T-S-Fuzzy-Model-Based Approximation and Controller Design for General Nonlinear Systems

Optimized Takagi–Sugeno Fuzzy Mixed H2/H∞ Robust Controller Design Based on CPSOGSA Optimization Algorithm for Hydraulic Turbine Governing System

The hydraulic turbine governing system (HTGS) is a complex nonlinear system that regulates the rotational speed and power of a hydro-generator set. In this work, an incremental form of an HTGS nonlinear model was established and the Takagi–Sugeno (T-S) fuzzy linearization and mixed H2/H∞ robust control theory was applied to the design of an HTGS controller. A T-S fuzzy H2/H∞ controller for an HTGS based on modified hybrid particle swarm optimization and gravitational search algorithm integrated with chaotic maps (CPSOGSA) is proposed in this paper. The T-S fuzzy model of an HTGS that integrates multiple-state space equations was established by linearizing numerous equilibrium points. The linear matrix inequality (LMI) toolbox in MATLAB was used to solve the mixed H2/H∞ feedback coefficients using the CPSOGSA intelligent algorithm to optimize the weighting matrix in the process so that each mixed H2/H∞ feedback coefficients in the fuzzy control were optimized under the constraints to improve the performance of the controller. The simulation results show that this method allows the HTGS to perform well in suppressing system frequency deviations. In addition, the robustness of the method to system parameter variations is also verified.

Resilient Distributed Fuzzy Load Frequency Regulation for Power Systems Under Cross-Layer Random Denial-of-Service Attacks

In this article, a novel distributed fuzzy load frequency control (LFC) approach is investigated for multiarea power systems under cross-layer attacks. The nonlinear factors existing in turbine dynamics and governor dynamics as well as the uncertain parameters therein are modeled and analyzed under the interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy framework. The cross-layer attacks threatening the stability of power systems are considered and modeled as an independent Bernoulli process, including denial-of-service (DoS) attacks in the cyber layer and phasor measurement unit (PMU) attacks in the physical layer. By using the Lyapunov theory, an area-dependent Lyapunov function is proposed and the sufficient conditions guaranteeing the system's asymptotically stability with the area control error (ACE) signals satisfying H_∞ performance are deduced. In simulations, we adopt a four-area power system to verify the resiliency enhancement of the presented distributed fuzzy control strategy against random cross-layer DoS attacks. Results show that the designed resilient controller can effectively regulate the load frequency under different cross-layer DoS attack probabilities.

Performance-Based Fault Detection and Fault-Tolerant Control for Nonlinear Systems With T-S Fuzzy Implementation

This article addresses the performance-based fault detection (FD) and fault-tolerant control (FTC) issues for nonlinear systems. For this purpose, in the first part of this article, the performance-based FD and FTC scheme is investigated with the aid of the nonlinear factorization technique. To be specific, the controller parameterization for nonlinear systems is first discussed. The so-called fault-tolerant margin is introduced as an indicator of the system fault-tolerant ability. Then, the FD scheme aiming at estimating and detecting the stability performance degradation of the closed-loop system caused by the system faults is developed. Furthermore, to recover the system performance, the performance-based FTC strategy is presented. In the second part of this article, the design approach of the performance-based FD and FTC scheme is studied by applying the Takagi-Sugeno fuzzy dynamic modeling technique. The achieved results are demonstrated in the end by a case study on the three-tank system.

Observer-Based State Estimation of Discrete-Time Fuzzy Systems Based on a Joint Switching Mechanism for Adjacent Instants

The problem of observer-based state estimation of discrete-time fuzzy systems is investigated by constructing a joint switching mechanism for adjacent instants. Thanks to the usage of both the proposed spatial partitioning method and a set of new free matrix-valued variables, abundant information about size differences of all the normalized fuzzy weighting functions for adjacent instants can be interactively integrated into the fuzzy observer design for the first time. Compared with the recent result from three important aspects (conservatism level, online computational burden, and offline computational burden), three positive results can be obtained: 1) it provides a chance for reducing the conservatism by a large margin; 2) the required online computational burden remains unchanged as referred ones; and 3) as a tradeoff, the required offline computational burden increases to some extent but is still affordable from the view of complexity analysis. Finally, two numerical simulations have been given to validate the effectiveness of our developed theoretical results.

