Piecewise Affine Hybrid Automata Representation of a Multistage Fuzzy PID Controller
Mathhew A Clark, K.S. Rattan · National Conference on Artificial Intelligence · 2014
As cyber physical systems become more complex, modeling for the purposes of verification and validation (V&V) becomes a primary barrier. Additionally, this complexity drives an increased disconnect between the system implementation and the original human generated requirements. Therefore, a key challenge is to model cyber physical systems at the appropriate level of abstraction required for V&V while maintaining a clear and understandable linkage between the human designer and the system under design. Fuzzy logic is a method to synthesize linguistic, natural language requirements into real world models. It has also been shown that fuzzy logic is a suitable method to learn the behavior of a nonlinear system when a model is not present. A fuzzy logic controller is a special class of hybrid system and provides a mechanism to relate a system model to human specified requirements. Leveraging the wealth of verification techniques for hybrid systems, the goal of this paper is to provide a mechanism capable of modeling and analyzing the safety and stability of learning and adaptive systems while maintaining a direct relationship to the original system requirements. This paper focuses on the model synthesis of a multistage PID fuzzy controller designed for a second-order plant, converting it from linguistic rule based requirements into a piecewise affine hybrid system and simulated using Matlab.