Special issue on: nonlinear systems theory and design

Theory of nonlinear systems

The confluence of nonlinearity, unavailable states, and unknown time-varying parameters poses profound estimation challenges in fractional-order dynamical systems. This paper presents a novel adaptive observer design for nonlinear fractional-order Lipschitz systems with unknown, slowly time-varying parameters. Drawing on recent advancements in fractional-order calculus, a rigorous stability analysis is conducted, deriving the updating law and formulating the observer’s viability and stability conditions in terms of linear matrix inequalities (LMIs) and linear matrix equalities (LMEs). The proposed observer ensures the stability of both state observation and parameter estimation errors, along with the asymptotic convergence of the observation error norm square mean value to zero. Empirical results from a case study on a fractional-order financial system validate the efficacy of the proposed observer, thereby advancing the field of states and parameters estimation theory for non-integer order nonlinear systems.

This paper mainly focuses on the attitude control problem of rigid spacecraft, and conducts the design and research of control methods based on the theory of nonlinear negative imaginary systems. A feedback control law is designed for the attitude control model of the rigid spacecraft, ensuring that the closed-loop system satisfies the nonlinear negative imaginary property. Subsequently, according to the stability theory of nonlinear negative imaginary interconnected systems, a strictly negative imaginary controller is designed to achieve the asymptotic stability of the attitude of the rigid spacecraft during its operation. The numerical simulation results verify the effectiveness of the proposed control synthesis method for the rigid spacecraft system.

: The Commanding General, Marine Corps Combat Development Command (MCCDC) asked the Center for Naval Analyses to assess the general applicability of the new science to land warfare. New Sciences is a catch-all phrase that refers to the tools and methodologies used in nonlinear dynamics and complex systems theory to study physical dynamical systems exhibiting a complicated dynamics. This report concludes that the concepts, ideas, theories, tools and general methodologies of nonlinear dynamics and complex systems theory show enormous, almost unlimited, potential for not just providing better solutions for certain existing problems of land combat, but for fundamentally altering our general understanding of the basic processes of war, at all levels. Indeed, the new sciences' greatest legacy may, in the end, prove to be not just a set of creative answers to old questions but and entirely new set of questions to be asked of what really happens on the battlefield The central thesis of this paper is that land combat is a complex adaptive system. That is to say, that land combat is essentially a nonlinear dynamical system composed of many interacting semi-autonomous and hierarchically organized agents continuously adapting to a changing environment.

Systems theory and some canonical representations are introduced for a class of nonlinear systems. Techniques are devised to identify, synthesize, and model such systems and their signals. Nonlinear systems theory is introduced at a fundamental level. To identify a system from input and output (or just output) data, parameters are estimated for a canonical state-space or difference-equation representation, depending on which representation is most convenient for further analysis. >

We show how frequency domain design procedures can be effectively used in nonlinear fuzzy control systems. For this purpose, theoretical justifications of the approach discussed here are provided to show that solid notions from nonlinear system and control theory can be successfully applied in the fuzzy control domain. The methodology proposed is very simple, but powerful, effective and practical. In addition, it supports systematic control system design and stability analysis in the frequency domain for systems described by mathematical, linguistic or experimental models. Several case studies are included to illustrate the usefulness of frequency response in conventional fuzzy control systems analysis and design.

International audience

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.

Fuzzy systems are naturally nonlinear. As the theory of fuzzy systems and the theory of nonlinear systems are not completely developed, universal control laws cannot easily be obtained for fuzzy/nonlinear control systems. However, it may be possible for us to design special controllers for a class of fuzzy/nonlinear systems. In this chapter, we introduce several techniques for controller design of nonlinear systems based on the fuzzy hyperbolic model.KeywordsController DesignLinear Matrix InequalityFuzzy ControllerInverted PendulumOptimal ControllerThese 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.

The purpose of this paper is to offer a “Gedankenexperiment” related to the question of amplification of innovation. We assume a simple innovation ecosystem in which its different actors (research communities, industry and public and private investors) interact in parallel but pursue different (but not necessarily incompatible) goals. Our approach is inspired by chaos and non-linear dynamical system theories and the famous “butterfly effect”. An arm-chair recipe on how to amplify innovation is casually offered and some concrete examples are outlined.

An optimization-based multilayer operability framework is introduced for the process design of nonlinear energy systems that are challenged by complexity and highly constrained environments. In the first layer of this framework, a mixed-integer linear programming (MILP)-based iterative algorithm considers the minimization of the footprint and the achievement of process intensification targets. Then, in the second layer, an operability analysis is performed to incorporate into the approach key features for optimality and feasibility, accounting for the system operation with changeable input conditions. The outcome of the framework consists of a set of modular designs, considering the aspects of both size and process operability. For this study, the nonlinear system is represented by multiple linearized models, resulting in low computational expense and efficient quantification of operability regions. The developed framework is applied to a membrane reactor for direct methane aromatization conversion to hyd...

The purpose of this chapter is to introduce current research and theory on systems design for change, or systemic change, in the fields of education and training. Systems design is the process for determining what characteristics a new system should have, resulting in a model of the new system and a plan for creating it. Systemic change is the process of changing a system from one paradigm to another by applying systems thinking and systems theory. Repeated calls for massive reform of current educational and training practices have consistently been published over the last several decades. This has resulted in an increasing recognition of the need for systemic change in education as numerous structured, piecemeal approaches to education reform have been implemented and failed to significantly improve the state of education. This chapter first presents a description of design theory and systems theory as the foundations for systems design. Design theory is the concepts and principles that help to develop strategies and methods for designing. The term system has been defined in various ways by different researchers, but the core concept is one of relationships among components comprising the whole.

The concept of generalized polynomial operators is introduced and applied to the theory of non-linear systems. Several properties similar to those previously derived for systems described e.g. by Volterra functional series are studied. The main attention is given to inverting of the operators in question. A local inverse is constructed and the region where it is valid is determined. The construction is applied to solving of certain types of non-linear differential equations and to seeking sufficient conditions for BIBO stability of the corresponding systems.

Practical stability analysis and synthesis for nonlinear singular systems .- 3 Strongly absolute stability analysis for Lur'e singular .- 4 Input-to-state stability analysis and design for Lur'e singular systems .- 5 Observer design for nonlinear singular systems .- 6 Absolute stability of Lur'e singularly perturbed systems .- 7 Multi-objective control for T-S fuzzy singularly perturbed systems. 4 Input-to-state stability analysis and design for Lur'e singular systems .- 5 Observer design for nonlinear singular systems .- 6 Absolute stability of Lur'e singularly perturbed systems .- 7 Multi-objective control for T-S fuzzy singularly perturbed systems.

Fundamentals of the theory of non-linear pluse control systems