On robustness in system identification

Identification for Control: From the Early Achievements to the Revival of Experiment Design*

On the Two Practical Issues in System Identification with Wavelets

Systems described by nonlinear difference equations, linear-in-the-parameters, which expand the current output in terms of present and past inputs and past outputs are considered NARMAX (Nonlinear AutoRegressive, Moving Average eXogenous) models. Many systems are described by NARMAX models using only a few terms. However, depending on the order of the system, the number of candidate terms can be very large. Selection of a subset of these candidate terms is necessary for an efficient system description. This remains an unresolved issue in system identification for over-parameterized models. A bootstrap based structure detection algorithm is proposed as a means of determining the structure of highly over-parameterized models. The performance of our bootstrap structure detection technique was evaluated by using it to estimate the structure of two NARMAX models, with colored input and white, zero-mean, output additive noise, and comparing the results to those of the t-test and stepwise regression. The proposed method is simple to use and is robust in the presence of noise.

The study of nonlinear and dynamic systems, as well as the field of practical systems, both make system identification extremely important. Because the vast majority of practical systems do not have any previous information on their behaviour, mathematical modelling is essential. To address this issue of system identification, the authors in this work suggest a Deep-Extreme Learning Machine (DELM) model trained on discrete wavelet transform coefficients. A voice model is considered, similar to the Autoregressive model (AR), for identification. The goal is to create a voice model using machine learning techniques and its identification with level-3 Haar DWT coefficients of the voice signal. The results of the comparison are presented in the result section. The mean square error (MSE) is the metric that is used to assess performance. The proposed DELM model outperforms the models developed with RNN, Bi-LSTM, and LPC-RBF. The findings of this work are able to improve prediction accuracy while reducing convergence time.

This paper considers linear systems subject to sensor and actuator saturations, for which a dynamic output feedback controller has been a priori designed. The effects of unmodeled dynamics appearing as additive uncertainties are studied with respect to the regional (local) stability of the closed-loop system. Constructive conditions based on matrix inequalities, or at least linear matrix inequalities (LMI) are proposed in order to minimize the influence of these unmodeled dynamics on both the estimate of the closed-loop system basin of attraction and on the performance.

Control of industrial plants is an important engineering field of study, where the optimization of such processes can lead to better product quality and higher profit. The present work deals with the optimization of an industrial gasifier, proposed as a benchmark challenge by ALSTOM Power Technologies in 2002. Researchers from around the globe proposed different methods for optimizing such system, using linear and nonlinear system identification techniques, different controller schemes, such as proportional-integral-derivative and model predictive controllers, and search methods for controller tuning. The authors care for the study of a methodology that can generalize the controller optimization process of real industrial systems, where linear system identification can lead to simpler systems, which are used to design more robust controllers. The proposed work deals with linear system identification and multiobjective optimization for the gasifier's controller design. To do so, the authors divide the problem in two steps, the linear system identification, where step functions are fed to the gasifier in order to detect the output response of the system, and the design of a proportional-integral-derivative controller, where spherical pruned multi-objective differential evolution algorithm is used in order to optimize the controller gains. The proposed method, unfortunately, does not provide an optimal controller, which can be explained by the complexity of the benchmark system. With such results, the authors believe a better multi-objective problem definition is necessary. Also, it is concluded that such benchmark presents a real challenge for future controller design methndologies.

System identification with binary-valued output observations under either-or communication and data packet dropout

Identification of Linear Systems Containing Unknown Gain Elements

March 1-3, 1995, San Diego, California Evolutionary programming is one of the predominate algorithms withing the rapidly expanding field of evolutionary computation. These edited contributions to the Fourth Annual Conference on Evolutionary Programming are by leading scientists from academia, industry, and defense. The papers describe both the theory and practical application of evolutionary programming, as well as other methods of evolutionary computation including evolution strategies, genetic algorithms, genetic programming, and cultural algorithms.Topics include :- Novel Areas of Evolutionary Programming and Evolution Strategies.- Evolutionary Computation with Medical Applications.- Issues in Evolutionary Optimization Pattern Discovery, Pattern Recognition, and System Identification.- Hierarchical Levels of Learning.- Self-Adaptation in Evolutionary Computation.- Morphogenic Evolutionary Computation.- Issues in Evolutionary Optimization.- Evolutionary Applications to VLSI and Part Placement.- Applications of Evolutionary Computation to Biology and Biochemistry Control.- Applications of Evolutionary Computation.- Genetic and Inductive Logic Programming.- Genetic Neural Networks.- The Future of Evolutionary Computation.A Bradford Book. Complex Adaptive Systems series

