Identification of smooth nonlinear dynamical systems with non-smooth steady-state features

This work discusses the identification of single-block smooth nonlinear discrete-time polynomial models with non-smooth steady-state features. Based on bifurcation theory, conditions are developed and used to determine some general aspects of the model structure and also to determine some constraints on the parameters required to guarantee the aforementioned features. The procedure uses only smooth functions of the regressors, a single possibly smooth input and some prior knowledge about the steady-state behavior. The non-smooth static function is here obtained by interchanging the stability of two sets of equilibria at the break-point, which corresponds to guaranteeing a transcritical bifurcation. This work discusses how to determine the domain over which the results are valid. The procedure is illustrated with simulated and experimental data.     

Auxiliary model-based least-squares identification methods for Hammerstein output-error systems

The difficulty in identification of a Hammerstein (a linear dynamical block following a memoryless nonlinear block) nonlinear output-error model is that the information vector in the identification model contains unknown variables—the noise-free (true) outputs of the system. In this paper, an auxiliary model-based least-squares identification algorithm is developed. The basic idea is to replace the unknown variables by the output of an auxiliary model. Convergence analysis of the algorithm indicates that the parameter estimation error consistently converges to zero under a generalized persistent excitation condition. The simulation results show the effectiveness of the proposed algorithms.     

A simplified NARMAX method using nonlinear input-output data

A system identification method for nonlinear systems with unknown structure is presented using short input-output data. The method simplifies the original NARMAX method. It introduces more general model structures for nonlinear systems. The group method of data handling (GMDH) method is employed to obtain the model terms and parameters. Effectiveness of the proposed method is illustrated by a typical nonlinear system with unknown structure and deficient input-output data.     

A simplified NARMAX method using nonlinear input-output data

A system identification method for nonlinear systems with unknown structure is presented using short input-output data. The method simplifies the original NARMAX method. It introduces more general model structures for nonlinear systems. The group method of data handling （GMDH） method is employed to obtain the model terms and parameters. Effectiveness of the proposed method is illustrated by a typical nonlinear system with unknown structure and deficient input-output data.     

Linear estimator stabilization of nonlinear sampled-data systems

It has been shown that the state of a linear system can be constructed from observations of its inputs and outputs. The observer which performs the construction is itself a linear system with time constants which may be chosen by the designer. This linear asymptotic estimator has been used previously to stabilize certain types of contimuous nonlinear systems. In this paper, a linear sampled-data estimator is developed. This estimator is used first to stabilize a linear sampled-data system and then it is used to stabilize a class of nonlinear sampled-data systems by the choice of the estimator's time constants and the feedback gain. Typical example applications are analyzed to illustrate the theoretical investigations.     

A multiple model approach for predictive control of nonlinear hybrid systems

This paper presents modeling and control of nonlinear hybrid systems using multiple linearized models. Each linearized model is a local representation of all locations of the hybrid system. These models are then combined using Bayes theorem to describe the nonlinear hybrid system. The multiple models, which consist of continuous as well as discrete variables, are used for synthesis of a model predictive control (MPC) law. The discrete-time equivalent of the model predicts the hybrid system behavior over the prediction horizon. The MPC formulation takes on a similar form as that used for control of a continuous variable system. Although implementation of the control law requires solution of an online mixed integer nonlinear program, the optimization problem has a fixed structure with certain computational advantages. We demonstrate performance and computational efficiency of the modeling and control scheme using simulations on a benchmark three-spherical tank system and a hydraulic process plant.     

An algorithm for bounded-error identification of nonlinear systems based on DC functions

This paper presents a guaranteed method for the parameter estimation of nonlinear models in a bounded-error context. This method is based on functions which consists of the difference of two convex functions, called DC functions. The method considers DC representations of the functional form of the dynamic system to obtain an outer bound of the set of parameters that are consistent with the measurements, the system and the considered bounded error. At each iteration, the proposed algorithm solves several convex optimization problems to discard from the initial search region subregions that are proved not consistent. This operation is repeated while the obtained solution is improved. Four examples are provided to clarify the proposed identification algorithm.     

