By Sundarapandian Vaidyanathan, Christos Volos
The publication experiences at the most up-to-date advances and functions of nonlinear regulate platforms. It comprises 30 contributed chapters by way of topic specialists who're really good within the a number of subject matters addressed during this publication. The precise chapters were introduced out within the extensive parts of nonlinear keep an eye on platforms resembling robotics, nonlinear circuits, strength structures, memristors, underwater automobiles, chemical strategies, observer layout, output rules, backstepping keep watch over, sliding mode keep watch over, time-delayed keep watch over, variables constitution regulate, strong adaptive keep an eye on, fuzzy common sense keep an eye on, chaos, hyperchaos, jerk structures, hyperjerk structures, chaos keep an eye on, chaos synchronization, and so on. detailed significance was once given to chapters providing functional ideas, modeling and novel keep an eye on tools for the new study difficulties in nonlinear keep watch over systems.
This e-book will function a reference ebook for graduate scholars and researchers with a easy wisdom of electric and keep an eye on platforms engineering. The ensuing layout tactics at the nonlinear keep an eye on structures are emphasised utilizing MATLAB software.
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The publication studies at the newest advances and purposes of nonlinear keep an eye on platforms. It contains 30 contributed chapters by way of topic specialists who're really good within the a variety of issues addressed during this e-book. The exact chapters were introduced out within the huge parts of nonlinear keep watch over platforms resembling robotics, nonlinear circuits, energy platforms, memristors, underwater automobiles, chemical strategies, observer layout, output legislation, backstepping keep watch over, sliding mode keep an eye on, time-delayed regulate, variables constitution keep an eye on, strong adaptive keep an eye on, fuzzy common sense keep watch over, chaos, hyperchaos, jerk platforms, hyperjerk platforms, chaos regulate, chaos synchronization, and so forth.
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Extra resources for Advances and Applications in Nonlinear Control Systems
IEEE Trans Autom Control 2:190–197 22. Ogata K (2009) Modern control engineerng, 5th edn. Prentice Hall, New Jersey 23. Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64(8):821– 824 24. Pehlivan I, Moroz IM, Vaidyanathan S (2014) Analysis, synchronization and circuit design of a novel butterfly attractor. J Sound Vib 333(20):5077–5096 25. Rasappan S, Vaidyanathan S (2012a) Global chaos synchronization of WINDMI and Coullet chaotic systems by backstepping control.
Since the equilibrium x = x is Lyapunov stable, by Sundarapandian’s theorem (Theorem 1), we obtain the following result, which gives a construction of nonlinear observer for the two species Lotka–Volterra system. Theorem 2 The two species Lotka–Volterra system (11) with the output (13) has a local exponential observer of the form z˙ 1 z˙ 2 = z 1 (a − bz 2 ) + K y − z 1 + x1 z 2 (−c + dz 1 ) (17) where K is a matrix chosen such that A − K C is Hurwitz. Since (C, A) is observable, a gain matrix K can be found such that the error matrix E = A − K C has arbitrarily assigned set of stable eigenvalues.
In this work, the methodology based on Sundarapandian’s theorem (2002) for exponential observer design is applied for the monitoring of two species and three species Lotka–Volterra population systems. Under the condition of stable coexistence of all the species, an exponential observer is constructed near a non-trivial equilibrium of the Lotka–Volterra population ecology system for both two species and three species Lotka–Volterra population systems using Sundarapandian’s theorem (2002). Numerical examples have been illustrated in detail for the nonlinear observer design of both two species and three species Lotka–Volterra population systems.
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