Method of Hybrid Approximations for Modelling of Multidimensional Nonlinear Systems

Presenting an important potential in the representation of nonlinear systems, the multimodel approach remains an attractive axis for research. One of the important problems in the multimodel structure concerns the validity calculation which is a fundamental point especially when the process is corrupted with noise and/or its parameters are of high variations. A new approach based on the use of both two type of validity is proposed. A developed specification of the need of each one is explained by an optimization procedure. The conduct of this approach requires, first, the classification of the numerical data into a set of clusters. The frequency-sensitive competitive learning (FSCL) algorithm is used to select the number of models and the fuzzy k-means algorithm identify the operating clusters. From the satisfactory results in terms of precision and robustness obtained on theoretical examples, we are incited to confirm our contribution to real process reactor. The results obtained are compared to the classical approaches showing its ability to represent adequately the nonlinear process with a superior precision and accuracy and from this the classic strategy of multimodel representation is oriented towards a multifaceted approach.

A new discretization method for the calculation of a sampled-data representation of nonlinear continuous-time system is proposed. The suggested method is based on the well-known Taylor-series expansion and zero-order hold (ZOH) assumption. The mathematical structure of the new discretization method is analyzed. On the basis of this structure the sampled-data representation of nonlinear system with time-delayed multi-input is derived. First the new approach is applied to nonlinear systems with two inputs. And then the delayed multi-input general equation has been derived. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. And ’hybrid’ discretization schemes that result from a combination of the ’scaling and squaring’ technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method’s parameters to meet CPU time and accuracy requirements, are examined as well. A performance of the proposed method is evaluated using a nonlinear system with time-delay: maneuvering an automobile.KeywordsNonlinear SystemDiscretization MethodNonlinear Control SystemTaylor MethodFast Time ConstantThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A new convergence analysis for the Volterra series representation of nonlinear systems

A good number of lexical and grammatical models make use of systems of meaning representation which are based on a theory of event structure. Theories of event structure quite often take aspectual features as the backbone for the semantic representation of symbolic units, i.e predicates and constructions. One of the most comprehensive and detailed proposals for the aspectual characterization of both lexical units and argumental constructions can be found in the Lexical Constructional Model, which in turn is based on the system for semantic representations from Role and Reference Grammar. However, such a system presents some drawbacks, which stem mainly from not establishing a neat distinction between what is properly lexical and what is contributed by higher constructional units in the denotation of specific events. Taking such a distinction as a basic premise for a sound characterization of events, in this paper a reassessment of the typology of aspectual classes from these models is made; this critical revision is followed by a hierarchical reorganization of such aspectual classes.

A new time-discretization method for the development of a discrete-time (sampled-data) representation of a nonlinear continuous-time control system with time-delay is proposed. It is based on the Taylor-Lie series expansion method and zero-order hold (ZOH) assumption. The mathematical structure of the new discretization scheme is explored and characterized as useful for establishing concrete connections between numerical and system-theoretic properties. The effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. The resulting time-discretization provides a finite-dimensional representation for nonlinear control systems with time-delay enabling the application of existing controller design techniques. The performance of the proposed discretization procedure is evaluated using a case study.

Effective process monitoring, and control rely on precise dynamic models that can capture the inherent nonlinearities of chemical systems. However, rigorous modeling of complex industrial processes can be computationally demanding. Meta modeling using machine learning methodologies offers a viable approach to generate computationally efficient surrogate representations. Specifically, Echo State Networks (ESNs) are a promising neural network approach for meta-modeling nonlinear dynamical systems. ESNs simplify training through fixed input weights while they focus learning on output weights. This study explores the development of ESN-based digital twins for a nonlinear dynamic process. An ESN is employed to construct a meta-model of a simulated continuously stirred tank reactor with biochemical kinetic. The network was trained on input-output data obtained from the simulation of an ordinary differential equation system, and the performance was evaluated both in-sample and out-of-sample. The results indicate that the ESN meta-model can successfully approximate the underlying dynamics, accurately capturing temporal evolution. A closed-loop digital twin deployment using the ESN surrogate also showed reliable behavior. This work presents initial steps toward developing digital twins of chemical processes using ESN-driven meta-modeling. The findings suggest ESNs can effectively generate computationally efficient surrogate representations of nonlinear dynamical systems. Such digital twins hold promise for online process monitoring and optimized control of industrial plants.

The output delay is always existent in the practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via digital computer. In this paper a new method for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed. This method is applied to the sampled-data representation of a nonlinear system with constant output time-delay. A performance of the proposed method is evaluated using a nonlinear system with time-delay output.

