the approach presented does not follow the characteristics and therefore applies mutatis mutandis to o

properties of generalized predictive control control design using long range prediction based on a dynamic model of the plant has become an important contender for high performance applications the model can be derived analytically but more typically it is provided by simple experiments or in the adaptive context by recursive estimation many methods have been proposed in the literature depending on the assumed model structure and the choice of cost function here the approach called generalized predictive control or gpc is reviewed of special interest is the derivation of prediction equations using an observer polynomial and a demonstration that the selection of particular horizons the costing horizons and the control horizon leads to well understood basic techniques such as dead beat pole placement and lq simulated examples show that gpc is suitable for controlling a complex plant such as unstable inverse unstable systems and how the observer polynomial independently tailors the response to the disturbances preprogrammed set points as with robot trajectory control and actuator nonlinearities can also be catered for a discussion of adaptive applications of gpc to several industrial process concludes that the method is easy to use and effective

global existence for a new periodic integrable equation we establish the local well posedness for a new periodic integrable equation we show that the equation has classical solutions that blowup in finite time as well as classical solutions which exist globally in time

paper the role of the interactor matrix in multivariable stochastic adaptive control this paper is concerned with the extension of the well known minimum variance control strategy to the multi input multi output case it is shown that this extension is straightforward when the system interactor matrix is diagonal but presents some unexpected difficulties in the general case we develop a suitable stochastic controller for the general case as a logical extension of the single input algorithm we also explore the properties of the algorithm in detail we also address the question of adaptive control of multivariable stochastic systems and investigate one possible strategy for overcoming the requirement of knowing the system interactor matrix a priori

colliding peakons and the formation of shocks in the degasperis procesi equation the degasperisprocesi equation dp is one of several equations known to model important nonlinear effects such as wave breaking and shock creation it is however a special property of the dp equ

generalized mixed μ bounds for real and complex multiple block uncertainty with internal matrix structure new absolute stability results that unify and extend existing structured singular value bounds for mixed uncertainty are developed using frequency domain arguments these bounds generalize prior upper bounds for mixed by permitting the treatment of non diagonal real uncertain blocks as well as accounting for internal matrix structure in the uncertainty several specializations to well known absolute stability criteria from the classical literature are given which allow for a systematic comparison of these results in addressing the problem of robust stability for real parameter uncertainty

adaptive generalized predictive controller for mimo systems the multivariate generalized predictive controller gpc is studied clarke 1987a shah 1987 the multivariable gpc algorithm is presented in a stochastic framework and a model following capability is introduced in the control law the method is described for a controlled autoregressive integrated moving average carima model and for the equivalent state space representation in its innovation form the closed loop system equations are derived and analyzed using the state space approach

the recursive generalized predictive feedback control theory and experiments the proposed adaptive control algorithm combines the recursive least squares system identification algorithm and the generalized predictive control gpc design algorithm referred to as recursive generalized predictive control rgpc in the gpc design process the prediction horizon and control horizon are the constants to be chosen two new parameters are defined to describe the effects of the prediction and control horizons and those parameters provide the effective ranges of the horizons the rgpc algorithm adjusts the control penalty based on the stability of a closed loop system model a time varying algorithm for the control penalty allows to design an aggressive controller the multi sampling rate algorithm is added between the system identification and the control design in order to design a higher order controller the rgpc algorithm is applied to three different systems a cantilevered beam a sound enclosure and an optical jitter suppression testbed

a separate bias u d factorization filter two forms of friedland s separate bias estimation algorithm with u d factorization of the covariance matrices are provided each is suited to implementation in a particular computing environment we consider matlab and compiled computer languages we reduce the computation time substantially primarily at the time propagation stage by using a separated bias formulation while retaining the desirable numerical properties of the u d factorization the perecentage reduction typically increases with ratio of bias state dimension to dynamic state dimension a numerical evaluation is given for the matlab algorithm

