Nonlinear Block Research Articles

One-shot set-membership identification of Wiener models with polynomial nonlinearities

In this paper we propose a novel approach for set-membership identification of Wiener models when the static output map is a polynomial nonlinearity which, in general, is not assumed to be invertible. Two different estimators are considered in the paper. A setvalued estimator for the computation of the so-called parameter uncertainty intervals and a pointwise estimator aimed at the minimization of the error between the output of the estimated system and the measured one (output error minimization). A unified approach based on the formulation of a suitable semialgebraic optimization problem is proposed for the solution of the considered estimation problems. The proposed approach, which takes to one-shot estimation of the parameters values of both the linear and the nonlinear block, overcomes the main limitations of the approaches already available in the literature for set-membership identification of Wiener models. More precisely, it is not needed anymore any restrictive assumption on the nonlinearity invertibility. Effectiveness of the proposed algorithm is shown by means of a simulation example.

A Novel Ant Colony Optimization Based Scheme for Substitution Box Design

Abstract Efficient substitution boxes have crucial importance in the design of cryptographically strong modern block encryption algorithms. They are the only nonlinear blocks that decide the security strength of entire cryptosystem. In this paper, a meta-heuristic approach based on Ant Colony Optimization and chaos is put forward to retrieve a suitable configuration of strong 8×8 substitution box. The optimization is carried out by transforming initial S-box to travelling salesman problem through edge matrix. The cryptographic strength of optimized S-box is investigated against standard tests such as bijectivity, nonlinearity, strict avalanche criterion, output bits independence criterion and differential approximation probability. The performance comparison of generated S-box with some recent chaos-based S-boxes evidently proves that the proposed scheme is proficient to discover strong nonlinear component of block encryption systems.

Supramolecular self-assembly of novel thermo-responsive double-hydrophilic and hydrophobic Y-shaped [MPEO-b-PEtOx-b-(PCL)2] terpolymers

Nonlinear amphiphilic block copolymer architectures with precisely controlled structures bring new challenges to biomedical materials research.

Reconfigurable Control of Input Affine Nonlinear Systems under Actuator Fault

This paper proposes a fault tolerant control method for input-affine nonlinear systems using a nonlinear reconfiguration block (RB). The basic idea of the method is to insert the RB between the plant and the nominal controller such that fault tolerance is achieved without re-designing the nominal controller. The role of the RB is twofold: on one hand it transforms the output of the faulty system such that its behaviour is similar to that of the nominal one from the controller's viewpoint; on the other hand it modifies the control input to the faulty system such that the stability of the reconfigured loop is preserved. The RB is realized by a virtual actuator and a REFERENCE model. Using notions of incremental and input-to-state stability (ISS), it is shown that ISS of the closed-loop reconfigured system can be achieved by the separate design of the virtual actuator. The proposed method does not need any knowledge of the nominal controller and only assumes that the nominal closed-loop system is ISS. The method is demonstrated on a dynamic positioning system for an offshore supply vessel, where the virtual actuator is designed using backstepping.

Twin Support Vector Machine Method for Identification of Wiener Models

Twin support vector regression is applied to identify nonlinear Wiener system, consisting of a linear dynamic block in series with static nonlinearity. The linear block is expanded in terms of basis functions, such as Laguerre or Kautz filters, and the static nonlinear block is determined using twin support vector machine regression. Simulation of a control valve model and pH neutralization process have been presented to show the features of the proposed algorithm over support vector machine based algorithm.

A Dual Neural Network as an Identifier for a Robot Arm

A novel dual recurrent neural network is presented and is used to identify the dynamics for a robot arm with three-Degrees of freedom (DoF) and trained with a filtered error algorithm. The dual neural network has a structure of two recurrent neural networks working simultaneously fighting each other to obtain the best identification values, being the criteria for the selection of the vest values: the standard deviation for the identification error. The neural identifier provides important information to a nonlinear block control transformation form acting as a control law to solve the trajectory tracking problem for the robotic plant's behavior.

Iterative identification of nonlinear dynamic systems with output backlash using three-block cascade models

The paper deals with the parameter identification of nonlinear dynamic systems with both actuator and sensor nonlinearities using three-block cascade models with nonlinear static, linear dynamic and nonlinear dynamic blocks. Multiple application of a decomposition technique provides special expressions for the corresponding nonlinear model description that are linear in parameters. A least-squares-based iterative technique allows estimation of all the model parameters based on measured input/output data. Illustrative examples of nonlinear systems identification with two-segment polynomial input block and backlash output block characteristics are included.