Nonlinearities and system uncertainties are the most important difficulties in designing controllers that ensure stability and acceptable closed-loop performance. Many significant results on the stability and robust control of uncertain nonlinear systems using the TS fuzzy model have been reported over the past decades, and considerable advances have been made (Connor et al. 1992; Chen et al. 1996; Rocha et al. 2005; Boukhezzar et al. 2006; Kamal et al. 2011, 2012a, 2013; Khanl et al. 2011). However, as stated in Khan and Hossain (2011), many approaches for stability and robust control of uncertain systems are often characterized by conservatism when dealing with uncertainties. It has been well known that the TS fuzzy model is very effective representation of complex nonlinear systems. In the TS fuzzy model, the state space of a nonlinear system is divided into different fuzzy regions with a local linear model being used in each region. The overall model output is obtained by defuzzification using the center of gravity (COG) method. Once the fuzzy model is obtained, control design can be carried out via the so-called parallel and distributed computing (PDC) approach, which employs multiple linear controllers corresponding to the locally linear plant models (Boukhezzar et al. 2006). This class of systems is described as a weighted sum of some simple linear subsystems, and thus is easily analyzable.

This paper discusses different issues in the construction and knowledge representation of an intelligent dictionary help system. The Intelligent Dictionary Help System (IDHS) is conceived as a monolingual (explanatory) dictionary system for human use (Artola and Evrard, 1992). The fact that it is intended for people instead of automatic processing distinguishes it from other systems dealing with the acquisition of semantic knowledge from conventional dictionaries. The system provides various access possibilities to the data, allowing to deduce implicit knowledge from the explicit dictionary information. IDHS deals with reasoning mechanisms analogous to those used by humans when they consult a dictionary. User level functionality of the system has been specified and a prototype has been implemented (Agirre et al., 1994a). A methodology for the extraction of semantic knowledge from a conventional dictionary is described. The method followed in the construction of the phrasal pattern hierarchies required by the parser (Alshawi, 1989) is based on an empirical study carried out on the structure of definition sentences. The results of its application to a real dictionary has shown that the parsing method is particularly suited to the analysis of short definition sentences, as it was the case of the source dictionary. As a result of this process, the characterization of the different lexical-semantic relations between senses is established by means of semantic rules (attached to the patterns); these rules are used for the initial construction of the Dictionary Knowledge Base (DKB). The representation schema proposed for the DKB (Agirre et al., 1994b) is basically a semantic network of frames representing word senses. After construction of the initial DKB, several enrichment processes are performed on the DKB to add new facts to it; these processes are based on the exploitation of the properties of lexical-semantic relations, and also on specially conceived deduction mechanisms. The result of the enrichment processes show the suitability of the representation schema chosen to deduce implicit knowledge. Erroneous deductions are mainly due to incorrect word sense disambiguation.

A new time-discretization method for the development of a sampled-data representation of a nonlinear continuous-time input-driven system with time delay is proposed. It is based on the Taylor-Lie series expansion method and zero-order hold assumption. The mathematical structure of the new discretization scheme is explored and characterized as useful for establishing concrete connections between numerical and system-theoretic properties. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. The resulting time-discretization provides a finite-dimensional representation for nonlinear control systems with time-delay enabling the application of existing controller design techniques. The performance of the proposed discretization procedure is evaluated using the case study of a two-degree-of-freedom mechanical system that exhibits nonlinear behavior. Various sampling rates and time-delay values are considered.

Wiener-Hermite functional representation of nonlinear stochastic systems

Prior informed regularization of recursively updated latent-variables-based models with missing observations

Vibration actuators are widely used in handheld devices to provide vibrotactile feedback or silent notification to the users. In most cases, miniature DC motors with eccentric rotors or the so‐called coin‐type shaftless vibration motors are utilized. The common disadvantage of the single rotor designs is that the frequency and the intensity of the generated vibration cannot be adjusted separately. The construction composed of two independently driven coaxial eccentric rotors – which makes a strongly coupled nonlinear system – allows for the separate control of the frequency and amplitude by the adjustment of the angular speed and the total eccentricity. This paper presents a complete control design approach based on quasi‐linear parameter varying (qLPV) modelling and linear matrix inequality (LMI)‐based synthesis utilizing the tensor product (TP) model transformation to determine the convex polytopic representation of the parameter dependent nonlinear system. The design approach is demonstrated via a concrete numerical example using the parameters of a real dual‐excenter prototype device. The control performance is validated through numerical simulations. This case study goes through a complete nonlinear control problem from the modelling phase to the implementation‐ready controller, while drawing generalizable conclusions for qLPV modelling.

The authors study various types of input/output representations for nonlinear continuous-time systems. The algebraic and analytic I/O equations studied in previous work by the authors are generalized to integral and integro-differential equations, and an abstract notion is also considered. New results are given on generic observability, and these results are then applied to give conditions under which the minimal order of an equation equals the minimal possible dimension of a realization, just as with linear systems but in contrast to discrete-time nonlinear theory. >

In this paper, a general approach to design stabilization and fault detection with residual generators for nonlinear systems described by a Takagi-Sugeno model is presented. The first step consists on the presentation of the process and introduction of T-S representation for nonlinear systems. In the second part of this work, we present the problem of the design fault detection. The principle of the proposed strategy is to transform the problem of simultaneously minimizing the perturbation effect and maximizing the fault effect, on the residual vector, in a simple problem of L2-norm minimization.