new forms of extended kalman filter via transversal linearization and applications to structural system identification two novel forms of the extended kalman filter ekf are proposed for parameter estimation in the context of problems of interest in structural mechanics these filters are based on variants of the derivative free locally transversal linearization ltl and multi step transversal linearization mtrl schemes thus unlike the conventional ekf the proposed filters do not need computing jacobian matrices at any stage while the ltl based filter provides a single step procedure the mtrl based filter works over multiple time steps and finds the system transition matrix of the conditionally linearized vector field through magnus expansion other major advantages of the new filters over the conventional ekf are in their superior numerical accuracy and considerably less sensitivity to the choice of timestep sizes a host of numerical illustrations covering single as well as multi degree of freedom oscillators with time invariant parameters and those with discontinuous temporal variations are presented to confirm the numerical advantages of the novel forms of ekf over the conventional one

stable generalized predictive control with constraints and bounded disturbances disturbances in the presence of constraints can drive predictive control into infeasibility and instability this problem has attracted little research effort despite its significant practical importance earlier work has given stability conditions but these are restricted to systems with at most one unstable pole and do not lead to suitable algorithms because they apply to infinite horizons only here we modify the constraint limits and derive an algorithm with guaranteed stability and asymptotic tracking available degrees of freedom are given up in order to optimize performance the results of the paper are illustrated by means of numerical examples

on the uniqueness of discontinuous solutions to the degasperis procesi equation abstract we prove uniqueness within a class of discontinuous solutions to the nonlinear and third order dispersive degasperis procesi equation t u t x x 3 u 4 u x u 3 x u x x 2 u u x x x 3 u in a recent paper g m coclite k h karlsen on the well posedness of the degasperis procesi equation j funct anal 233 2006 60 91 we proved for this equation the existence and uniqueness of l 1 bv weak solutions satisfying an infinite family of kru kov type entropy inequalities the purpose of this paper is to replace the kru kov type entropy inequalities by an ole nik type estimate and to prove uniqueness via a nonlocal adjoint problem an implication is that a shock wave in an entropy weak solution to the degasperis procesi equation is admissible only if it jumps down in value like the inviscid burgers equation

optimal solution of the two stage kalman estimator the two stage kalman estimator was originally proposed to reduce the computational complexity of the augmented state kalman filter it was also applied to the tracking of maneuvering targets by treating the target acceleration as a bias term except in certain restrictive conditions the conventional two stage estimators are suboptimal in the sense that they are not equivalent to the augmented state filter in this paper the authors propose a new two stage kalman estimator i e new structure which is an extension of friedland s estimator and is optimal in general conditions in addition we provide some analytic results to demonstrate the computational advantages of two stage estimators over augmented ones

speed and rotor flux estimation of induction machines using a two stage extended kalman filter this paper presents an effective implementation of an extended kalman filter used for the estimation of both rotor flux and rotor velocity of an induction motor an algorithm proposed by hsieh and chen in hsieh c s chen f c 1999 optimal solution of the two stage kalman estimator ieee transactions on automatic control 44 1 194 199 for linear parameter estimation is extended to non linear estimation where parameters such as the velocity of an induction machine are present in the transition matrix and in the augmented state space compared to a straightforward implementation of an extended kalman filter our modified optimal two stage kalman estimator reduces the number of arithmetic operations by 25 allowing higher sampling rate or the use of a cheaper microcontroller

uniqueness via the adjoint problems for systems of conservation laws we prove a result of uniqueness of the entropy weak solution to the cauchy problem for a class of nonlinear hyperbolic systems of conservation laws that includes in particular the p system of isentropic gas dynamics our result concerns weak solutions satisfying the as we call it wave entropy condition or wec for short introduced in this paper the main feature of this condition is that it concerns both shock waves and rarefaction waves present in a solution for the proof of uniqueness we derive an existence result respectively a uniqueness result for the backward respectively forward adjoint problem associated with the nonlinear system our method also applies to obtain results of existence or uniqueness for some linear hyperbolic systems with discontinuous coefficients 1993 john wiley sons inc

numerical integration approach to on line identification of continuous time systems abstract the problem of estimating the parameters in linear continuous differential equation models from sampled data is treated using a linear integral filter we can obtain an identification model that is parametrized directly in the continuous time model parameters the unknown initial states of the system do not require estimation the choice of the sampling interval and the design of the linear integral filter are discussed considering the accuracy of parameter estimates and the computational burden by applying the results from discrete time model identification with the obtained identification model a discrete time parameter estimation method is developed and the necessary condition as well as the sufficient condition on the input for consistency are explicitly derived and discussed in particular situations a simulation study is also included to confirm the theoretical results

