A fast iterative recursive least squares algorithm for Wiener model identification of highly nonlinear systems

In this paper, an online identification algorithm is presented for nonlinear systems in the presence of output colored noise. The proposed method is based on extended recursive least squares (ERLS) algorithm, where the identified system is in polynomial Wiener form. To this end, an unknown intermediate signal is estimated by using an inner iterative algorithm. The iterative recursive algorithm adaptively modifies the vector of parameters of the presented Wiener model when the system parameters vary. In addition, to increase the robustness of the proposed method against variations, a robust RLS algorithm is applied to the model. Simulation results are provided to show the effectiveness of the proposed approach. Results confirm that the proposed method has fast convergence rate with robust characteristics, which increases the efficiency of the proposed model and identification approach. For instance, the FIT criterion will be achieved 92% in CSTR process where about 400 data is used.     

Time-domain filtering for estimation of linear systems with colored noises using recent finite measurements

To date, finite impulse response (FIR) filters have been proposed to estimate linear systems with white Gaussian noises, but to the best of our knowledge, no solution exists for linear systems with colored noises. In this paper, we propose a new FIR filter to estimate linear state-space models with both process and measurement noises through state augmentation. In addition, we suggest a modified form of the colored-noise FIR filter to deal with the computational burden and singularity problem. Numerical examples are presented to describe the effectiveness of the colored-noise FIR filter.     

Identification of a class of Wiener and Hammerstein-type nonlinear processes with monotonic static gains

In this paper a non-iterative approach to identifying Wiener and Hammerstein models, including model structure and parameters, is proposed. A single symmetrical relay test is conducted to determine the structure and then the parameters of the block-oriented nonlinear model possessing a static nonlinearity and a linear process in cascade. The static nonlinearity block is represented by a memoryless and monotonic function and the linear process by a second order transfer function model. A relay with hysteresis induces the limit cycle output signal and one cycle data of the output signal is used to identify the block-oriented nonlinear model. The proposed identification method is simple and gives better performance than previous methods for processes with static nonlinearity.     

Tracking control of nonlinear lumped mechanical continuous-time systems: A model-based iterative learning approach

This paper presents a nonlinear model-based iterative learning control procedure to achieve accurate tracking control for nonlinear lumped mechanical continuous-time systems. The model structure used in this iterative learning control procedure is new and combines a linear state space model and a nonlinear feature space transformation. An intuitive two-step iterative algorithm to identify the model parameters is presented. It alternates between the estimation of the linear and the nonlinear model part. It is assumed that besides the input and output signals also the full state vector of the system is available for identification. A measurement and signal processing procedure to estimate these signals for lumped mechanical systems is presented. The iterative learning control procedure relies on the calculation of the input that generates a given model output, so-called offline model inversion. A new offline nonlinear model inversion method for continuous-time, nonlinear time-invariant, state space models based on Newton's method is presented and applied to the new model structure. This model inversion method is not restricted to minimum phase models. It requires only calculation of the first order derivatives of the state space model and is applicable to multivariable models. For periodic reference signals the method yields a compact implementation in the frequency domain. Moreover it is shown that a bandwidth can be specified up to which learning is allowed when using this inversion method in the iterative learning control procedure. Experimental results for a nonlinear single-input-single-output system corresponding to a quarter car on a hydraulic test rig are presented. It is shown that the new nonlinear approach outperforms the linear iterative learning control approach which is currently used in the automotive industry on durability test rigs.     

Application of memetic algorithm in modelling discrete-time multivariable dynamics systems

Evolutionary algorithm (EA) such as genetic algorithm (GA) has demonstrated to be an effective method for identification of single-input–single-output (SISO) system. However, for multivariable systems, increasing the orders and the non-linear degrees of the model will result in excessively complex model and the identification procedure for the systems is more often difficult because couplings between inputs and outputs. There are more possible structures to choose from and more parameters are required to obtain a good fit. In this work, a new model structure selection in system identification problems based on a modified GA with an element of local search known as memetic algorithm (MA) is adopted. This paper describes the procedure and investigates the performance and the effectiveness of MA based on a few case studies. The results indicate that the proposed algorithm is able to select the model structure of a system successfully. A comparison of MA with other algorithms such as GAs demonstrates that MA is capable of producing adequate and parsimonious models effectively.     

Recursive generalized extended least squares and RML algorithms for identification of bilinear systems with ARMA noise

Bilinear systems are considered as a particular class of nonlinear systems including the state variables which are typically used for online identification. By using a recursive identification method and the maximum likelihood principle, this paper presents two recursive-based algorithms to identify the parameters of bilinear in parameter systems with ARMA noise. In this regard, recursive generalized extended least squares (RGELS) and recursive Maximum Likelihood (RML) algorithms have been proposed for identification of bilinear systems. These algorithms can be used as an alternative choice in system identification with acceptable performance. The proposed algorithms estimate the correlated noise parameters with high accuracy by making full use of the measurement data. Simulation results indicate that the proposed algorithms are effective for online identification of bilinear in parameter systems with high convergence speed.     

