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

A search algorithm for constrained engineering optimization and tuning the gains of controllers

In this work, the application of an optimization algorithm is investigated to optimize static and dynamic engineering problems. The methodology of the approach is to generate random solutions and find a zone for the initial answer and keep reducing the zones. The generated solution in each loop is independent of the previous answer that creates a powerful method. Simplicity as its main advantage and the interlaced use of intensification and diversification mechanisms--to refine the solution and avoid local minima/maxima--enable the users to apply that for a variety of problems. The proposed approach has been validated by several previously solved examples in structural optimization and scored good results. The method is also employed for dynamic problems in vibration and control. A modification has also been done on the method for high-dimensional test functions (functions with very large search domains) to converge fast to the global minimum or maximum; simulated for several well-known benchmarks successfully. For validation, a number of 9 static and 4 dynamic constrained optimization benchmark applications and 32 benchmark test functions are solved and provided, 45 in total. All the codes of this work are available as supplementary material in the online version of the paper on the journal website

Health Monitoring of Nonlinear Systems with Application to Gas Turbine Engines

Health monitoring and prognosis of nonlinear systems is mainly concerned with system health tracking and its evolution prediction to future time horizons. Estimation and prediction schemes constitute as principal components of any health monitoring framework. In this thesis, the main focus is on development of novel health monitoring techniques for nonlinear dynamical systems by utilizing model-based and hybrid prognosis and health monitoring approaches. First, given the fact that particle filters (PF) are known as a powerful tool for performing state and parameter estimation of nonlinear dynamical systems, a novel dual estimation methodology is developed for both time-varying parameters and states of a nonlinear stochastic system based on the prediction error (PE) concept and the particle filtering scheme. Estimation of system parameters along with the states generate an updated model that can be used for a long-term prediction problem. Next, an improved particle filtering-based methodology is developed to address the prediction step within the developed health monitoring framework. In this method, an observation forecasting scheme is developed to extend the system observation profiles (as time-series) to future time horizons. Particles are then propagated to future time instants according to a resampling algorithm in the prediction step. The uncertainty in the long-term prediction of the system states and parameters are managed by utilizing dynamic linear models (DLM) for development of an observation forecasting scheme. A novel hybrid architecture is then proposed to develop prognosis and health monitoring methodologies for nonlinear systems by integration of model-based and computationally intelligent-based techniques. Our proposed hybrid health monitoring methodology is constructed based on a framework that is not dependent on the structure of the neural network model utilized in the implementation of the observation forecasting scheme. Moreover, changing the neural network model structure in this framework does not significantly affect the prediction accuracy of the entire health prediction algorithm. Finally, a method for formulation of health monitoring problems of dynamical systems through a two-time scale decomposition is introduced. For this methodology the system dynamical equations as well as the affected damage model, are investigated in the two-time scale system health estimation and prediction steps. A two-time scale filtering approach is developed based on the ensemble Kalman filtering (EnKF) methodology by taking advantage of the model reduction concept. The performance of the proposed two-time scale ensemble Kalman filters is shown to be more accurate and less computationally intensive as compared to the well-known particle filtering approach for this class of nonlinear systems. All of our developed methods have been applied for health monitoring and prognosis of a gas turbine engine when it is affected by various degradation damages. Extensive comparative studies are also conducted to validate and demonstrate the advantages and capabilities of our proposed frameworks and methodologies

Mathematical and Numerical Aspects of Dynamical System Analysis

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

14th Conference on Dynamical Systems Theory and Applications DSTA 2017 ABSTRACTS

From Preface: This is the fourteen time when the conference “Dynamical Systems – Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and the Ministry of Science and Higher Education. It is a great pleasure that our invitation has been accepted by so many people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcome nearly 250 persons from 38 countries all over the world. They decided to share the results of their research and many years experiences in the discipline of dynamical systems by submitting many very interesting papers. This booklet contains a collection of 375 abstracts, which have gained the acceptance of referees and have been qualified for publication in the conference proceedings [...]

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored

Advances in Theoretical and Computational Energy Optimization Processes

The paradigm in the design of all human activity that requires energy for its development must change from the past. We must change the processes of product manufacturing and functional services. This is necessary in order to mitigate the ecological footprint of man on the Earth, which cannot be considered as a resource with infinite capacities. To do this, every single process must be analyzed and modified, with the aim of decarbonising each production sector. This collection of articles has been assembled to provide ideas and new broad-spectrum contributions for these purposes

15th Conference on Dynamical Systems Theory and Applications DSTA 2019 ABSTRACTS

From Preface: This is the fifteen time when the conference „Dynamical Systems – Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and the Ministry of Science and Higher Education. It is a great pleasure that our invitation has been accepted by so many people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcome nearly 255 persons from 47 countries all over the world. They decided to share the results of their research and many years experiences in the discipline of dynamical systems by submitting many very interesting papers. This booklet contains a collection of 338 abstracts, which have gained the acceptance of referees and have been qualified for publication in the conference edited books.Technical editor and cover design: Kaźmierczak, MarekCover design: Ogińska, Ewelina; Kaźmierczak, Mare