Home About us Contact | |||

## Nonlinear Systems (nonlinear + system)
Kinds of Nonlinear Systems
## Selected Abstracts## ADAPTIVE SLIDING MODE BACKSTEPPING CONTROL OF NONLINEAR SYSTEMS WITH UNMATCHED UNCERTAINTY ASIAN JOURNAL OF CONTROL, Issue 4 2004Ali J. KoshkoueiABSTRACT This paper considers an adaptive backstepping algorithm for designing the control for a class of nonlinear continuous uncertain processes with disturbances that can be converted to a parametric semi-strict feedback form. Sliding mode control using a combined adaptive backstepping sliding mode control (SMC) algorithm, is also studied. The algorithm follows a systematic procedure for the design of adaptive control laws for the output tracking of nonlinear systems with matched and unmatched uncertainty. [source] ## BACKLASH COMPENSATION IN NONLINEAR SYSTEMS USING DYNAMIC INVERSION BY NEURAL NETWORKS ASIAN JOURNAL OF CONTROL, Issue 2 2000Rastko R. SelmicABSTRACT A dynamic inversion compensation scheme is presented for backlash. The compensator uses the backstepping technique with neural networks (NN) for inverting the backlash nonlinearity in the feedforward path. The technique provides a general procedure for using NN to determine the dynamic preinverse of an invertible dynamical system. A tuning algorithm is presented for the NN backlash compensator which yields a stable closed-loop system. [source] ## Model-Based Failure Detection on Nonlinear Systems: Theory and Transition NAVAL ENGINEERS JOURNAL, Issue 2 2007KIMBERLY J. DRAKEFailure detection is an active area of Navy research due to its many important applications. Recently, an approach for multi-model identification and fault detection in the presence of bounded energy noise over finite time intervals has been introduced. This family of algorithms was originally designed to work on linear systems that can be modeled analytically. In this paper, efforts made toward extending this algorithm for fault detection to nonlinear systems along with efforts in testing this family of algorithms on real systems are discussed. [source] ## Output Regulation Of A Class Of Singular Nonlinear Systems With The Normal Output Feedback Controller ASIAN JOURNAL OF CONTROL, Issue 1 2003Wei WangABSTRACT Existing results for output regulation of singular nonlinear systems via normal output feedback control require the normalizability assumption. In this paper, we will show that, for a large class of singular nonlinear systems, it is possible to construct a normal output feedback control to solve the regulation problem without the normalizability assumption. The major result is illustrated by an example. [source] ## Adaptive Dynamic Output Feedback Stabilisation of Nonlinear Systems ASIAN JOURNAL OF CONTROL, Issue 3 2002A. IlchmannABSTRACT An adaptive dynamical output feedback controller is introduced for a class of nonlinear non-minimum phase systems. This adaptive controller achieves practical stabilisation, that means the output will asymptotically tend to a pre-specified neighbourhood of the origin. In case of linear systems, we can even prove adaptive stabilisation. [source] ## Recursive Back-Stepping Design of An Adaptive Fuzzy Controller for Strict Output Feedback Nonlinear Systems ASIAN JOURNAL OF CONTROL, Issue 3 2002Wei-Yen WangABSTRACT In this paper, a back-stepping adaptive fuzzy controller is proposed for strict output feedback nonlinear systems. The unknown nonlinearity and external disturbances of such systems are considered. We assume that only the output of the system is available for measurement. As a result, two filters are constructed to estimate the states of strict output feedback systems. Since fuzzy systems can uniformly approximate nonlinear continuous functions to arbitrary accuracy, the adaptive fuzzy control theory combined with a tuning function scheme is developed to derive the control laws of strict output feedback systems that possess unknown functions. Moreover, the H, performance condition is introduced to attenuate the effect of the modeling error and external disturbances. Finally, an example is simulated in order to confirm the applicability of the proposed method. [source] ## Simple Recurrent Neural Network-Based Adaptive Predictive Control for Nonlinear Systems ASIAN JOURNAL OF CONTROL, Issue 2 2002Xiang LiABSTRACT Making use of the neural network universal approximation ability, a nonlinear predictive control scheme is studied in this paper. On the basis of a uniform structure of simple recurrent neural networks, a one-step neural predictive controller (OSNPC) is designed. The whole closed-loop system's asymptotic stability and passivity are discussed, and stable conditions for the learning rate are determined based on the Lyapunov stability theory for the whole neural system. The effectiveness of OSNPC is verified via exhaustive simulations. [source] ## Neural Network Adaptive Robust Control Of Siso Nonlinear Systems In A Normal Form ASIAN JOURNAL OF CONTROL, Issue 2 2001J.Q. GongABSTRACT In this paper, performance oriented control laws are synthesized for a class of single-input-single-output (SISO) n -th order nonlinear systems in a normal form by integrating the neural networks (NNs) techniques and the adaptive robust control (ARC) design philosophy. All unknown but repeat-able nonlinear functions in the system are approximated by the outputs of NNs to achieve a better model compensation for an improved performance. While all NN weights are tuned on-line, discontinuous projections with fictitious bounds are used in the tuning law to achieve a controlled