Recursive Construction of n-gonal Codes on the Basis of Block Design

In the article are defined nonlinear n-gonal block codes. The methods of constructing n-gonal codes are considered. Suggest efficient universal recursive methods of constructing codes great length on the basis of block design for error-correcting code. On the basis of these methods can be constructed error-correcting codes for any predetermined number of errors. Among the codes with a predetermined length codeword and a predetermined number of units in the word, these codes will have a maximum number of codewords. Dignity of these codes is speed of encoding and decoding. Also possibility of fast change of a code without change of tables of encoding and decoding. This makes it possible to use these in cryptosystems.

Nonlinear predictive control for Hammerstein–Wiener systems

This paper discusses a nonlinear Model Predictive Control (MPC) algorithm for multiple-input multiple-output dynamic systems represented by cascade Hammerstein–Wiener models. The block-oriented Hammerstein–Wiener model, which consists of a linear dynamic block embedded between two nonlinear steady-state blocks, may be successfully used to describe numerous processes. A direct application of such a model for prediction in MPC results in a nonlinear optimisation problem which must be solved at each sampling instant on-line. To reduce the computational burden, a linear approximation of the predicted system trajectory linearised along the future control scenario is successively found on-line and used for prediction. Thanks to linearisation, the presented algorithm needs only quadratic optimisation, time-consuming and difficult on-line nonlinear optimisation is not necessary. In contrast to some control approaches for cascade models, the presented algorithm does not need inverse of the steady-state blocks of the model. For two benchmark systems, it is demonstrated that the algorithm gives control accuracy very similar to that obtained in the MPC approach with nonlinear optimisation while performance of linear MPC and MPC with simplified linearisation is much worse.

Adaptive control of Hammerstein–Wiener nonlinear systems

The Hammerstein–Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein–Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.

Modeling of testosterone regulation by pulse-modulated feedback.

The continuous part of a hybrid (pulse-modulated) model of testosterone (Te) feedback regulation in the human male is extended with infinite-dimensional and nonlinear blocks, to obtain the dynamics that better agree with the hormone concentration profiles observed in clinical data. A linear least-squares based optimization algorithm is developed for the purpose of detecting impulses of gonadotropin-releasing hormone (GnRH) from measured concentration of luteinizing hormone (LH). The estimated impulse parameters are instrumental in evaluating the frequency and amplitude modulation functions parameterizing the pulse-modulated feedback. The proposed approach allows for the identification of all model parameters from the hormone concentrations of Te and LH. Simulation results of the complete estimated closed-loop system exhibiting similar to the clinical data behavior are provided.

An Equivalent Circuit Model With Variable Effective Capacity for <inline-formula> <tex-math notation="TeX">$\hbox{LiFePO}_{4}$</tex-math></inline-formula> Batteries

A new approach to equivalent circuit models for LiFePO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> batteries is presented in this paper. The proposed battery model is a semi-physical nonlinear dynamic model with variable effective capacity. Fuzzy logic has been used to capture the nonlinear behavior of the battery in combination with continuous-time differential equations. Fuzzy logic blocks are embedded in a state-space dynamic model as nonlinear constructive blocks. The proposed model has been validated for three different LiFePO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> batteries. The model provides an intuitive physical analogy between charging LiFePO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> batteries and filling a semi-rigid tank, which is useful for explanatory purposes.

Compact, Wearable Antennas for Battery-Less Systems Exploiting Fabrics and Magneto-Dielectric Materials

In this paper, we describe some promising solutions to the modern need for wearable, energy-aware, miniaturized, wireless systems, whose typical envisaged application is a body area network (BAN). To reach this goal, novel materials are adopted, such as fabrics, in place of standard substrates and metallizations, which require a systematic procedure for their electromagnetic characterization. Indeed, the design of such sub-systems represents a big issue, since approximate approaches could result in strong deviations from the actual system performance. To face this problem, we demonstrate our design procedure, which is based on the concurrent use of electromagnetic software tools and nonlinear circuit-level techniques, able to simultaneously predict the actual system behavior of an antenna system, consisting of the radiating and of the nonlinear blocks, at the component level. This approach is demonstrated for the design of a fully-wearable tri-band rectifying antenna (rectenna) and of a button-shaped, electrically-small antenna deploying a novel magneto-dielectric substrate. Simulations are supported by measurements, both in terms of antenna port parameters and far-field results.

Hierarchical Least Squares Identification for Hammerstein Nonlinear Controlled Autoregressive Systems

This paper considers the parametric identification problems of a Hammerstein nonlinear system which consists of a static nonlinear block followed by a linear dynamic subsystem. A hierarchical least squares algorithm is developed by using the hierarchical identification principle, which decomposes a nonlinear system into several subsystems with smaller dimensions and fewer variables and estimates the parameters of each subsystem, respectively. The performance analysis indicates that the parameter estimates given by the proposed algorithm converge to their true values and the proposed algorithm requires higher computational efficiencies compared with the recursive least squares algorithm.

