In this paper a class of uncertain linear dynamical systems called fuzzy fractional linear dynamical systems is investigated. The aim is to find control inputs to keep the states of the fuzzy fractional dynamical systems near the zero in an optimal manner. The optimality criterion is in a form of a granular fuzzy integral whose integrand is a quadratic function of the state variables and control inputs. The fuzzy fractional dynamical system is described using Fuzzy Fractional Differential Equations (FFDEs). In order to achieve the aim, an effective approach for solving FFDEs should be at disposal. Due to some restrictions imposed by the previous approaches dealing with FFDEs, a new approach is proposed. The proposed approach is based on the granular derivative and the so-called relative-distance-measure fuzzy interval arithmetic. New definitions of fuzzy fractional derivatives and integral called left and right granular Riemann-Liouville fuzzy fractional derivatives, left and right granular Caputo fuzzy fractional derivatives, and the left and right granular fuzzy fractional integral are also presented. In addition, the concepts of granular fuzzy partial derivative and granular fuzzy chain rule are introduced. By the approximations of the granular fuzzy fractional integral and the granular Caputo fuzzy fractional derivative, the approximation solution to the FFDEs is obtained. Consequently, based on the new concepts and theorems, the solution to the fuzzy fractional quadratic regulator problem is given by a theorem. The paper closes with an example of regulating the motion of Boeing 747 in longitudinal direction with the presence of uncertainty in the initial conditions and the coefficients.

The complex cyber layer challenges the accuracy of cooperative tracking motion for the networked multiple linear motors system. This article focuses on model predictive control (MPC) for networked control system with the denial-of-service (DoS) attack and network-induced time delay. In order to improve tracking accuracy and control performance of the system, several topologies for linear motion models are studied. The DoS attack and time delay are modeled as constraint models in the time domain. Combining dynamic prediction horizon with the buffer compensation in the controller to actuator (C-A) channel, the proposed networked control strategy based on MPC effectively solves the impact of DoS attacks and time delays on the tracking performance of multiple linear motors. In order to ensure the recursive feasibility of the MPC optimization problem and the uniform global asymptotic stability of system, the output terminal constraint and dynamic prediction horizon constraint are considered by combining four DoS attack cases of the networked control strategy, and a Lyapunov function is constructed. Finally, three linear motors with different topologies are built, and the simulation results verify the control effectiveness of the proposed control strategy on the motor tracking performance under cyber constraints.