learning. Robust control terms are then constructed to attenuate model uncertainties for a guaranteed output tracking transient performance and a guaranteed final tracking accuracy. Furthermore, if the unknown nonlinear functions are in the functional ranges of the NNs and the ideal NN weights fall within the fictitious bounds, asymptotic output tracking is achieved to retain the perfect learning capability of NNs. The precision motion control of a linear motor drive system is used as a case study to illustrate the proposed NNARC strategy. [source] ## Nonlinear systems possessing linear symmetry INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2007Daizhan ChengAbstract This paper tackles linear symmetries of control systems. Precisely, the symmetry of affine nonlinear systems under the action of a sub-group of general linear group GL(n,,). First of all, the structure of state space (briefly, ss) symmetry group and its Lie algebra for a given system is investigated. Secondly, the structure of systems, which are ss-symmetric under rotations, is revealed. Thirdly, a complete classification of ss-symmetric planar systems is presented. It is shown that for planar systems there are only four classes of systems which are ss-symmetric with respect to four linear groups. Fourthly, a set of algebraic equations are presented, whose solutions provide the Lie algebra of the largest connected ss-symmetry group. Finally, some controllability properties of systems with ss-symmetry group are studied. As an auxiliary tool for computation, the concept and some properties of semi-tensor product of matrices are included. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Probabilistic Approach for Nonlinear Modal Control of MDOF Structures Subjected to Multiple Excitations COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 1 2005Kyung-Won MinFor the modal control of the MDOF structure, a new eigenvalue assignment algorithm that modifies the dynamic characteristics of only the specific mode is proposed. For the probabilistic evaluation of the proposed nonlinear modal control, the joint probability density function (PDF) of the equivalent nonlinearly controlled single-degree-of-freedom (SDOF) system is obtained by the solution of the reduced Fokker,Planck equation for the equivalent nonlinear system. To overcome the difficulty in the application of the joint PDF to the MDOF structure controlled by the hybrid mass damper (HMD) system and subjected to multiple excitations, the equivalent damping ratio is proposed. The results of the analysis indicate that the proposed nonlinear modal control strategy is effective for the control of MDOF structures requiring a significantly smaller peak control force than the linear quadratic Gaussian (LQG) controller to produce a similar control performance level. [source] ## Stability improvement in power systems with non-linear TCSC control strategies EUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 6 2000X. LeiIn this paper, a non-linear control scheme for the TCSC (thyristor-controlled series compensator) to dampen power oscillations and to improve the transient stability of power systems is presented. Based on an one-machine-infinite-bus system, a non-linear mathematical model is established which is proven as an affine nonlinear system. With the help of the feedback linearization technique, the affine non-linear model is exactly transferred to a linear model, and then the control scheme is designed for the TCSC based on the global linearization, where the input signal uses local measurements only. The effectiveness and robustness of the proposed non-linear control scheme are demonstrated with an one-machine test system, where the TCSC modelling and power system simulations are performed by using the program system NETOMAC. In comparison with a conventional control scheme, significant improvements of dynamical performance in the test power' system are achieved by the proposed non-linear control strategy for the TCSC. [source] ## A subspace algorithm for simultaneous identification and input reconstruction INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 12 2009Harish J. Palanthandalam-MadapusiAbstract This paper considers the concept of input and state observability, that is, conditions under which both the unknown input and initial state of a known model can be determined from output measurements. We provide necessary and sufficient conditions for input and state observability in discrete-time systems. Next, we develop a subspace identification algorithm that identifies the state-space matrices and reconstructs the unknown input using output measurements and known inputs. Finally, we present several illustrative examples, including a nonlinear system in which the unknown input is due to the endogenous nonlinearity. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Passivity-based sliding mode control for nonlinear systems INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 9 2008Ali J. KoshkoueiAbstract Passivity with sliding mode control for a class of nonlinear systems with and without unknown parameters is considered in this paper. In fact, a method for deriving a nonlinear system with external disturbances to a passive system is considered. Then a passive sliding mode control is designed corresponding to a given storage function. The passivity property guarantees the system stability while sliding mode control techniques assures the robustness of the proposed controller. When the system includes unknown parameters, an appropriate updated law is obtained so that the new transformed system is passive. The passivation property of linear systems with sliding mode is also analysed. The linear and nonlinear theories are applied to a simple pendulum model and the gravity-flow/pipeline system, respectively. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Measurement of climate complexity using sample entropy INTERNATIONAL JOURNAL OF CLIMATOLOGY, Issue 15 2006Li ShuangchengAbstract A climate system is a complex nonlinear system. Estimation of the complexity is of great interest in climatic forecast and prediction. In this paper, we propose the use of sample entropy (SampEn), an entropy-based algorithm, to measure the complexity of daily temperature series. Estimations of SampEn were calculated for 50 meteorological stations in the mountains of Southwest China, particularly in Yunnan Province. On the basis of these data, stations were grouped in climatically homogenous regions (climate provinces), and the spatial pattern of SampEn for each climate province was investigated. The SampEn value of spatial distribution of climate provinces reflects the varying degree of influence of the monsoonal air masses. High SampEn values occur in interactive regions of different air masses, owing to large regional differences in weather processes, while the southwest region is under the influence of the Southwest Monsoon leading to a homogenous climatic environment, low SampEn values and small spatial variations of SampEn. The results suggest that SampEn is an alternative nonlinear approach for analyzing and predicting complexity of climatic time series. Copyright © 2006 Royal Meteorological Society [source] ## Emergence of self-learning fuzzy systems by a new virus DNA,based evolutionary algorithm INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 3 2003Lihong RenIn this article, we propose a new approach to the virus DNA,based evolutionary algorithm (VDNA-EA) to implement self-learning of a class of Takagi-Sugeno (T-S) fuzzy controllers. The fuzzy controllers use T-S fuzzy rules with linear consequent, the generalized input fuzzy sets, Zadeh fuzzy logic and operators, and the generalized defuzzifier. The fuzzy controllers are proved to be nonlinear proportional-integral (PI) controllers with variable gains. The fuzzy rules are discovered automatically and the design parameters in the input fuzzy sets and the linear rule consequent are optimized simultaneously by the VDNA-EA. The VDNA-EA uses the VDNA encoding method that stemmed from the structure of the VDNA to encode the design parameters of the fuzzy controllers. We use the frameshift decoding method of the VDNA to decode the DNA chromosome into the design parameters of the fuzzy controllers. In addition, the gene transfer operation and bacterial mutation operation inspired by a microbial evolution phenomenon are introduced into the VDNA-EA. Moreover, frameshift mutation operations based on the DNA genetic operations are used in the VDNA-EA to add and delete adaptively fuzzy rules. Our encoding method can significantly shorten the code length of the DNA chromosomes and improve the encoding efficiency. The length of the chromosome is variable and it is easy to insert and delete parts of the chromosome. It is suitable for complex knowledge representation and is easy for the genetic operations at gene level to be introduced into the VDNA-EA. We show how to implement the new method to self-learn a T-S fuzzy controller in the control of a nonlinear system. The fuzzy controller can be constructed automatically by the VDNA-EA. Computer simulation results indicate that the new method is effective and the designed fuzzy controller is satisfactory. © 2003 Wiley Periodicals, Inc. [source] ## Reduced-order impulsive control for a class of nonlinear systems INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2010Yan-Wu WangAbstract Impulsive control of nonlinear systems is an attractive topic and a number of interesting results have been obtained in the recent years. However, most of the available results need to employ full information of the system states to achieve the desired objectives. In this paper, a reduced-order impulsive control strategy that needs only part of state components is studied for a general class of nonlinear system, which is feasible for the case when some of the system states are not available or controllable. Typical chaotic systems, such as Lorenz system, Chua's oscillator, and Chen's system, are taken as examples. A systematic design scheme is proposed to select the impulsive intervals. After some theoretical analysis, simulation results illustrate the effectiveness of the proposed control scheme. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Numerical nonlinear observers using pseudo-Newton-type solvers INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 17 2008Shigeru HanbaArticle first published online: 12 DEC 200Abstract In constructing a globally convergent numerical nonlinear observer of Newton-type for a continuous-time nonlinear system, a globally convergent nonlinear equation solver with a guaranteed rate of convergence is necessary. In particular, the solver should be Jacobian free, because an analytic form of the state transition map of the nonlinear system is generally unavailable. In this paper, two Jacobian-free nonlinear equation solvers of pseudo-Newton type that fulfill these requirements are proposed. One of them is based on the finite difference approximation of the Jacobian with variable step size together with the line search. The other uses a similar idea, but the estimate of the Jacobian is mostly updated through a BFGS-type law. Then, by using these solvers, globally stable numerical nonlinear observers are constructed. Numerical results are included to illustrate the effectiveness of the proposed methods. