Fractional-order neural networks play a vital role in modeling the information processing of neuronal interactions. It is still an open and necessary topic for fractional-order neural networks to investigate their global stability. This paper proposes some simplified linear matrix inequality (LMI) stability conditions for fractional-order linear and nonlinear systems. Then, the global stability analysis of fractional-order neural networks employs the results from the obtained LMI conditions. In the LMI form, the obtained results include the existence and uniqueness of equilibrium point and its global stability, which simplify and extend some previous work on the stability analysis of the fractional-order neural networks. Moreover, a generalized projective synchronization method between such neural systems is given, along with its corresponding LMI condition. Finally, two numerical examples are provided to illustrate the effectiveness of the established LMI conditions.

In this article, a multi-underwater unmanned vehicle (UUV) maneuvering decision-making algorithm is proposed for a counter-game with a dynamic target scenario. The game is modeled with interval-valued intuitionistic fuzzy rules, and an optimal maneuvering strategy is realized using a fractional-order recurrent neural network (RNN). First, underwater environments with weak connectivity, underwater noise, and dynamic uncertainties are analyzed and incorporated into the interval-valued intuitionistic fuzzy set. Then, the maneuvering decision-making model and the expected return of the multi-UUV countermeasure are designed based on the interval-valued intuitionistic fuzzy rules. Subsequently, to optimize the counter-game maneuvering strategy, a fractional-order RNN is formulated based on the Karush–Kuhn–Tucker optimality conditions. In addition, the existence and uniqueness of the optimal maneuvering solutions as well as the stability of the equilibrium point are discussed. Finally, simulation and experimental results are compared to determine the effectiveness of the proposed algorithm. The influence of the fractional order on the convergence rate and optimization error of the proposed algorithm is also minutely examined.

A fuzzy fractional-order PID control algorithm for a general type industrial temperature control system is proposed in this paper. In order to improve the production quality and controlled model accuracy, a fractional-order elementary system is used to describe the temperature control process. The gain coefficients of the proposed fractional-order PID controller is updated online based on a set of fractional-order fuzzy rules which are defined by Mittag–Leffler functions and follow fat-tailed distributions. Therefore, the proposed controller parameters could be auto-tuned according to model uncertainties, noise disturbance, random delay, and etc. Examples of the studied temperature control systems are shown to verify the effectiveness of the proposed controller. The superiority of fractional calculus is fully explored in the presented control methodology. The controlled temperature profile with the proposed algorithm could realize more satisfactory dynamic performance, better robustness respect to environment changes caused by internal and external disturbance.