Observer Design of Discrete-Time Fuzzy Systems Based on an Alterable Weights Method

This paper proposes an improvement on observer design of discrete-time fuzzy systems based on an alterable weights method. Different from the recent result, a more effective ranking-based switching mechanism is developed by introducing a bank of alterable weights for the sake of making use of the size difference information of the normalized fuzzy weighting functions more freely than before. Therefore, a positive result can be provided in this paper, that is, less conservative conditions of designing feasible fuzzy observers can be obtained than those existing results, while the computational cost of designing feasible fuzzy observers is even less than the up-to-date one. Finally, two numerical examples are given to show the progressiveness of the proposed method.

Real-Time Fault Detection Approach for Nonlinear Systems and its Asynchronous T-S Fuzzy Observer-Based Implementation

This paper is concerned with a real-time observer-based fault detection (FD) approach for a general type of nonlinear systems in the presence of external disturbances. To this end, in the first part of this paper, we deal with the definition and the design condition for an L _∞ / L ₂ type of nonlinear observer-based FD systems. This analytical framework is fundamental for the development of real-time nonlinear FD systems with the aid of some well-established techniques. In the second part, we address the integrated design of the L _∞ / L ₂ observer-based FD systems by applying Takagi-Sugeno (T-S) fuzzy dynamic modeling technique as the solution tool. This fuzzy observer-based FD approach is developed via piecewise Lyapunov functions, and can be applied to the case that the premise variables of the FD system is nonsynchronous with the premise variables of the fuzzy model of the plant. In the end, a case study on the laboratory setup of three-tank system is given to show the efficiency of the proposed results.

Multitask TSK fuzzy system modeling by mining intertask common hidden structure

The classical fuzzy system modeling methods implicitly assume data generated from a single task, which is essentially not in accordance with many practical scenarios where data can be acquired from the perspective of multiple tasks. Although one can build an individual fuzzy system model for each task, the result indeed tells us that the individual modeling approach will get poor generalization ability due to ignoring the intertask hidden correlation. In order to circumvent this shortcoming, we consider a general framework for preserving the independent information among different tasks and mining hidden correlation information among all tasks in multitask fuzzy modeling. In this framework, a low-dimensional subspace (structure) is assumed to be shared among all tasks and hence be the hidden correlation information among all tasks. Under this framework, a multitask Takagi-Sugeno-Kang (TSK) fuzzy system model called MTCS-TSK-FS (TSK-FS for multiple tasks with common hidden structure), based on the classical L2-norm TSK fuzzy system, is proposed in this paper. The proposed model can not only take advantage of independent sample information from the original space for each task, but also effectively use the intertask common hidden structure among multiple tasks to enhance the generalization performance of the built fuzzy systems. Experiments on synthetic and real-world datasets demonstrate the applicability and distinctive performance of the proposed multitask fuzzy system model in multitask regression learning scenarios.

SOS based robust H(∞) fuzzy dynamic output feedback control of nonlinear networked control systems

In this paper, a methodology for designing a fuzzy dynamic output feedback controller for discrete-time nonlinear networked control systems is presented where the nonlinear plant is modelled by a Takagi-Sugeno fuzzy model and the network-induced delays by a finite state Markov process. The transition probability matrix for the Markov process is allowed to be partially known, providing a more practical consideration of the real world. Furthermore, the fuzzy controller's membership functions and premise variables are not assumed to be the same as the plant's membership functions and premise variables, that is, the proposed approach can handle the case, when the premise of the plant are not measurable or delayed. The membership functions of the plant and the controller are approximated as polynomial functions, then incorporated into the controller design. Sufficient conditions for the existence of the controller are derived in terms of sum of square inequalities, which are then solved by YALMIP. Finally, a numerical example is used to demonstrate the validity of the proposed methodology.

Nonlinear systems modeling based on self-organizing fuzzy-neural-network with adaptive computation algorithm

In this paper, a self-organizing fuzzy-neural-network with adaptive computation algorithm (SOFNN-ACA) is proposed for modeling a class of nonlinear systems. This SOFNN-ACA is constructed online via simultaneous structure and parameter learning processes. In structure learning, a set of fuzzy rules can be self-designed using an information-theoretic methodology. The fuzzy rules with high spiking intensities (SI) are divided into new ones. And the fuzzy rules with a small relative mutual information (RMI) value will be pruned in order to simplify the FNN structure. In parameter learning, the consequent part parameters are learned through the use of an ACA that incorporates an adaptive learning rate strategy into the learning process to accelerate the convergence speed. Then, the convergence of SOFNN-ACA is analyzed. Finally, the proposed SOFNN-ACA is used to model nonlinear systems. The modeling results demonstrate that this proposed SOFNN-ACA can model nonlinear systems effectively.