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Stability and Stabilization of Fractional Order Linear Time Invariant Swarm Systems

Naderi Soorki, Mojtaba | 2015

736 Viewed
  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 49541 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Tavazoei, Mohammad Saleh
  7. Abstract:
  8. In this thesis, stability and stabilization of fractional-order linear time invariant swarm systems are studied. In recent years it has been proved that the exact model of dynamic agents in most of the swarm systems can be modeled more accurate by fractional order differential equations. Stating the motivation of choosing this subject, the achievements of the thesis can be divided into two general parts: Investigating the stability of fractional-order swarm systems and how to stabilize such systems. After introducing the fractional-order systems and fractional-order model of swarm systems in the introduction part, the literature review is presented in Chapter 2. In Chapter 3 the results obtained on the stability of fractional-order linear time invariant swarm systems are presented. In this chapter, the necessary and sufficient conditions for asymptotic swarm stability are derived. Also time response analysis of agents in an asymptotically swarm stable fractional-order swarm system are investigated and compared with that of their integer-order counterpart. In adition, the necessary and sufficient conditions for swarm stability in the presence of self and communication time-delays are obtained in this chapter. At the end of this chapter, the controllability conditions of these systems by considering various form of input and state delays are obtained. Chapter 4 deals with stabilization of fractional-order linear time invariant swarm systems. At first, an adaptive controller for asymptotic swarm stabilization of fractional-order linear time invariant swarm systems is proposed in which, the matrices describing the agent’s dynamics and the interactive dynamics between agents are unknown. Moreover, this adaptive controller is also modified to force the agents to track a desired trajectory while achieving consensus. In the rest of this chapter, the problem of constrained swarm stabilization is investigated. Input saturation as a practical constraint in the swarm systems is considered in the dynamic model of agents and accordingly, a saturated controller is designed to achieve consensus in fractional order swarm systems. Also, in Chapter 4 asymptotic swarm stabilization of fractional-order swarm systems in the presence of two different kind of model uncertainties and external disturbances while the upper bound of the uncertainties is a linear function of pseudo states norm with unknown coefficients is studied. To this end, first a new fractional-integral sliding manifold is constructed and then an adaptive-robust sliding mode controller is designed to guarantee the asymptotic swarm stability in a fractional-order linear time invariant swarm system under a directed interaction graph. At the end of this chapter, asymptotic swarm stabilization is studied by applying the input control to only a limit number of agents. To this end, a fractional-adaptive pining control is designed to achieve asymptotic swarm stability by applying the input control to the pinned agents. In the all sections of this thesis, simulation results are provided to show the effectiveness of the proposed methodologies
  9. Keywords:
  10. Stability ; Stabilization ; Swarm Control ; Adaptive Controller ; Fractional Order System ; Fractional Order Linear Time Invariant System

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