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Predictor-based repetitive learning control for a class of remote control nonlinear systems INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 16 2007Ya-Jun PanAbstract In this paper, a repetitive learning control (RLC) approach is proposed for a class of remote control nonlinear systems satisfying the global Lipschitz condition. The proposed approach is to deal with the remote tracking control problem when the environment is periodic or repeatable over infinite time domain. Since there exist time delays in the two transmission channels: from the controller to the actuator and from the sensor to the controller, tracking a desired trajectory through a remote controller is not an easy task. In order to solve the problem caused by time delays, a predictor is designed on the controller side to predict the future state of the nonlinear system based on the delayed measurements from the sensor. The convergence of the estimation error of the predictor is ensured. The gain design of the predictor applies linear matrix inequality (LMI) techniques developed by Lyapunov Kravoskii method for time delay systems. The RLC law is constructed based on the feedback error from the predicted state. The overall tracking error tends to zero asymptotically over iterations. The proof of the stability is based on a constructed Lyapunov function related to the Lyapunov Kravoskii functional used for the proof of the predictor's convergence. By well incorporating the predictor and the RLC controller, the system state tracks the desired trajectory independent of the influence of time delays. A numerical simulation example is shown to verify the effectiveness of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Multivariable override control for systems with output and state constraints INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 13-14 2004Matthew C. TurnerAn override control strategy for systems having limits on their outputs, states or linear combinations of the two, is discussed. The technique described is applicable to all nonlinear system-controller combinations which can be written in a certain linear closed-loop form. The discussion is first confined to the synthesis of a compensator where the limited states/outputs are perfectly known, and is then broadened to include an observer-based compensator for the case when these measurements are not directly available. It is shown that, although a form of ,separation principle' indeed holds for the observer-based problem, the type of solution available for this form of override control is not quite as strong as that available when an observer is not required. The results are illustrated using a simple multivariable example. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Robust nonlinear ship course-keeping control by H, I/O linearization and , -synthesis INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2003Shr-Shiung HuAbstract In this paper, the H, input/output (I/O) linearization formulation is applied to design an inner-loop nonlinear controller for a nonlinear ship course-keeping control problem. Due to the ship motion dynamics are non-minimum phase, it is impossible to use the ordinary feedback I/O linearization to resolve. Hence, the technique of H, I/O linearization is proposed to obtain a nonlinear H, controller such that the compensated nonlinear system approximates the linear reference model in I/O behaviour. Then a , -synthesis method is employed to design an outer-loop robust controller to address tracking, regulation, and robustness issues. The time responses of the tracking signals for the closed-loop system reveal that the overall robust nonlinear controller is able to provide robust stability and robust performance for the plant uncertainties and state measurement errors. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Comments on "Gradient-Induced Acoustic and Magnetic Field Fluctuations in a 4T Whole-Body MR Imager" ,, MAGNETIC RESONANCE IN MEDICINE, Issue 2 2001Alan BarnettAbstract The results published in the article Gradient-Induced Acoustic and Magnetic Field Fluctuations in a 4T Whole-Body MR Imager by Wu et al. (Magn Reson Med 2000;44:532,536) appear to be consistent with the response of a time-stationary linear system. Since a linear system is more simply described than a nonlinear system, the authors are urged to reanalyze their data to test the linear-system hypothesis. Magn Reson Med 46:207, 2001. Published 2001 Wiley-Liss, Inc. [source] ## Convergence of coercive approximations for a model of gradient type in poroplasticity MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2009Sebastian OwczarekAbstract We study the existence theory to the quasi-static initial-boundary-value problem of poroplasticity. In this article the classical quasi-static Biot model is considered for soil consolidation coupled with a nonlinear system of differential equations. This work, for the poroplasticity model of monotone-gradient type, presents a convergence result of the coercive approximation to the solution of the original noncoercive problem. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## A meshless method using the radial basis functions for numerical solution of the regularized long wave equation NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2010Ali ShokriAbstract This article discusses on the solution of the regularized long wave (RLW) equation, which is introduced to describe the development of the undular bore, has been used for modeling in many branches of science and engineering. A numerical method is presented to solve the RLW equation. The main idea behind this numerical simulation is to use the collocation and approximating the solution by radial basis functions (RBFs). To avoid solving the nonlinear system, a predictor-corrector scheme is proposed. Several test problems are given to validate the new technique. The numerical simulation, includes the propagation of a solitary wave, interaction of two positive solitary waves, interaction of a positive and a negative solitary wave, the evaluation of Maxwellian pulse into stable solitary waves and the development of an undular bore. The three invariants of the motion are calculated to determine the conservation properties of the algorithm. The results of numerical experiments are compared with analytical solution and with those of other recently published methods to confirm the accuracy and efficiency of the presented scheme.© 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 [source] ## A multigrid upwind strategy for accelerating steady-state computations of waves propagating with curvature-dependent speeds NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2002Jonathan RochezAbstract A multigrid strategy using upwind finite differencing is developed for accelerating the steady state computations of waves, [14] propagating with curvature-dependent speeds. This will allow the rapid computation of a "burn table." In a high explosive material, a burn table will allow the elimination of solving chemical reaction ODEs by feeding in source terms to the reactive flow equations for solution of the system of ignition of the high explosive material. Standard iterative methods show a quick reduction of the residual followed by a slow final convergence to the solution at high iterations. Such systems, including a nonlinear system such as this, are excellent choices for the use of multigrid methods to speed up convergence. Numerical steady-state solutions to the eikonal equation on several test grids are conducted. Results are presented for these cases in 2D and a cubic grid in 3D using a Runge-Kutta time iteration for the smoothing operator until steady state is reached. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 179,192, 2002; DOI 10.1002/num.1002 [source] ## Incorporating a class of constraints into the dynamics of optimal control problems OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 6 2009K. GraichenAbstract A method is proposed to systematically transform a constrained optimal control problem (OCP) into an unconstrained OCP, which can be treated in the standard calculus of variations. The considered class of constraints comprises up to m input constraints and m state constraints with well-defined relative degree, where m denotes the number of inputs of the given nonlinear system. Starting from an equivalent normal form representation, the constraints are incorporated into a new system dynamics by means of saturation functions and differentiation along the normal form cascade. This procedure leads to a new unconstrained OCP, where an additional penalty term is introduced to avoid the unboundedness of the saturation function arguments if the original constraints are touched. The penalty parameter has to be successively reduced to converge to the original optimal solution. The approach is independent of the method used to solve the new unconstrained OCP. In particular, the constraints cannot be violated during the numerical solution and a successive reduction of the constraints is possible, e.g. to start from an unconstrained solution. Two examples in the single and multiple input case illustrate the potential of the approach. For these examples, a collocation method is used to solve the boundary value problems stemming from the optimality conditions. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Homogenization in the Theory of Viscoplasticity PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005Sergiy NesenenkoWe study the homogenization of the quasistatic initial boundary value problem with internal variables which models the deformation behavior of viscoplastic bodies with a periodic microstructure. This problem is represented through a system of linear partial differential equations coupled with a nonlinear system of differential equations or inclusions. Recently it was shown by Alber [2] that the formally derived homogenized initial boundary value problem has a solution. From this solution we construct an asymptotic solution for the original problem and prove that the difference of the exact solution and the asymptotic solution tends to zero if the lengthscale of the microstructure goes to zero. The work is based on monotonicity properties of the differential equations or inclusions. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Fault isolation in nonlinear systems with structured partial principal component analysis and clustering analysis THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 3 2000Yunbing HuangAbstract Partial principal component analysis (PCA) and parity relations are proven to be useful methods in fault isolation. To overcome the limitation of applying partial PCA to nonlinear problems, a new approach utilizing clustering analysis is proposed. By dividing a partial data set into smaller subsets, one can build more accurate PCA models with fewer principal components, and isolate faults with higher precision. Simulations on a 2 × 2 nonlinear system and the Tennessee Eastman (TE) process show the advantages of using the clustered partial PCA method over other nonlinear approaches. L'analyse des principaux constituants partielle et les relations de parité s'avèrent des méthodes utiles pour isoler les défaillances. Mais étant donné les limites d'application de l'analyse partielle des principaux constituants, on propose une nouvelle méthode reposant sur l'analyse de la formation des grappes. En divisant un jeu de données partielles en plusieurs sous-groupes plus petits, on peut créer des modèles d'analyse des principaux constituants plus précis avec un nombre de constituants moins importants et isoler les défaillances avec une meilleure précision. Les simulations sur un système non linéaire 2 × 2 et le procédé Tennessee Eastman (TE) montrent les avantages de la méthode d'analyse des principaux constituants partielle par grappes par rapport aux autres methodes non linéaires. [source] ## On the equivalence between Kalman smoothing and weak-constraint four-dimensional variational data assimilation THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 613 2005M. FisherAbstract The fixed-interval Kalman smoother produces optimal estimates of the state of a system over a time interval, given observations over the interval, together with a prior estimate of the state and its error covariance at the beginning of the interval. At the end of the interval, the Kalman smoother estimate is identical to that produced by a Kalman filter, given the same observations and the same initial state and covariance matrix. For an imperfect model, the model error term in the covariance evolution equation acts to reduce the dependence of the estimate on observations and prior states that are well separated in time. In particular, if the assimilation interval is sufficiently long, the estimate at the end of the interval is effectively independent of the state and covariance matrix specified at the beginning of the interval. In this case, the Kalman smoother provides estimates at the end of the interval that are identical to those of a Kalman filter that has been running indefinitely. For a linear model, weak-constraint four-dimensional variational data assimilation (4D-Var) is equivalent to a fixed-interval Kalman smoother. It follows that, if the assimilation interval is made sufficiently long, the 4D-Var analysis at the end of the assimilation interval will be identical to that produced by a Kalman filter that has been running indefinitely. The equivalence between weak-constraint 4D-Var and a long-running Kalman filter is demonstrated for a simple analogue of the numerical weather-prediction (NWP) problem. For this nonlinear system, 4D-Var analysis with a 10-day assimilation window produces analyses of the same quality as those of an extended Kalman filter. It is demonstrated that the current ECMWF operational 4D-Var system retains a memory of earlier observations and prior states over a period of between four and ten days, suggesting that weak-constraint 4D-Var with an analysis interval in the range of four to ten days may provide a viable algorithm with which to implement an unapproximated Kalman filter. Whereas assimilation intervals of this length are unlikely to be computationally feasible for operational NWP in the near future, the ability to run an unapproximated Kalman filter should prove invaluable for assessing the performance of cheaper, but suboptimal, alternatives. Copyright © 2005 Royal Meteorological Society [source] ## Explicit nonlinear predictive control for a magnetic levitation system, ASIAN JOURNAL OF CONTROL, Issue 3 2010A. UlbigAbstract The paper presents a methodology for the construction of an explicit nonlinear control law via approximation of the nonlinear constrained finite-time optimal control (CFTOC). This is achieved through an approximate mapping of a general nonlinear system in a set of linear piecewise affine (PWA) systems. The key advantages of this methodology are two-fold. First, the construction of an analytic solution of the CFTOC problem leads to an efficient explicit implementation. Second, by taking advantage of model predictive control's systematic fashion to handle constraints, an improved performance can be obtained for the closed-loop system. The proposed theory is applied in real-time for a system with fast dynamics: a magnetic levitation benchmark. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] ## Recursive identification for dynamic systems with backlash, ASIAN JOURNAL OF CONTROL, Issue 1 2010Ruili DongAbstract A recursive algorithm for identification of nonlinear dynamic systems with backlash is proposed in this paper. In this method, the backlash, which is a non-smooth function, is decomposed into a combination of a group of piecewise linearized models so that all the parameters of the backlash can be estimated separately. Moreover, the model of the backlash is embedded into a Hammerstein-type model. Thus, a pseudo-Hammerstein model with backlash is constructed. The estimation of the parameters for such a non-smooth nonlinear system can be implemented through a so-called recursive general identification algorithm (RGIA). Then, the corresponding convergence analysis of the RGIA for the model with backlash is also investigated. After that, two examples are presented to show the performance of the proposed method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] |