Optimal interval type-2 fuzzy fractional order super twisting algorithm: A second order sliding mode controller for fully-actuated and under-actuated nonlinear systems

In this paper, a novel interval type-2 fuzzy fractional order super twisting algorithm (IT2FFOSTA) which is essentially a second order sliding mode controller is presented. The proposed IT2FFOSTA enhances fractional order super twisting algorithm (FOSTA) by taking advantage of an interval type-2 fuzzy fractional order sliding surface (IT2FFOSS) for some classes of fully-actuated and under-actuated nonlinear systems in presence of uncertainty. The FOSTA significantly reduces the amount of chattering and the IT2FFOSS results in decreasing the tracking error, control effort, and chattering level. In order to control under-actuated systems, a hierarchical sliding surface is employed. The multi-tracker optimization algorithm is utilized to adjust the controller’s parameters; this leads to an optimal performance for the IT2FFOSTA. To examine the performance of the IT2FFOSTA, some simulation and experimental tests on three examples of different classes of fully-actuated and under-actuated systems, including ball and plate, inverted pendulum, and ball and beam systems are carried out. The simulation and experimental results demonstrate the superiority of the IT2FFOSTA in reducing the amount of chattering, tracking error, and control effort compared to those of the other control methods.     

Global weak solutions to a spatio-temporal fractional Landau–Lifshitz–Bloch equation

The present paper deals with global existence of weak solutions of a time-space fractional Landau–Lifshitz–Bloch equation involving the weak Caputo derivative and a fractional Laplacian. We use Faedo–Galerkin method with some commutator estimates in order to prove global existence of weak solutions for the model. The uniqueness is also discussed in a special one dimensional case.     

考虑节点过载的碳排放空间关联系统级联失效模型

为提高突发事件级联失效对现实碳排放关联系统破坏程度的评估可信性，在传统复杂网络的"负载-容量"级联失效模型基础上，考虑个体成员对负载的冗余能力，提出一种过载失效概率，构建了考虑节点过载状态的级联失效模型，并基于节点特性提出了6种过载节点负载分配策略。仿真结果表明：在过载节点负载分配策略中，综合分配策略整体上较优，能够有效控制级联失效的规模，增加网络鲁棒性；在一定范围内提升过载参数有助于降低级联失效的影响，但提升到一定程度时改善效果不明显；在不同负载分配策略下，剩余系数存在一个最优值，容量可调参数存在最优区间，可以使碳排放关联网络保持较好鲁棒性的同时，花费较小的构建成本，其中紧密度分配策略对应的网络构建成本较高。     

An efficient numerical scheme for solving fractional infinite-horizon optimal control problems

This paper presents an efficient numerical method to solve fractional infinite-horizon optimal control problems, where the dynamic control system depends on Caputo fractional derivatives. First, by a suitable change of variable, we transform the fractional infinite-horizon optimal control problem to a finite-horizon one. Then, with the help of an approximation, we replace the Caputo derivative to integer order derivative. According to the Pontryagin minimum principle (PMP) for optimal control problems and by constructing an error function, we define an unconstrained minimization problem. In the optimization problem, we use trial solutions for state, costate and control functions where these trial solutions are constructed by using two-layered perceptron neural network. Some numerical results are introduced to explain our main results.     

Stability analysis of a class of fractional order nonlinear systems with order lying in (0, 2)

This paper investigates the stability of n-dimensional fractional order nonlinear systems with commensurate order 0 <α<2. By using the Mittag-Leffler function, Laplace transform and the Gronwall–Bellman lemma, one sufficient condition is attained for the local asymptotical stability of a class of fractional order nonlinear systems with order lying in (0, 2). According to this theory, stabilizing a class of fractional order nonlinear systems only need a linear state feedback controller. Simulation results demonstrate the effectiveness of the proposed theory.     

Design of two-channel filter bank using nature inspired optimization based fractional derivative constraints

In this article, a novel approach for 2-channel linear phase quadrature mirror filter (QMF) bank design based on a hybrid of gradient based optimization and optimization of fractional derivative constraints is introduced. For the purpose of this work, recently proposed nature inspired optimization techniques such as cuckoo search (CS), modified cuckoo search (MCS) and wind driven optimization (WDO) are explored for the design of QMF bank. 2-Channel QMF is also designed with particle swarm optimization (PSO) and artificial bee colony (ABC) nature inspired optimization techniques. The design problem is formulated in frequency domain as sum of L₂ norm of error in passband, stopband and transition band at quadrature frequency. The contribution of this work is the novel hybrid combination of gradient based optimization (Lagrange multiplier method) and nature inspired optimization (CS, MCS, WDO, PSO and ABC) and its usage for optimizing the design problem. Performance of the proposed method is evaluated by passband error (ϕ_p), stopband error (ϕ_s), transition band error (ϕ_t), peak reconstruction error (PRE), stopband attenuation (A_s) and computational time. The design examples illustrate the ingenuity of the proposed method. Results are also compared with the other existing algorithms, and it was found that the proposed method gives best result in terms of peak reconstruction error and transition band error while it is comparable in terms of passband and stopband error. Results show that the proposed method is successful for both lower and higher order 2-channel QMF bank design. A comparative study of various nature inspired optimization techniques is also presented, and the study singles out CS as a best QMF optimization technique.     

Fractional fixed-structure H∞ controller design using Augmented Lagrangian Particle Swarm Optimization with Fractional Order Velocity

The optimization of a fixed-structure controller is in general computationally intractable, posing a challenge to control system engineers. This paper introduces a novel technique for designing such control techniques by formulating it as a nonlinear non-convex constrained problem. A novel PSO algorithm, namely the Augmented Lagrangian Particle Swarm Optimization with Fractional Order Velocity (ALPSOFV), is proposed for improving the convergence rate. The structure of the controller is selectable and, therefore, the Fractional Order Proportional Integral Derivative (FOPID) algorithm is chosen in the scope of the study. The results for three test examples show the good performance of the ALPSOFV.