The Research on Establishing Method of the Broadband Nonlinear Transformer Model

The transformer model is one of the most needed to improving components of the modern transient simulation software. A new nonlinear broadband frequency (50Hz-10MHz) model of power transformer is proposed in this paper. The model is divided into a linear block and a nonlinear block by a reasonable equivalent transformation. The linear block is set up through measuring and synthesizing. And the nonlinear block is derived by the impendence of iron core. The final circuit model is built in Simulink, and the comparisons between the simulation and measurement results verify the feasibility and validity of the model.

Parameter estimation of piecewise Hammerstein systems

The system is often described as a series of blocks linked together in non-linear system identification. Such block-oriented models are built with static non-linear subsystems and linear dynamic systems. This paper deals with the parameter estimation of Hammerstein systems with piecewise non-linearities, which is a blocked-oriented model where a static non-linear blocking is followed by a linear dynamic system. The basic idea is as follows. The key term separation technique is applied initially, and then a corresponding auxiliary model is constructed. Hence, the identification problem of the system is converted to a non-linear function optimization problem over parameter space. Once again, the estimates of all the parameters are obtained by a proposed particle swarm optimization algorithm. Finally, compared with the existing methods, the simulation results confirm that the presented method is valid. Moreover, the presented method is further extended to estimate Hammerstein systems with discontinuity non-linearities.

Identification of multivariable nonlinear systems in the presence of colored noises using iterative hierarchical least squares algorithm

This paper presents an efficient method for identification of nonlinear Multi-Input Multi-Output (MIMO) systems in the presence of colored noises. The method studies the multivariable nonlinear Hammerstein and Wiener models, in which, the nonlinear memory-less block is approximated based on arbitrary vector-based basis functions. The linear time-invariant (LTI) block is modeled by an autoregressive moving average with exogenous (ARMAX) model which can effectively describe the moving average noises as well as the autoregressive and the exogenous dynamics. According to the multivariable nature of the system, a pseudo-linear-in-the-parameter model is obtained which includes two different kinds of unknown parameters, a vector and a matrix. Therefore, the standard least squares algorithm cannot be applied directly. To overcome this problem, a Hierarchical Least Squares Iterative (HLSI) algorithm is used to simultaneously estimate the vector and the matrix of unknown parameters as well as the noises. The efficiency of the proposed identification approaches are investigated through three nonlinear MIMO case studies.

Nonlinear fractional‐order power system stabilizer for multi‐machine power systems based on sliding mode technique

SummaryThis paper presents two novel nonlinear fractional‐order sliding mode controllers for power angle response improvement of multi‐machine power systems. First, a nonlinear block control is used to handle nonlinearities of the interconnected power system. In the second step, a decentralized fractional‐order sliding mode controller with a nonlinear sliding manifold is designed. Practical stability is achieved under the assumption that the upper bound of the fractional derivative of perturbations and interactions are known. However, when an unknown transient perturbation occurs in the system, it makes the evaluation of perturbation and interconnection upper bound troublesome. In the next step, an adaptive‐fuzzy approximator is applied to fix the mentioned problem. The fuzzy approximator uses adjacent generators relative speed as own inputs, which is known as semi‐decentralized control strategy. For both cases, the stability of the closed‐loop system is analyzed by the fractional‐order stability theorems. Simulation results for a three‐machine power system with two types of faults are illustrated to show the performance of the proposed robust controllers versus the conventional sliding mode. Additionally, the fractional parameter effects on the system transient response and the excitation voltage amplitude and chattering are demonstrated in the absence of the fuzzy approximator. Finally, the suggested controller is combined with a simple voltage regulator in order to keep the system synchronism and restrain the terminal voltage variations at the same time. Copyright © 2014 John Wiley &amp; Sons, Ltd.

Self-Tuning Control of Linear Systems Followed by Deadzones

The aim of the present paper is to increase the efficiency of self-tuning generalized minimum variance (GMV) control of linear time-invariant (LTI) systems followed by deadzone nonlinearities. An approach, based on reordering of observations to be processed for the reconstruction of an unknown internal signal that acts between LTI system and a static nonlinear block of the closed-loop Wiener system, has been developed. The results of GMV self-tuning control of the second order LTI system with an ordinary deadzone are given.

Identification of parallel Wiener-Hammerstein systems with a decoupled static nonlinearity

Block-oriented models are often used to model a nonlinear system. This paper presents an identification method for parallel Wiener-Hammerstein systems, where the obtained model has a decoupled static nonlinear block. This decoupled nature makes the interpretation of the obtained model more easy. First a coupled parallel Wiener-Hammerstein model is estimated. Next, the static nonlinearity is decoupled using a tensor decomposition approach. Finally, the method is validated on real-world measurements using a custom built parallel Wiener-Hammerstein test system.