Fuzzy state space modeling for solving inverse problems in multivariable dynamic systems

Abstract

The main objective of this study is to develop a novel inverse modeling technique, known as Fuzzy State Space Model (FSSM). This model is used for optimization of input parameters in multivariable dynamic systems. In this approach, the flexibility of fuzzy modeling is incorporated with the crisp state space models proposed in the modern control theory. The vagueness and uncertainty of the parameters are represented in the model construction, as a way of increasing the available information in order to achieve a more precise model of reality. Subsequently, the inverse Fuzzy State Space algorithm is formulated for a multipleinput single-output system, which leads to the derivation of Modified Optimized Defuzzified Value Theorem. This algorithm is enhanced to address the optimization of parameters for a multiple-input multiple-output system, which leads to the derivation of an Extension of Optimized Defuzzified Value Theorem. The proofs of these theorems are presented. To facilitate the implementation of these algorithms, a semi-automated computational tool using Matlab® programming facilities is developed. The effectiveness of this modeling approach is illustrated by implementing it to the state space model of a furnace system of a combined cycle power plant. The results obtained in this application demonstrate that the proposed new modeling approach is reasonable and provides an innovative tool for decision-makers. In addition, the investigations on the properties and characteristics of FSSM have resulted in the derivation of some lemma and theorems related to convexity and normality of the induced solution of the model, and bounded stability of the Fuzzy State Space system. Finally, the properties of the induced solution of a single FSSM are generalized to the multi-connected systems of FSSM. Some algebraic views related to the systems of FSSM are also discussed.