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Nonlinear dynamics --- Regression analysis --- Statistics

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Many nonlinear systems around us can generate a very complex and counter-intuitive dynamics that contrasts with their simplicity, but their understanding requires concepts that are outside the basic training of most science students. This textbook, which is the fruit of graduate courses that the authors have taught at their respective universities, provides a richly illustrated introduction to nonlinear dynamical systems and chaos and a solid foundation for this fascinating subject. It will satisfy those who want discover this field, including at the undergraduate level, but also those who need a compact and consistent overview, gathering the concepts essential to nonlinear scientists.The first and second chapters describe the essential concepts needed to describe nonlinear dynamical systems as well as their stability. The third chapter introduces the concept of bifurcation, where the qualitative dynamical behavior of a system changes. The fourth chapter deals with oscillations, from their birth to their destabilization, and how they respond to external driving. The fifth and sixth chapters discuss complex behaviors that only occur in state spaces of dimension three and higher: quasi-periodicity and chaos, from their general properties to quantitative methods of characterization. All chapters are supplemented by exercises ranging from direct applications of the notions introduced in the corresponding chapter to elaborate problems involving concepts from different chapters, as well as numerical explorations.

Dynamics. --- Bifurcation. --- Chaos Theory. --- Dynamic System. --- Nonlinear Dynamics. --- Strange Attractor.

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Differential geometry. Global analysis --- Nonlinear Dynamics --- Evolution --- Chaotic behavior in systems --- Evolution (Biology) --- Philosophers --- Scientists --- Chaos --- Evolution (Biologie) --- Philosophes --- Scientifiques --- Interviews --- Entretiens --- Chaotic behavior in systems. --- Evolution (Biology). --- Interviews. --- Nonlinear Dynamics.

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This book covers the most recent developments in adaptive dynamic programming (ADP). The text begins with a thorough background review of ADP making sure that readers are sufficiently familiar with the fundamentals. In the core of the book, the authors address first discrete- and then continuous-time systems. Coverage of discrete-time systems starts with a more general form of value iteration to demonstrate its convergence, optimality, and stability with complete and thorough theoretical analysis. A more realistic form of value iteration is studied where value function approximations are assumed to have finite errors. Adaptive Dynamic Programming also details another avenue of the ADP approach: policy iteration. Both basic and generalized forms of policy-iteration-based ADP are studied with complete and thorough theoretical analysis in terms of convergence, optimality, stability, and error bounds. Among continuous-time systems, the control of affine and nonaffine nonlinear systems is studied using the ADP approach which is then extended to other branches of control theory including decentralized control, robust and guaranteed cost control, and game theory. In the last part of the book the real-world significance of ADP theory is presented, focusing on three application examples developed from the authors’ work: • renewable energy scheduling for smart power grids; • coal gasification processes; and • water–gas shift reactions. Researchers studying intelligent control methods and practitioners looking to apply them in the chemical-process and power-supply industries will find much to interest them in this thorough treatment of an advanced approach to control. Advances in Industrial Control aims to report and encourage the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.

Control engineering. --- Computational intelligence. --- Statistical physics. --- Control and Systems Theory. --- Computational Intelligence. --- Applications of Nonlinear Dynamics and Chaos Theory.

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The drive towards reducing aircraft engines' aerodynamic losses has led engineers to reduce the clearances between blade tips and their surrounding casing, thereby increasing the risk of blade/casing contact interactions. Tools to accurately predict subsequent nonlinear dynamics are thus essential at design stage. Design of Experiments and the construction of surrogate models are very effective in studying complex and costly experimental blade/casing devices. Nonetheless, the convergence of surrogate models is linked to the smoothness of the response, evidencing the requirement of new approximation approaches for discontinuous responses. In this context, this report proposes a methodology to localize discontinuities in a 2D Design of Experiments inputs space in order to apply approximation methods on the smooth subdomains subsequently. First, a mesh is constructed on the inputs parameter space using a Delaunay triangulation and gradient-based indicators along with polynomial annihilation are then used as refinement indicators. The proposed methodology makes use of the Support Vector Machine to create a smooth approximation of the discontinuity location. Local improvement of the solution is finally completed. The applicability and the robustness of the proposed discontinuity localization tool are then tested on a variety of analytical models. The test cases have demonstrated satisfactory localization of closed discontinuities, multiple discontinuities in the same model, and discontinuities running partially through the domain. The numerically costly engineering model of blade/casing contact interactions is then considered and the proposed methodology is used to localize a jump in the response.

Discontinuities localization --- Blade/casing contact interactions --- Nonlinear dynamics --- Design of Experiments --- Machine learning --- Ingénierie, informatique & technologie > Ingénierie aérospatiale