By Kazuyuki Aihara, Jun-ichi Imura, Tetsushi Ueta
This e-book is the 1st to record on theoretical breakthroughs on keep watch over of complicated dynamical platforms constructed by means of collaborative researchers within the fields of dynamical structures thought and keep watch over conception. in addition, its simple viewpoint is of 3 forms of complexity: bifurcation phenomena topic to version uncertainty, advanced habit together with periodic/quasi-periodic orbits in addition to chaotic orbits, and community complexity rising from dynamical interactions among subsystems. Analysis and keep an eye on of complicated Dynamical Systems bargains a important source for mathematicians, physicists, and biophysicists, in addition to for researchers in nonlinear technology and keep an eye on engineering, permitting them to enhance a greater basic realizing of the research and keep watch over synthesis of such advanced systems.
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Extra info for Analysis and Control of Complex Dynamical Systems: Robust Bifurcation, Dynamic Attractors, and Network Complexity
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Thus our method operates the system to avoid chaos. 7 Conclusion In this Chap. 3, robustification of a dynamical system is considered along the approach in the previous chapter and a technique with a matrix inequality is introduced. Although the stability index considered here is not differentiable in general, its optimization can be formulated into a differentiable optimization problem. Since the resulting optimization problem has a nonlinear matrix inequality constraint, we use the penalty function method of Koˇcvara–Stingl to obtain an update rule of the parameter.
Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994) 5. : PENNON: a code for convex nonlinear semidefinite programming. Optim. Methods Softw. 1 Introduction The aim of our study is to construct a system that is robust to sudden environmental changes and major incidents. Such changes trigger instabilities in the system, called bifurcations. In biological systems, for example, dynamical diseases such as CheyneStokes respiration and chronic granulocytic leukemia are caused by bifurcations due to variations in system parameters [1, 2].
Analysis and Control of Complex Dynamical Systems: Robust Bifurcation, Dynamic Attractors, and Network Complexity by Kazuyuki Aihara, Jun-ichi Imura, Tetsushi Ueta