Design of an interval type-2 fuzzy neural network sliding mode robust controller for higher stability of magnetic spacecraft attitude control

This paper designs an interval type-2 fuzzy neural network sliding mode robust controller (IT2FNNSMRC) to improve the stability of the vibrational angle of the orbital plane in magnetic rigid spacecraft attitude control. The control system consists of an interval type-2 fuzzy neural network (IT2FNN) controller, a PD controller, and a robust controller in parallel connection. The IT2FNN controller, as a nonlinear regulator, compensates the nonlinearity of the controlled object; the PD controller, as a feedback controller, ensures the global asymptotic stability of the control system; the robust controller inhibits input load disturbance. The IT2FNN controller hereof has a self-organizing function which enables it to automatically determine the network structure and parameters online. At the stage of IT2FNN structure learning, the standard on rule growth is set according to the incentive intensities of IT2FNN rule premises. A new rule is generated when the incentive intensities of rules are all smaller than a certain threshold; next, a significance index is set for each rule. When the significance index of some rule decays to a certain threshold, the corresponding rule shall be deleted to achieve the goals of optimizing IT2FNN structure and reducing system complexity. At the stage of parameter learning, adaptive adjustment of IT2FNN parameters is made via the sliding mode control theory learning algorithm, and the stabilities of the algorithm and control system are proven using Lyapunov function. Finally, the proposed control scheme is used in the control of a magnetic rigid spacecraft, as compared to three other designed control methods. Simulation results show that IT2FNNSMRC has superior control precision and stability. And the IT2FNN which adopts the proposed learning algorithm can address uncertainty satisfactorily, with higher computational implementability.

An Elementary Solution to a Duffing Equation

In this work, we study the Duffing equation. Analytical solution for undamped and unforced case is provided for any given arbitrary initial conditions. An approximate analytical solution is given for the damped or trigonometrically forced Duffing equation for arbitrary initial conditions. The analytical solutions are expressed in terms of elementary trigonometric functions as well as in terms of the Jacobian elliptic functions. Examples are added to illustrate the obtained results. We also introduce new functions for approximating the Jacobian and Weierstrass elliptic functions in terms of the trigonometric functions sine and cosine. Results are high accurate.

Event-Triggered Cooperative Global Robust Practical Output Regulation for Second-Order Uncertain Nonlinear Multiagent Systems

In this paper, we study the cooperative global robust practical output regulation problem for a class of second-order uncertain nonlinear multiagent systems via a distributed event-triggered state feedback control strategy. Compared with the existing work, one of the main challenges is that we need to design two distributed internal models to learn both the desired steady-state state and steady-state input for each agent. Moreover, to obtain a directly implementable digital control law, the two distributed internal models of each agent only depend on the sampled states of the neighboring agents and itself. As a result, the resulting augmented system is more complicated, and the control law needs to be recursively designed. To overcome the difficulty, we propose a novel distributed event-triggered control law and a novel distributed event-triggered mechanism to deal with our problem. By adjusting a design parameter in the proposed event-triggered mechanism, we show that the Zeno behavior does not happen and the ultimate bound of the tracking error can be made arbitrarily small. Our design will be illustrated by two examples.

A decentralized adaptive robust method for chaos control

This paper presents a control strategy, which is based on sliding mode control, adaptive control, and fuzzy logic system for controlling the chaotic dynamics. We consider this control paradigm in chaotic systems where the equations of motion are not known. The proposed control strategy is robust against the external noise disturbance and system parameter variations and can be used to convert the chaotic orbits not only to the desired periodic ones but also to any desired chaotic motions. Simulation results of controlling some typical higher order chaotic systems demonstrate the effectiveness of the proposed control method.