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Control of Continuous-Time Chaotic Systems by Minimizing the Entropy Function Constructed on Conditional Probability

Norouzi, Mohammad | 2023

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 56725 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Salarieh, Hassan
  7. Abstract:
  8. In this research, we explore a novel approach for controlling continuous-time chaotic systems with unknown equations and exclusively using one measurable state variable. In pursuit of this objective, the study unveils two efficient approaches: one tailored for autonomous systems and the other designed for systems with external excitation. In both approaches, our methodology centers on minimizing the conditional entropy which is derived based on the conditional probability distribution of the only observable state variable. Considering the numerical nature of entropy calculations in practical issues, we have employed the Poincare map to discretize the continuous-time system. In the following, to identify the optimal control signal for achieving the aforementioned objectives, both Genetic Algorithms and the Particle Swarm Optimization technique have been employed. The proposed innovative algorithm has been successfully applied to the Lorenz, Rössler, and Duffing chaotic systems, demonstrating promising results.This thesis comprises five chapters. The first chapter introduces preliminary discussions and problem definition. The subsequent chapter provides a review of works done in the field of chaos control. In the third chapter, fundamental mathematical concepts related to the research are detailed. The fourth chapter simulates the control algorithms on chaotic systems and reports their outcomes. In the concluding chapter, a final discussion on the results is conducted, and necessary recommendations are presented
  9. Keywords:
  10. Chaos Theory ; Nonlinear Control ; Takens Theorem ; Poincare Map ; Conditional Entropy Minimization

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