Least squares-based iterative identification methods for linear-in-parameters systems using the decomposition technique

By extending the least squares-based iterative (LSI) method, this paper presents a decomposition-based LSI (D-LSI) algorithm for identifying linear-in-parameters systems and an interval-varying D-LSI algorithm for handling the identification problems of missing-data systems. The basic idea is to apply the hierarchical identification principle to decompose the original system into two fictitious sub-systems and then to derive new iterative algorithms to estimate the parameters of each sub-system. Compared with the LSI algorithm and the interval-varying LSI algorithm, the decomposition-based iterative algorithms have less computational load. The numerical simulation results demonstrate that the proposed algorithms work quite well

Networked Control System Design and Parameter Estimation

Networked control systems (NCSs) are a kind of distributed control systems in which the data between control components are exchanged via communication networks. Because of the attractive advantages of NCSs such as reduced system wiring, low weight, and ease of system diagnosis and maintenance, the research on NCSs has received much attention in recent years. The first part (Chapter 2 - Chapter 4) of the thesis is devoted to designing new controllers for NCSs by incorporating the network-induced delays. The thesis also conducts research on filtering of multirate systems and identification of Hammerstein systems in the second part (Chapter 5 - Chapter 6). Network-induced delays exist in both sensor-to-controller (S-C) and controller-to-actuator (C-A) links. A novel two-mode-dependent control scheme is proposed, in which the to-be-designed controller depends on both S-C and C-A delays. The resulting closed-loop system is a special jump linear system. Then, the conditions for stochastic stability are obtained in terms of a set of linear matrix inequalities (LMIs) with nonconvex constraints, which can be efficiently solved by a sequential LMI optimization algorithm. Further, the control synthesis problem for the NCSs is considered. The definitions of H₂ and H∞ norms for the special system are first proposed. Also, the plant uncertainties are considered in the design. Finally, the robust mixed H₂/H∞ control problem is solved under the framework of LMIs. To compensate for both S-C and C-A delays modeled by Markov chains, the generalized predictive control method is modified to choose certain predicted future control signal as the current control effort on the actuator node, whenever the control signal is delayed. Further, stability criteria in terms of LMIs are provided to check the system stability. The proposed method is also tested on an experimental hydraulic position control system. Multirate systems exist in many practical applications where different sampling rates co-exist in the same system. The l₂-l∞ filtering problem for multirate systems is considered in the thesis. By using the lifting technique, the system is first transformed to a linear time-invariant one, and then the filter design is formulated as an optimization problem which can be solved by using LMI techniques. Hammerstein model consists of a static nonlinear block followed in series by a linear dynamic system, which can find many applications in different areas. New switching sequences to handle the two-segment nonlinearities are proposed in this thesis. This leads to less parameters to be estimated and thus reduces the computational cost. Further, a stochastic gradient algorithm based on the idea of replacing the unmeasurable terms with their estimates is developed to identify the Hammerstein model with two-segment nonlinearities. Finally, several open problems are listed as the future research directions

Integrated Pre-Processing for Bayesian Nonlinear System Identification with Gaussian Processes

We introduce GP-FNARX: a new model for nonlinear system identification based on a nonlinear autoregressive exogenous model (NARX) with filtered regressors (F) where the nonlinear regression problem is tackled using sparse Gaussian processes (GP). We integrate data pre-processing with system identification into a fully automated procedure that goes from raw data to an identified model. Both pre-processing parameters and GP hyper-parameters are tuned by maximizing the marginal likelihood of the probabilistic model. We obtain a Bayesian model of the system's dynamics which is able to report its uncertainty in regions where the data is scarce. The automated approach, the modeling of uncertainty and its relatively low computational cost make of GP-FNARX a good candidate for applications in robotics and adaptive control.Comment: Proceedings of the 52th IEEE International Conference on Decision and Control (CDC), Firenze, Italy, December 201

Identification of continuous-time model of hammerstein system using modified multi-verse optimizer

his thesis implements a novel nature-inspired metaheuristic optimization algorithm, namely the modified Multi-Verse Optimizer (mMVO) algorithm, to identify the continuous-time model of Hammerstein system. Multi-Verse Optimizer (MVO) is one of the most recent robust nature-inspired metaheuristic algorithm. It has been successfully implemented and used in various areas such as machine learning applications, engineering applications, network applications, parameter control, and other similar applications to solve optimization problems. However, such metaheuristics had some limitations, such as local optima problem, low searching capability and imbalance between exploration and exploitation. By considering these limitations, two modifications were made upon the conventional MVO in our proposed mMVO algorithm. Our first modification was an average design parameter updating mechanism to solve the local optima issue of the traditional MVO. The essential feature of the average design parameter updating mechanism is that it helps any trapped design parameter jump out from the local optima region and continue a new search track. The second modification is the hybridization of MVO with the Sine Cosine Algorithm (SCA) to improve the low searching capability of the conventional MVO. Hybridization aims to combine MVO and SCA algorithms advantages and minimize the disadvantages, such as low searching capability and imbalance between exploration and exploitation. In particular, the search capacity of the MVO algorithm has been improved using the sine and cosine functions of the Sine Cosine Algorithm (SCA) that will be able to balance the processes of exploration and exploitation. The mMVO based method is then used for identifying the parameters of linear and nonlinear subsystems in the Hammerstein model using the given input and output data. Note that the structure of the linear and nonlinear subsystems is assumed to be known. Moreover, a continuous-time linear subsystem is considered in this study, while there are a few methods that utilize such models. Two numerical examples and one real-world application, such as the Twin Rotor System (TRS) are used to illustrate the efficiency of the mMVO-based method. Various nonlinear subsystems such as quadratic and hyperbolic functions (sine and tangent) are used in those experiments. Numerical and experimental results are analyzed to focus on the convergence curve of the fitness function, the parameter variation index, frequency and time domain response and the Wilcoxon rank test. For the numerical identifications, three different levels of white noise variances were taken. The statistical analysis value (mean) was taken from the parameter deviation index to see how much our proposed algorithm has improved. For Example 1, the improvements are 29%, 33.15% and 36.68%, and for the noise variances, 0.01, 0.25, and 1.0 improvements can be found. For Example 2, the improvements are 39.36%, 39.61% and 66.18%, and for noise variances, the improvements are by 0.01, 0.25 and 1.0, respectively. Finally, for the real TRS application, the improvement is 7%. The numerical and experimental results also showed that both Hammerstein model subsystems are defined effectively using the mMVO-based method, particularly in quadratic output estimation error and a differentiation parameter index. The results further confirmed that the proposed mMVObased method provided better solutions than other optimization techniques, such as PSO, GWO, ALO, MVO and SCA

Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems

Metaheuristics algorithms to identify nonlinear Hammerstein model: A decade survey

Metaheuristics have been acknowledged as an effective solution for many difficult issues related to optimization. The metaheuristics, especially swarm’s intelligence and evolutionary computing algorithms, have gained popularity within a short time over the past two decades. Various metaheuristics algorithms are being introduced on an annual basis and applications that are more new are gradually being discovered. This paper presents a survey for the years 2011-2021 on multiple metaheuristics algorithms, particularly swarm and evolutionary algorithms, to identify a nonlinear block-oriented model called the Hammerstein model, mainly because such model has garnered much interest amidst researchers to identify nonlinear systems. Besides introducing a complete survey on the various population-based algorithms to identify the Hammerstein model, this paper also investigated some empirically verified actual process plants results. As such, this article serves as a guideline on the fundamentals of identifying nonlinear block-oriented models for new practitioners, apart from presenting a comprehensive summary of cutting-edge trends within the context of this topic area