A novel data filtering based multi-innovation stochastic gradient algorithm for Hammerstein nonlinear systems

The identification of nonlinear systems is a hot topic in the identification fields. In this paper, a data filtering based multi-innovation stochastic gradient algorithm is derived for Hammerstein nonlinear controlled autoregressive moving average systems by adopting the key-term separation principle and the data filtering technique. The proposed algorithm provides a reference to improve the identification accuracy of the nonlinear systems with colored noise. The simulation results show that the new algorithm can more effectively estimate the parameters of the Hammerstein nonlinear systems than the multi-innovation stochastic gradient algorithm.     

Fault isolation for nonlinear dynamic systems based on parameter intervals

The study of fault detection and isolation for nonlinear dynamic systems has been receiving significant attention. Up to now few literatures pay attention to the speed of fault isolation. However, it is a crucial problem for the design of the fault-tolerant control (FTC) of the nonlinear dynamic systems. In this article a new method of fault isolation for nonlinear dynamic systems is proposed. The method is based on the monotonous characteristic of the prediction error of the observer with respect to singular parameter difference between the system and the observer. The proposed method has the advantage of the methods based on adaptive observers that fits a large kind of nonlinear dynamic systems, while it does not have their disadvantage that take a long time to identify the system parameter: Therefore the fault isolation of this method is quicker. The performance of the method is illustrated by simulation results using a nonlinear dynamic model of an alcoholic fermentation process.     

Parameter identification for nonlinear systems: Guaranteed confidence regions through LSCR

In this paper we consider the problem of constructing confidence regions for the parameters of nonlinear dynamical systems. The proposed method uses higher order statistics and extends the LSCR (leave-out sign-dominant correlation regions) algorithm for linear systems introduced in Campi and Weyer [2005, Guaranteed non-asymptotic confidence regions in system identification. Automatica 41(10), 1751-1764. Extended version available at 〈http://www.ing.unibs.it/∼campi〉]. The confidence regions contain the true parameter value with a guaranteed probability for any finite number of data points. Moreover, the confidence regions shrink around the true parameter value as the number of data points increases. The usefulness of the proposed approach is illustrated on some simple examples.     

A PWA model identification method based on optimal operating region partition with the output-error minimization for nonlinear systems

When piecewise affine (PWA) model-based control methods are applied to nonlinear systems, the first question is how to get sub-models and corresponding operating regions. Motivated by the fact that the operating region of each sub-model is an important component of a PWA model and the parameters of a sub-model are strongly coupled with the operating region, a new PWA model identification method based on optimal operating region partition with the output-error minimization for nonlinear systems is initiated. Firstly, construct local data sets from input-output data and get local models by using the least square (LS) method. Secondly, cluster local models according to the feature vectors and identify the parameter vectors of sub-models by weighted least squares (WLS) method. Thirdly, get the initial operating region partition by using a normalized exponential function, which is to partition the operating space completely. Finally, simultaneously determine the optimal parameter vectors of sub-models and the optimal operating region partition underlying the output-error minimization, which is executed by particle swarm optimization (PSO) algorithm. Simulation results demonstrate that the proposed method can improve model accuracy compared with two existing methods.     

A methodology for control-relevant nonlinear system identification using restricted complexity models

A broadly-applicable, control-relevant system identification methodology for nonlinear restricted complexity models (RCMs) is presented. Control design based on RCMs often leads to controllers which are easy to interpret and implement in real-time. A control-relevant identification method is developed to minimize the degradation in closed-loop performance as a result of RCM approximation error. A two-stage identification procedure is presented. First, a nonlinear ARX model is estimated from plant data using an orthogonal least squares algorithm; a Volterra series model is then generated from the nonlinear ARX model. In the second stage, a RCM with the desired structure is estimated from the Volterra series model through a model reduction algorithm that takes into account closed-loop performance requirements. The effectiveness of the proposed method is illustrated using two chemical reactor examples.     