paper self tuning control of nonminimum phase systems the instability that arises from the pole zero cancellation of elementary self tuners and most mrac algorithms has given rise to a misapprehension that nonminimum phase systems can pose insoluble problems with the application of adaptive control since most practical processes exhibit some form of nonminimum phase behaviour particularly when controlled digitally this appeared to restrict the usefulness of self tuning methods however during the last few years new algorithms have been suggested which partly overcome these difficulties and have been shown to be effective in industrial trials the paper describes the practical features that a self tuning controller must possess and discusses how plant dead time and excess continuous time poles can lead to discrete time nonminimum phase zeros the source of instability of elementary self tuners is analysed and various suggested approaches for overcoming this problem are reviewed these include the use of a generalized minimum variance cost function incorporating control weighting factorization methods which avoid cancellation of the offending zeros adaptive control based on state space linear quadratic gaussian lqg theory and explicit pole placement via solution of a diophantine or bezoutian equation gawthrop s hybrid controller which avoids those nonminimum phase zeros due to continuous time pole excess is briefly discussed a series of simulations in which a nonminimum phase plant is subjected to a pattern of set point changes is presented to show some of the features of the algorithms in applications the order of the process is unlikely to be known or indeed be finite the pole placement algorithm which is particularly effective in the known order case is shown to lack robustness to underspecified order the use of a large control weighting however restores stability to the generalized minimum variance controller the conclusions are that with appropriate design and engineering judgement adaptive control is viable even for nonminimum phase processes

an alternate derivation and extension of friendland s two stage kalman estimator an alternate simplified derivation of friedland s two stage kalman estimator is given for a somewhat more general class of problems than considered by friedland friedland s result is also extended to encompass two variations on the basic idea which are of practical interest

global weak solutions for a new periodic integrable equation with peakon solutions abstract we prove the existence of global weak solutions for a new periodic integrable equation with peakon solutions

conservative finite difference schemes for the degasperis procesi equation we consider the numerical integration of the degasperis procesi equation which was recently introduced as a completely integrable shallow water equation for the equation we propose nonlinear and linear finite difference schemes that preserve two invariants associated with the bi hamiltonian form of the equation at the same time we also prove the unique solvability of the schemes and show some numerical examples

on the optimality of two stage state estimation in the presence of random bias sufficient conditions for the optimality of a two stage state estimator in the presence of random bias are derived under an algebraic constraint on the correlation between the state and bias process noises the optimal estimate of the system state can be obtained as a linear combination of the output of the first stage a bias free filter and the second stage a bias filter because the algebraic constraint is restrictive in practice the results indirectly indicate that for most practical systems the proposed solution to the two stage estimation problem will be suboptimal

comments on optimal solution of the two stage kalman estimator the optimal two stage kalman estimator otske is analyzed c s hsieh and f c chen see ibid vol 44 p 194 9 1999 comparison with two estimators shows that the optimal two stage kalman estimator has no advantage especially no computational advantage over the augmented state kalman filter

robust stabilization for continuous time systems with slowly time varying uncertain real parameters the authors construct a class of parameter dependent lyapunov functions to guarantee robust stability in the presence of time varying rate restricted plant uncertainty extensions to a class of time varying nonlinear uncertainty that generalize the multivariable popov criterion are also considered these results are then used for controller synthesis to address the problem of robust stabilization in the presence of slowly time varying real parameters

an operator splitting method for the degasperis procesi equation an operator splitting method is proposed for the degasperis procesi dp equation by which the dp equation is decomposed into the burgers equation and the benjamin bona mahony bbm equation then a second order tvd scheme is applied for the burgers equation and a linearized implicit finite difference method is used for the bbm equation furthermore the strang splitting approach is used to construct the solution in one time step the numerical solutions of the dp equation agree with exact solutions e g the multipeakon solutions very well the proposed method also captures the formation and propagation of shockpeakon solutions and reveals wave breaking phenomena with good accuracy

