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Stabilizing chaotic system on periodic orbits using multi-interval and modern optimal control strategies

Abedini, M ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1016/j.cnsns.2012.02.004
  3. Publisher: Elsevier , 2012
  4. Abstract:
  5. In this paper, optimal approaches for controlling chaos is studied. The unstable periodic orbits (UPOs) of chaotic system are selected as desired trajectories, which the optimal control strategy should keep the system states on it. Classical gradient-based optimal control methods as well as modern optimization algorithm Particle Swarm Optimization (PSO) are utilized to force the chaotic system to follow the desired UPOs. For better performance, gradient-based is applied in multi-intervals and the results are promising. The Duffing system is selected for examining the proposed approaches. Multi-interval gradient-based approach can put the states on UPOs very fast and keep tracking UPOs with negligible control effort. The maximum control in PSO method is also low. However, due to its inherent random behavior, its control signal is oscillatory
  6. Keywords:
  7. Classical gradient-based optimal control ; Chaos control ; Control effort ; Control signal ; Controlling chaos ; Duffing system ; Gradient based ; Optimal control methods ; Optimal control strategy ; Optimal controls ; Optimization algorithms ; Periodic orbits ; Random behavior ; System state ; Unstable periodic orbits ; Algorithms ; Behavioral research ; Control ; Optimal control systems ; Particle swarm optimization (PSO) ; Chaotic systems
  8. Source: Communications in Nonlinear Science and Numerical Simulation ; Volume 17, Issue 10 , 2012 , Pages 3832-3842 ; 10075704 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S1007570412000603