DEEP LEARNING OF NONLINEAR DYNAMICAL SYSTEM

A data-driven approach, such as neural networks, is an alternative to traditional parametric-model methods for nonlinear system identification. Recently, long Short- Term Memory (LSTM) neural networks have been studied to model nonlinear dynamical systems. However, many of these contributions are made considering that the input to the system is known or measurable, which often may not be the case. This thesis presents a method based on LSTM for output-only modeling, identification, and prediction of nonlinear systems. A numerical study is performed and discussed on Duffing systems with various cubic nonlinearity

Modeling a quantum Hall system via elliptic equations

Quantum Hall systems are a suitable theme for a case study in the general area of nanotechnology. In particular, it is a good framework in which to search for universal principles relevant to nanosystem modeling, and nanosystem-specific signal processing. Recently, we have been able to construct a PDE model of a quantum Hall system, which consists of the Schr\"odinger equation supplemented with a special type nonlinear feedback loop. This result stems from a novel theoretical approach, which in particular brings to the fore the notion of quantum information. In this article we undertake to modify the original model by substituting the dynamics based on the Dirac operator. This leads to a model that consists of a system of three nonlinearly coupled first order elliptic equations in the plane.Comment: 1 figure, revised version (minor changes

Quadratic and nonlinear programming problems solving and analysis in fully fuzzy environment

AbstractThis paper presents a comprehensive methodology for solving and analyzing quadratic and nonlinear programming problems in fully fuzzy environment. The solution approach is based on the Arithmetic Fuzzy Logic-based Representations, previously founded on normalized fuzzy matrices. The suggested approach is generalized for the fully fuzzy case of the general forms of quadratic and nonlinear modeling and optimization problems of both the unconstrained and constrained fuzzy optimization problems. The constrained problems are extended by incorporating the suggested fuzzy logic-based representations assuming complete fuzziness of all the optimization formulation parameters. The robustness of the optimal fuzzy solutions is then analyzed using the recently newly developed system consolidity index. Four examples of quadratic and nonlinear programming optimization problems are investigated to illustrate the efficacy of the developed formulations. Moreover, consolidity patterns for the illustrative examples are sketched to show the ability of the optimal solution to withstand any system and input parameters changes effects. It is demonstrated that the geometric analysis of the consolidity charts of each region can be carried out based on specifying the type of consolidity region shape (such as elliptical or circular), slope or angle in degrees of the centerline of the geometric, the location of the centroid of the geometric shape, area of the geometric shape, lengths of principals diagonals of the shape, and the diversity ratio of consolidity points. The overall results demonstrate the consistency and effectiveness of the developed approach for incorporation and implementation for fuzzy quadratic and nonlinear optimization problems. Finally, it is concluded that the presented concept could provide a comprehensive methodology for various quadratic and nonlinear systems’ modeling and optimization in fully fuzzy environments

Modeling and simulation of the two-tank system within a hybrid framework

Most real-world dynamical systems are often involving continuous behaviors and discrete events, in this case, they are called hybrid dynamical systems (HDSs). To properly model this kind of systems, it is necessary to consider both the continuous and the discrete aspects of its dynamics. In this paper, a modeling framework based on the hybrid automata (HA) approach is proposed. This hybrid modeling framework allows combining the multi-state models of the system, described by nonlinear differential equations, with the system’s discrete dynamics described by finite state machines. To attest to the efficiency of the proposed modeling framework, its application to a two-tank hybrid system (TTHS) is presented. The TTHS studied is a typical benchmark for HDSs with four operating modes. The MATLAB Simulink and Stateflow tools are used to implement and simulate the hybrid model of the TTHS. Different simulations results demonstrate the efficiency of the proposed modeling framework, which allows us to appropriately have a complete model of an HDS

Model-based and Koopman-based predictive control:a braking control systems comparison

Anti-locking Braking systems are crucial safety systems in modern vehicles. In this work, we investigate the possibility to use Model Predictive Control (MPC) for braking systems by considering three different models identified from data. Specifically, we consider two models, whose structure and the identification procedure are driven by physics principles, and a third black-box modeling approach that relies on Koopman theory. By comparing the effectiveness of the three resulting MPC schemes in a high-fidelity simulation environment, we show that Koopman-based MPC can generally be a viable solution for the design of braking controllers, which might not be the case of nonlinear MPC or approximated scheme like the second one we test.</p

Deep-Learning-Based Identification of LPV Models for Nonlinear Systems

The framework of Linear Parameter-Varying (LPV) systems is part of the modern modeling and control design toolchain for addressing nonlinear system behaviors through linear surrogate models. Despite the significant research effort spent on LPV data-driven modeling, a key shortcoming of the current identification theory is that often the scheduling variable is assumed to be a given measured signal in the data set. In case of identifying an LPV model of a nonlinear system, the selection of the scheduling, i.e., the scheduling map that describes its relation to measurable signals in the system, is put on the users' shoulder, with only limited supporting tools available. Although, such a choice greatly affects the usability and the complexity of the resulting LPV model. This paper presents a deep-learning based approach to provide joint estimation of a scheduling map and an LPV state-space model of a nonlinear system from input-output data. The approach has consistency guarantees under general innovation type of noise conditions, and its efficiency is demonstrated on the identification problem of a control moment gyroscope.Comment: Submitted to the 61st IEEE Conference on Decision and Contro

Optimal design of stimulus experiments for robust discrimination of biochemical reaction networks

Motivation: Biochemical reaction networks in the form of coupled ordinary differential equations (ODEs) provide a powerful modeling tool for understanding the dynamics of biochemical processes. During the early phase of modeling, scientists have to deal with a large pool of competing nonlinear models. At this point, discrimination experiments can be designed and conducted to obtain optimal data for selecting the most plausible model. Since biological ODE models have widely distributed parameters due to, e.g. biologic variability or experimental variations, model responses become distributed. Therefore, a robust optimal experimental design (OED) for model discrimination can be used to discriminate models based on their response probability distribution functions (PDFs). Results: In this work, we present an optimal control-based methodology for designing optimal stimulus experiments aimed at robust model discrimination. For estimating the time-varying model response PDF, which results from the nonlinear propagation of the parameter PDF under the ODE dynamics, we suggest using the sigma-point approach. Using the model overlap (expected likelihood) as a robust discrimination criterion to measure dissimilarities between expected model response PDFs, we benchmark the proposed nonlinear design approach against linearization with respect to prediction accuracy and design quality for two nonlinear biological reaction networks. As shown, the sigma-point outperforms the linearization approach in the case of widely distributed parameter sets and/or existing multiple steady states. Since the sigma-point approach scales linearly with the number of model parameter, it can be applied to large systems for robust experimental planning. Availability: An implementation of the method in MATLAB/AMPL is available at http://www.uni-magdeburg.de/ivt/svt/person/rf/roed.html. Contact: [email protected] Supplementary information: Supplementary data are are available at Bioinformatics online