optimal two stage kalman filter in the presence of random bias abstract this paper gives an optimal solution of the two stage kalman filter for linear stochastic systems subject to random bias it is shown that the state estimate can be expressed as x k k x k k k k b k k where x k k is a modified bias free state estimate and b k k the optimal estimate of random bias

study of the transient phase of the forgetting factor rls we investigate the convergence properties of the forgetting factor rls algorithm in a stationary data environment using the settling time as our performance measure we show that the algorithm exhibits a variable performance that depends on the particular combination of the initialization and noise level specifically when the observation noise level is low high snr rls when initialized with a matrix of small norm it has an exceptionally fast convergence convergence speed decreases as we increase the norm of the initialization matrix in a medium snr environment the optimum convergence speed of the algorithm is reduced as compared with the previous case however rls becomes more insensitive to initialization finally in a low snr environment we show that it is preferable to initialize the algorithm with a matrix of large norm

initial boundary value problems for conservation laws with source terms and the degasperis procesi equation we consider conservation laws with source terms in a bounded domain with dirichlet boundary conditions we first prove the existence of a strong trace at the boundary in order to provide a simple formulation of the entropy boundary condition equipped with this formulation we go on to establish the well posedness of entropy solutions to the initial boundary value problem the proof utilizes the kinetic formulation and the averaging lemma finally we make use of these results to demonstrate the well posedness in a class of discontinuous solutions to the initial boundary value problem for the degasperis procesi shallow water equation which is a third order nonlinear dispersive equation that can be rewritten in the form of a nonlinear conservation law with a nonlocal source term

multipeakons of a two component modified camassa holm equation and the relation with the finite kac van moerbeke lattice abstract a spectral and the inverse spectral problem are studied for the two component modified camassa holm type for measures associated to interlacing peaks it is shown that the spectral problem is equivalent to an inhomogeneous string problem with dirichlet neumann boundary conditions the inverse problem is solved by stieltjes s continued fraction expansion leading to an explicit construction of peakon solutions sufficient conditions for global existence of solutions are given the large time asymptotics reveals that asymptotically peakons pair up to form bound states moving with constant speeds the peakon flow is shown to project to one of the isospectral flows of the finite kac van moerbeke lattice

general two stage kalman filters a general two stage kalman filter that is equivalent to but numerically more efficient than the standard single stage kalman filter is developed for general time varying linear discrete time systems analytical results defining the reduction in computational burdens are presented simulation results that validate the predicted efficiency improvements are shown as well

periodic solutions of the degasperis procesi equation well posedness and asymptotics abstract we prove the well posedness of periodic entropy discontinuous solutions for the degasperis procesi equation partly motivated by the bounded periodic solutions found by vakhnenko and parkes 21 we study the long time asymptotic behavior of periodic entropy solutions

oleinik type estimates for the ostrovsky hunter equation abstract the ostrovsky hunter equation provides a model of small amplitude long waves in a rotating fluid of finite depth this is a nonlinear evolution equation in this study we consider the well posedness of the cauchy problem associated with this equation within a class of bounded discontinuous solutions we show that we can replace the kruzkov type entropy inequalities with an oleinik type estimate and we prove the uniqueness via a nonlocal adjoint problem this implies that a shock wave in an entropy weak solution to the ostrovsky hunter equation is admissible only if it jumps down in value similar to the inviscid burgers equation

global well posedness and relaxation limits of a model for radiating gas abstract we study the initial value problem for a hyperbolic elliptic coupled system with arbitrary large discontinuous initial data we prove existence and uniqueness for that model by means of l1 contraction and comparison properties moreover after suitable scalings we study both the hyperbolic parabolic and the hyperbolic hyperbolic relaxation limits for that system

optimal multistage kalman estimators an optimal multistage kalman estimator omske is proposed as a generalization of the optimal two stage kalman estimator for the reduction of the computational burden of the kalman estimator ke for discrete time linear time varying systems with triangular transition matrices this new filer is obtained by applying a multistage u v transformation to decouple the covariances of the ke it is shown analytically that the computational complexity of the omske is less than that of the ke and is minimum when the system transition matrix has the maximum stage number