Identification of nonlinear dynamic systems using convex combinations of multiple adaptive radius basis function networks

To improve performance of nonlinear adaptive filter based on radius basis function (RBF) networks, a generalized combination scheme is proposed for nonlinear dynamic system identification in this paper. The nonlinear filter proposed is constructed by the convex combination of multiple RBF networks (MCRBF). Its adaptive algorithm with different step sizes is derived by the gradient descent rule, and can overcome the contradiction between convergence speed and precision of the stochastic gradient (SG) algorithm for RBF networks, which is imposed by the selection of a fixed value for the adaption step. Computer simulations demonstrate that the performance of the nonlinear filter proposed is superior to the RBF for nonlinear dynamic system identification in terms of convergence speed, steady state error and tracking capability.     

Identification and adaptive neural network control of a DC motor system with dead-zone characteristics

In this paper, an adaptive control approach based on the neural networks is presented to control a DC motor system with dead-zone characteristics (DZC), where two neural networks are proposed to formulate the traditional identification and control approaches. First, a Wiener-type neural network (WNN) is proposed to identify the motor DZC, which formulates the Wiener model with a linear dynamic block in cascade with a nonlinear static gain. Second, a feedforward neural network is proposed to formulate the traditional PID controller, termed as PID-type neural network (PIDNN), which is then used to control and compensate for the DZC. In this way, the DC motor system with DZC is identified by the WNN identifier, which provides model information to the PIDNN controller in order to make it adaptive. Back-propagation algorithms are used to train both neural networks. Also, stability and convergence analysis are conducted using the Lyapunov theorem. Finally, experiments on the DC motor system demonstrated accurate identification and good compensation for dead-zone with improved control performance over the conventional PID control.     

Identification and control of dynamical systems using different architectures of recurrent fuzzy system

Fuzzy logic based systems are very widely used for modeling and control of complex non-linear, plants. Fuzzy systems require the knowledge about the structure of the dynamic plant in order to achieve fruitful results. Recurrent Fuzzy systems (RFS) are a variation of fuzzy systems and have the ability to model and control dynamic plants without using the information about the structure of the plant. This paper presents identification and control of non-linear dynamical systems using two different architectures of recurrent fuzzy system (RFS). It highlights the importance of RFS over the conventional type-1 fuzzy based system. The objective of system identification as well as control has been achieved using both the architectures of RFS and the simulation results clearly show their efficiency. This paper also highlights yet another advantage of RFS over the conventional type-1 fuzzy systems which comes into light when dealing with higher order systems. The paper explains how the computational complexity can be greatly reduced by using RFS for higher order dynamical systems. A comparative analysis between the conventional type-1 fuzzy system and the two recurrent fuzzy systems has also been performed.     

Robust output feedback distributed model predictive control of networked systems with communication delays in the presence of disturbance

In this work, an output feedback cooperative distributed model predictive control is developed for a class of networked systems composed of interacting subsystems interconnected through their states, in which it handles bounded disturbances and time varying communication delays. A distributed buffer based prediction strategy is used to compensate bounded delays and predict those states, which are coupled between subsystems that their actual values may not available due to delays. In the design of robust distributed model predictive control, distributed moving horizon estimation is employed so that convergence and boundedness of the estimation error are ensured. Furthermore, robust exponential stability of the closed loop system is established. The effectiveness of the proposed method is illustrated using two interconnected continuous stirred tank reactors.     

Software sensor for on-line estimation of the microbial activity in activated sludge systems

This paper considers the design of a software sensor (or soft-sensor) for the on-line estimation of the biological activities of a colony of aerobic micro-organisms acting on activated sludge processes, where the carbonaceous waste degradation and nitrification processes are taken into account. These bioactivities are intimately related to the dissolved oxygen concentration. Two factors that affect the dynamics of the dissolved oxygen are the respiration rate or the oxygen uptake rate (OUR) and the oxygen transfer function (K(l)a). These items are challenging topics for the application of recursive identification due the nonlinear characteristic of the oxygen transfer function, and to the time-varying feature of the respiration rate. In this work, OUR and the oxygen transfer function are estimated through a software sensor, which is based on a modified version of the discrete extended Kalman filter. Numerical simulations are carried out in a predenitrifying activated sludge process benchmark and the obtained results demonstrate the applicability and efficiency of the proposed methodology, which should provide a valuable tool to supervise and control activated sludge processes.