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Iteratively Increasing Complexity During Optimization for Formally Verifiable Fuzzy Systems

Arnett, Timothy J.
http://orcid.org/0000-0001-6759-4593
http://rave.ohiolink.edu/etdc/view?acc_num=ucin156387481300899

Abstract Details

2019, PhD, University of Cincinnati, Engineering and Applied Science: Aerospace Engineering.
Fuzzy Inference Systems (FIS) have been developed to great effect for many decision-making and control problems. Their robustness, transparency, and approximation capabilities have established them as a powerful tool that can be constructed by a human designer or by advanced optimization algorithms. One area they have showed enormous promise in is complex control of Unmanned Aerial Vehicles (UAV). However, certain FIS implementations have issues with scalability that precludes them from being implemented in systems with more than a few variables. As a way around this, arranging multiple FISs in a hierarchy (hFIS), or cascade, can be performed to reduce the complexity. However, this reduction of rules comes with potential reduction in approximation capability if the rules are fully conjunctive. Additionally, when data or expert domain knowledge is unavailable, the search space for a fully conjunctive FIS increases exponentially. The system structure and number of parameters may not be known \textit{a priori} and therefore efficient methods for doing so are useful. Additionally, recently there has been an increasing push towards transparency and formal verification of these systems. In this work, a novel method for iteratively increasing the complexity of hierarchical Fuzzy Systems is presented. This is performed in two ways. First, the number of membership functions is adjusted dynamically based solely on the current state of the FIS. This allows the rule base to be built incrementally. When new membership functions are added, the FIS can then be optimized/tuned again starting from the previously found set of parameters. The second method for increasing the complexity is to iteratively combine FISs that are arranged in a hierarchy in order to increase the rule base granularity. This allows for coupled variables to interact with each other more closely. A method was developed for the direct transformation of an hFIS to a single FIS (sFIS) to facilitate this process. Additionally, all of the FISs used in this work, which are Mamdani-type, are constrained in such a way that they can be converted into an explicit polynomial representation. This allows their direct encoding into Formal Verification tools. These methods are then demonstrated on a number of example problems including a UAV tail chase scenario. The results show that iteratively increasing the complexity of the hFIS greatly reduces the time to find viable solutions. The solutions in this work can also then be directly analyzed using Formal Methods to verify correctness.
Kelly Cohen, Ph.D. (Committee Chair)
David Casbeer, Ph.D. (Committee Member)
Manish Kumar, Ph.D. (Committee Member)
Anoop Sathyan, Ph.D. (Committee Member)
Rajnikant Sharma, Ph.D. (Committee Member)
169 p.
Aerospace Materials
Genetic Fuzzy Systems; Fuzzy Inference Systems; Hierarchical Fuzzy Systems

Recommended Citations

Citations

  • Arnett, T. J. (2019). Iteratively Increasing Complexity During Optimization for Formally Verifiable Fuzzy Systems [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin156387481300899

    APA Style (7th edition)

  • Arnett, Timothy. Iteratively Increasing Complexity During Optimization for Formally Verifiable Fuzzy Systems. 2019. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin156387481300899.

    MLA Style (8th edition)

  • Arnett, Timothy. "Iteratively Increasing Complexity During Optimization for Formally Verifiable Fuzzy Systems." Doctoral dissertation, University of Cincinnati, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin156387481300899

    Chicago Manual of Style (17th edition)

ucin156387481300899
331
© 2019, some rights reserved.Creative Commons License Iteratively Increasing Complexity During Optimization for Formally Verifiable Fuzzy Systems by Timothy J. Arnett is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by University of Cincinnati and OhioLINK.