computationally efficient optimal output decentralized estimation this paper presents decentralized computational architectures for the optimal state estimation in stochastic large scale linear systems the main feature of the proposed architectures lies on elaborating each subsystem s decision not only by processing its own local data but also by adjusting this decision with all other related subsystem s local data this adjustment procedure ensures the optimality of the decentralized filter it is emphasized that the kalman filter algorithm operates more efficiently when measurements are processed into low order subsets especially when they are processed one at a time thus using this feature in a decentralized scheme significantly increases computational savings and numerical stability architectures presented in this paper for the mechanization of decentralized estimators allow a high degree of parallelism and can be implemented on a wide range of computer networks

multivariable adaptive control without a prior knowledge of the delay matrix this paper is concerned with the structure and role of the time delay matrix in discrete time multivariable processes interpretations and properties of this matrix as a multivariable generalization of the siso delay term are discussed it is formally shown that a finite time horizon or multi step cost function for the multivariable case can be minimized subject to a suitable choice of output and control horizons and without prior knowledge of the system delay matrix

robust stable generalized predictive control nominal models of linear systems subject to uncertainty are normally assumed to be most representative of the class of all possible models and are used for the purposes of design however in general the controllers derived do not have acceptable properties with respect to robust stability and relative stability the question then arises as to whether design should be based on models other than the nominal in this paper we consider this problem in the context of stable generalized predictive control and give a characterization of all models that lead to controllers with guaranteed robustness properties a procedure for selecting a particular controller is given and the results are illustrated by numerical examples these demonstrate very clearly that small amounts of detuning with respect to the response of the nominal model afford very significant gains by way of robustness

the periodic b equation and euler equations on the circle in this note we show that the periodic b equation can only be realized as a euler equation on the lie group diff s1 of all smooth and orientation preserving diffeomorphisms on the circle if b 2 i e for the camassa holm equation in this case the inertia operator generating the metric on diff s1 is given by a 1 x2 in contrast the degasperis procesi equation for which b 3 is not a euler equation on diff s1 for any inertia operator our result generalizes a recent result of kolev some geometric investigations on the degasperis procesi shallow water equation wave motion 46 412 419 2009

a polynomial approach to bias aware fixed lag smoothing problem in the present technical note a solution to the problem of fixed lag smoothing of siso systems in presence of a dynamical bias is presented in a polynomial framework the bias aware smoothing problem is solved in three steps namely the design of the general structure of the smoother the estimation of the dynamical bias by means of a deconvolution technique and then the combination of the previous results to obtain the bias aware fixed lag smoother applied to an example this approach shows its efficiency

optimal and suboptimal separate bias kalman estimators for a stochastic bias addresses two issues concerning the separate bias kalman estimator the first of these issues deals with the derivation of the optimal estimator for the general case in which the bias vector is stochastic in nature and the second issue deals with defining a suitable suboptimal realization of the generalized estimator

lax integrability and the peakon problem for the modified camassa holm equation peakons are special weak solutions of a class of nonlinear partial differential equations modelling non linear phenomena such as the breakdown of regularity and the onset of shocks we show that the natural concept of weak solutions in the case of the modified camassa holm equation studied in this paper is dictated by the distributional compatibility of its lax pair and as a result it differs from the one proposed and used in the literature based on the concept of weak solutions used for equations of the burgers type subsequently we give a complete construction of peakon solutions satisfying the modified camassa holm equation in the sense of distributions our approach is based on solving certain inverse boundary value problem the solution of which hinges on a combination of classical techniques of analysis involving stieltjes continued fractions and multi point pade approximations we propose sufficient conditions needed to ensure the global existence of peakon solutions and analyze the large time asymptotic behaviour whose special features include a formation of pairs of peakons that share asymptotic speeds as well as toda like sorting property

burgers poisson a nonlinear dispersive model equation a dispersive model equation is considered which has been proposed by whitham linear and nonlinear waves john wiley sons new york 1974 as a shallow water model and which can also be seen as a caricature of two species euler poisson problems a number of formal properties as well as similarities to other dispersive equations are derived a travelling wave analysis and some numerical tests are carried out the equation features wave breaking in finite time a local existence result for smooth solutions and a global existence result for weak entropy solutions are proved finally a small dispersion limit is carried out for situations where the solution of the limiting equation is smooth