On linear models for nonlinear systems

Best linear time-invariant (LTI) approximations are analysed for several interesting classes of discrete nonlinear time-invariant systems. These include nonlinear finite impulse response systems and a class of nonsmooth systems called bi-gain systems. The Fréchet derivative of a smooth nonlinear system is studied as a potential good LTI model candidate. The Fréchet derivative is determined for nonlinear finite memory systems and for a class of Wiener systems. Most of the concrete results are derived in an ?_∞ signal setting. Applications to linear controller design, to identification of linear models and to estimation of the size of the unmodelled dynamics are discussed.     

Identification of block-oriented nonlinear systems using orthonormal bases

In this paper, new noniterative algorithms for the identification of (multivariable) block-oriented nonlinear models consisting of the interconnection of linear time invariant systems and static nonlinearities are presented. The proposed algorithms are numerically robust, since they are based only on least squares estimation and singular value decomposition. Two different block-oriented nonlinear models are considered in this paper, viz., the Hammerstein model, and the Wiener model. For the Hammerstein model, the proposed algorithm provides consistent estimates even in the presence of colored output noise, under weak assumptions on the persistency of excitation of the inputs. For the Wiener model, consistency of the estimates can only be guaranteed in the noise free case. Key in the derivation of the results is the use of basis functions for the representation of the linear and nonlinear parts of the models. The performance of the proposed identification algorithms is illustrated through simulation examples of two benchmark problems drawn from the process control literature, viz., a binary distillation column and a pH neutralization process.     

A neural state estimator with bounded errors for nonlinear systems

A neural state estimator is described, acting on discrete-time nonlinear systems with noisy measurement channels. A sliding-window quadratic estimation cost function is considered and the measurement noise is assumed to be additive. No probabilistic assumptions are made on the measurement noise nor on the initial state. Novel theoretical convergence results are developed for the error bounds of both the optimal and the neural approximate estimators. To ensure the convergence properties of the neural estimator, a minimax tuning technique is used. The approximate estimator can be designed offline in such a way as to enable it to process on line any possible measure pattern almost instantly     

Identification of nonlinear systems using a piecewise-linear Hammerstein model

In the paper a method for nonlinear system identification is proposed. It is based on a piecewise-linear Hammerstein model, which is linear in the parameters. The model and the identification algorithm are adapted to allow the parameter identification in the presence of a special form of the excitation signal. The identification method is derived from a recursive least-squares algorithm, which is properly adapted to take into account the proposed model structure and the properties of the identification signal. The applicability of the approach is illustrated by an example in which a discontinuous nonlinear static function is connected to a dynamic block.     

Nonlinear feedback design for fixed-time tracking of a class of nonlinear systems

Fixed-time control is more preferable than finite-time control in practical applications since the settling time is independent of the system initial condition in a fixed-time control problem. Moreover, systems in real world usually suffer from unfavourable factors, such as unknown control coefficients and external disturbance. In this paper, we consider the fixed-time tracking control for a class of nonlinear systems by considering the aforementioned two points. A strategy for specifying the control input is established by the method of adding a power integrator. The designed control law guarantees that the reference signal can be followed in a fixed time. As an application, the bank-to-turn missile system is used to show the efficiency of the proposed fixed-time tracking scheme.     

A two-stage algorithm for identification of nonlinear dynamic systems

This paper investigates the two-stage stepwise identification for a class of nonlinear dynamic systems that can be described by linear-in-the-parameters models, and the model has to be built from a very large pool of basis functions or model terms. The main objective is to improve the compactness of the model that is obtained by the forward stepwise methods, while retaining the computational efficiency. The proposed algorithm first generates an initial model using a forward stepwise procedure. The significance of each selected term is then reviewed at the second stage and all insignificant ones are replaced, resulting in an optimised compact model with significantly improved performance. The main contribution of this paper is that these two stages are performed within a well-defined regression context, leading to significantly reduced computational complexity. The efficiency of the algorithm is confirmed by the computational complexity analysis, and its effectiveness is demonstrated by the simulation results.