March 1-3, 1995, San Diego, California Evolutionary programming is one of the predominate algorithms withing the rapidly expanding field of evolutionary computation. These edited contributions to the Fourth Annual Conference on Evolutionary Programming are by leading scientists from academia, industry, and defense. The papers describe both the theory and practical application of evolutionary programming, as well as other methods of evolutionary computation including evolution strategies, genetic algorithms, genetic programming, and cultural algorithms.Topics include :- Novel Areas of Evolutionary Programming and Evolution Strategies.- Evolutionary Computation with Medical Applications.- Issues in Evolutionary Optimization Pattern Discovery, Pattern Recognition, and System Identification.- Hierarchical Levels of Learning.- Self-Adaptation in Evolutionary Computation.- Morphogenic Evolutionary Computation.- Issues in Evolutionary Optimization.- Evolutionary Applications to VLSI and Part Placement.- Applications of Evolutionary Computation to Biology and Biochemistry Control.- Applications of Evolutionary Computation.- Genetic and Inductive Logic Programming.- Genetic Neural Networks.- The Future of Evolutionary Computation.A Bradford Book. Complex Adaptive Systems series

Separation of closely spaced modes by combining complex envelope displacement analysis with method of generating intrinsic mode functions through filtering algorithm based on wavelet packet decomposition

Dissolved oxygen concentration in a cultivation broth is an important variable for bioprocesses operation. The oxygen transfer from air to liquid is determined by the oxygen transfer coefficient, usually regulated by the air flow rate and agitation speed. However, many microscopic phenomena are involved in the oxygen transfer. In this paper, a deterministic estimation method for the oxygen transfer coefficient of a bioreactor is proposed. The inclusion of probe dynamics and assumptions of deterministic undermodeling errors improve estimation results when compared to classic least squares methods. The approach is based on Set Membership techniques, it allows the user to fix hard bounds on the effect of unmodeled dynamics and provides feasible coefficient intervals by means of convex optimization problems. Results from a laboratory-scale bioreactor show the effectiveness of the proposed scheme and its advantages over a least-squares solution.

A Frequency Domain Analysis of Direct Adaptive Pole Placement Algorithms in the Presence of Unmodelled Dynamics

Since a real system can hardly be modelled by an exact linear deterministic or stochastic system and in this case a small disturbance may cause instability of adaptive algorithms (Egardt, 1980,Riedle et al 1984,Rohrs,1982),it is of great importance to analyse the influence of the unmodelled dynamics contained in the system upon the behavior of the adaptive control system. For recent years there has been a vast amount of research devoted to this issue (Anderson et al,1986,Bitmead et al,1986,Goodwin et al, 1985,Hili et al,1985,Ioannou et al 1984a,b,Ioannou et ai,1985 and Kosut et al 1984). The authors have analysed the robustness of identification and adaptive control algorithms in (Chen & Guo,1986a,b) for disCreteand continuous-time stochastic systems respectively,when the extended least squares (ELS) identification is applied. Roughly speaking,there it is shown that the estimation error and the deviation of the tracking error from its minimum value is small when the unmodelled dynamics is small in a certain sense. In this paper we are concentrated on the robustness issue of identification for the discrete-time stochastic system which consists of a modelled part being a CARMA process and of an unmodelled part On,i.e. the system is described by

The issue of delay identification for autonomous nonlinear systems is addressed in this work. Using sliding modes control methods it is first proven that the estimation goal can be fulfilled by finding the global norm minimizer of an infinite dimensional mapping. This result is then exploited to design, under different assumptions on the system's knowledge, both a finite-time and an asymptotically convergent identifier.