Whereas many widely accepted methods and techniques exist for showing stability of traditional controllers, at this time standard methods have not been adopted for Fuzzy Logic Controllers (FLCs). Due to the highly non-linear nature of such systems it is quite difficult to use conventional techniques to prove controller stability. Because safety-critical systems (such as flight control systems) must be tested and verified to work as expected for all possible circumstances, the fact that FLCs cannot be proven to achieve such requirements poses limitations on the implementation for such systems. Therefore, alternative methods for verification of an FLC's behavior, including stability, need to be explored. In this study, a novel approach using formal verification methods to ensure the stability of an FLC is proposed. The research challenges include specification of requirements for a complex system, conversion of a traditional FLC to a piecewise polynomial representation, and using a formal verification tool in a non-linear solution space. Using the proposed architecture, the Fuzzy Logic Controller was found to always generate negative feedback, but was inconclusive for Lyapunov stability.
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