The Q-Fractionalism Reasoning Learning Method.

As the title suggests, in this work, a modern machine learning method called the Q-fractionalism reasoning is introduced. The proposed method is founded upon a synergy of the Q-learning and fractional fuzzy inference systems (FFISs). Unlike other approaches, the Q-fractionalism reasoning not only incorporates the knowledge base to understand how to perform but also explores a reasoning mechanism from the fractional order to justify what it has performed. This method suggests that the agent choose actions aimed at the characterization of reasoning. In fact, the agent deals with states termed as primary and secondary fuzzy states. The primary fuzzy states are unobservable and uncertain, for which the agent chooses actions. However, the projection of primary fuzzy states onto the knowledge base results in secondary fuzzy states, which are observable by the agent, allowing it to detect primary fuzzy states with degrees of detectability. With a practical experiment implemented on a linear switched reluctance motor (LSRM), the results demonstrate that the application of the Q-fractionalism reasoning in the real-time position control of the LSRM leads to a remarkable improvement of about 70% in the accuracy of the control objective compared with a typical fuzzy inference system (FIS) under the same setting.

Sub-optimal control of fuzzy linear dynamical systems under granular differentiability concept.

This paper deals with sub-optimal control of a fuzzy linear dynamical system. The aim is to keep the state variables of the fuzzy linear dynamical system close to zero in an optimal manner. In the fuzzy dynamical system, the fuzzy derivative is considered as the granular derivative; and all the coefficients and initial conditions can be uncertain. The criterion for assessing the optimality is regarded as a granular integral whose integrand is a quadratic function of the state variables and control inputs. Using the relative-distance-measure (RDM) fuzzy interval arithmetic and calculus of variations, the optimal control law is presented as the fuzzy state variables feedback. Since the optimal feedback gains are obtained as fuzzy functions, they need to be defuzzified. This will result in the sub-optimal control law. This paper also sheds light on the restrictions imposed by the approaches which are based on fuzzy standard interval arithmetic (FSIA), and use strongly generalized Hukuhara and generalized Hukuhara differentiability concepts for obtaining the optimal control law. The granular eigenvalues notion is also defined. Using an RLC circuit mathematical model, it is shown that, due to their unnatural behavior in the modeling phenomenon, the FSIA-based approaches may obtain some eigenvalues sets that might be different from the inherent eigenvalues set of the fuzzy dynamical system. This is, however, not the case with the approach proposed in this study. The notions of granular controllability and granular stabilizability of the fuzzy linear dynamical system are also presented in this paper. Moreover, a sub-optimal control for regulating a Boeing 747 in longitudinal direction with uncertain initial conditions and parameters is gained. In addition, an uncertain suspension system of one of the four wheels of a bus is regulated using the sub-optimal control introduced in this paper.