Fractional order PID controller was received attentions in control problems for it had 2 freedom adjustable parameters. Practices had proved that better results could be obtained by introduction of fractional order PID in control problems. And in recently years, fractional order PID combined with fuzzy logic system was gradually got attention, the typical of which was fractional order type-1 fuzzy PID controller. For fractional order PID and fractional order type-1 fuzzy PID controller couldn't deal with the uncertainty of system, so fractional order interval type-2 fuzzy PID controller was applied to solve this problem. But interval type-2 fuzzy sets were a simplification of type-2 fuzzy sets, and there may be have the defect of information loss. A fractional order general type-2 fuzzy PID controller was proposed in this article. The proposed controller based on general type-2 fuzzy logic system, which can make full use of the advantages of general type-2 fuzzy logic system in describing the uncertainty of the system. The fractional order general type-2 fuzzy PID controller utilized a simplified type reduction called NT type reduction algorithm. The NT type reduction algorithm can get the defuzzification result directly and avoided iterative process as KM type reduction commonly used in interval type-2 fuzzy controller. The simulations of 3 processes and a practical inverted pendulum system show that fractional order general type-2 fuzzy PID controller can reduce overshoot, improve system response speed and accelerate system stability time in comparing with other controllers. Especially, when the system has disturbance, parameters uncertainty or structure uncertainty, the fractional order general type-2 fuzzy PID controller has better control effects than other compared controllers. INDEX TERMS Fractional order control, fractional order fuzzy PID, general type-2 fuzzy sets, general type-2 fuzzy logic system, type reduction.

In multi-task learning, using task grouping structure has been shown to be effective in preventing inappropriate knowledge transfer among unrelated tasks. However, the group structure often has to be predetermined using prior knowledge or heuristics, which has no theoretical guarantee and could lead to unsatisfactory learning performance. In this paper, we present a flexible multi-task learning framework to identify latent grouping structures under agnostic settings, where the prior of the latent subspace is unknown to the learner. In particular, we relax the latent subspace to be full rank, while imposing sparsity and orthogonality on the representation coefficients of target models. As a result, the target models still lie on a low dimensional subspace spanned by the selected basis tasks, and the structure of the latent task subspace is fully determined by the data. The final learning process is formulated as a joint optimization procedure over both the latent space and the target models. Besides providing proofs of theoretical guarantee on learning performance, we also conduct empirical evaluations on both synthetic and real data. Experimental results and comparisons with competing approaches corroborate the effectiveness of the proposed method.

For the type reduction of general type-2 fuzzy sets based on α-plane representation was converted to type reduction of several interval type-2 fuzzy sets, so it was time consuming in real applications. In this paper, a unified general type-2 fuzzy PID (UGT2-FPID) controller using the upper and lower bounds of one α-plane is proposed, which has higher real time. The UGT2-FPID controller contains another two adjust parameters, and the analytical structure of UGT2-FPID controller is obtained by adapting input combination method. Furthermore, this paper discusses the parameter adjustment methods to achieve better controlling effects by the mathematical expressions of UGT2-FPID controller. The robustness and effectiveness of proposed general type-2 fuzzy PID controller are tested by two production process objects. The simulation results show that the controlling effects of proposed general type-2 fuzzy PID controller are better than PID, type-1 fuzzy PID, and interval type-2 fuzzy PID controller even if there are exit uncertainties, like controlled object structure changing, controller disturbance, or output noise.

Bed temperature in dense-phase zone is the key parameter of circulating fluidized bed (CFB) boiler for stable combustion and economic operation. It is difficult to establish an accurate bed temperature model as the complexity of circulating fluidized bed combustion system. T-S fuzzy model was widely applied in the system identification for it can approximate complex nonlinear system with high accuracy. Fuzzy c-regression model (FCRM) clustering based on hyper-plane-shaped distance has the advantages in describing T-S fuzzy model, and Gaussian function was adapted in antecedent membership function of T-S fuzzy model. However, Gaussian fuzzy membership function was more suitable for clustering algorithm using point to point distance, such as fuzzy c-means (FCM). In this paper, a hyper-plane-shaped FCRM clustering algorithm for T-S fuzzy model identification algorithm is proposed. The antecedent membership function of proposed identification algorithm is defined by a hyper-plane-shaped membership function and an improved fuzzy partition method is applied. To illustrate the efficiency of the proposed identification algorithm, the algorithm is applied in four nonlinear systems which shows higher identification accuracy and simplified identification process. At last, the algorithm is used in a circulating fluidized bed boiler bed temperature identification process, and gets better identification result.

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Establishing an accurate inverse model is a key problem in the design of adaptive inverse controllers. Most real objects have nonlinear characteristics, so mathematical expression of an inverse model cannot be obtained in most situation. A Takagi–Sugeno(T-S)fuzzy model can approximate real objects with high precision, and is often applied in the modeling of nonlinear systems. Since the consequent parameters of T-S fuzzy models are linear expressions, this paper firstly uses a fuzzy c-regression model (FCRM) clustering algorithm to establish inverse fuzzy model. As the least mean square (LMS) algorithm is only used to adjust consequent parameters of the T-S fuzzy model in the process of parameter adjustment, the premise parameters are fixed and unchanged in the process of adjustment. In this paper, the back propagation (BP) algorithm is applied to adjust the premise and consequent parameters of the T-S fuzzy model, simultaneously online. The simulation results show that the error between the system output controlled by proposed adaptive inverse controller and the desired output is smaller, also the system stability can be maintained when the system output has disturbances.

The modeling and control problem of networked control systems(NCSs) with bounded time-delay and data packet dropout are discussed. Using a full-order observer to compensate networked-induced delay, the system is modeled as an asynchronous dynamical system(ADS) with rate constraints on events by defining an augmented state vector. The criterion for the exponential stability of the networked control systems is presented. Finally, the simulation results are given to show the effectiveness of the presented method. Keywords: Networked control system, bounded time-delay, data packet dropout, linear matrix inequality(LMI), exponential stability.