Admissibility Analysis for Interval Type-2 Fuzzy Descriptor Systems Based on Sliding Mode Control

On Designing the Event-Triggered Multistep Model Predictive Control for Nonlinear System Over Networks With Packet Dropouts and Cyber Attacks

In this article, the event-triggered multistep model predictive control for the discrete-time nonlinear system over communication networks under the influence of packet dropouts and cyber attacks is studied. First, the interval type-2 Takagi-Sugeno fuzzy model is applied to express the discrete-time nonlinear system and an event-triggered mode, which is capable of determining whether the sampled signal ought to be delivered into the unreliable network, is designed to economize communication resources. Second, two Bernoulli processes are introduced to represent the randomly happening packet dropouts in the unreliable network and the randomly occurring deception attacks on the actuator side from the adversaries. Third, under the assumption that the system states are unmeasurable, a multistep parameter-dependent model predictive controller is synthesized via optimizing one series of feedback laws for a given period of time, which leads to improved control performance than that of the one-step approach. Moreover, the results on the recursive feasibility and closed-loop stability related to the networked system are achieved, which explicitly consider the external disturbance and input constraint. Finally, simulation experiments on the mass-spring-damping system are carried out to illustrate the rationality and effectiveness of the provided control strategy.

New Admissibility and Admissibilization Criteria for Nonlinear Discrete-Time Singular Systems by Switched Fuzzy Models

Admissibility analysis and control synthesis for nonlinear discrete-time singular systems are considered in this article. With regard to the type-1 and interval type-2 fuzzy singular systems, the partition of membership functions and scale transform is imposed, and new switched fuzzy systems, which are equivalent to the original systems, are established. A relaxed stability criterion is derived to ensure the admissibility of the system by using the piecewise Lyapunov function and singular value decomposition. Moreover, two classes of switched controllers are designed for the systems. One is for type 1 systems and the membership functions are consistent with those of the systems. The other can be applied to both of the fuzzy systems by introducing linear membership functions in each subregion. Two criteria are obtained to guarantee that the closed-loop systems are admissible. Several illustrative examples are provided to show the effectiveness of the developed methods.

Quantized Interval Type-2 Fuzzy Control for Persistent Dwell-Time Switched Nonlinear Systems With Singular Perturbations

This article investigates the problem of quantized fuzzy control for discrete-time switched nonlinear singularly perturbed systems, where the singularly perturbed parameter (SPP) is employed to represent the degree of separation between the fast and slow states. Taking a full account of features in such switched nonlinear systems, the persistent dwell-time switching rule, the technique of singular perturbation and the interval type-2 Takagi-Sugeno fuzzy model are introduced. Then, by means of constructing SPP-dependent multiple Lyapunov-like functions, some sufficient conditions with the ability to ensure the stability and an expected H_∞ performance of the closed-loop system are deduced. Afterward, through solving a convex optimization problem, the gains of the controller are obtained. Finally, the correctness of the proposed method and the effectiveness of the designed controller are demonstrated by an explained example.

Stabilization of Interval Type-2 Fuzzy-Based Reliable Sampled-Data Control Systems

This article investigates the stabilization problem of the Takagi-Sugeno (T-S) fuzzy-based interval type-2 (IT-2) reliable sampled-data control system. Different from the existing studies, the information for the entire sampling interval with a relation of the augmented state vectors is considered for designing the reliable sampled-data control of IT-2 T-S fuzzy systems. In this regard, we construct the suitable looped Lyapunov-Krasovskii functional (LKF) with the information of the fuzzy membership function that feeds back the time derivative of the membership function to derive sufficient conditions. These sufficient conditions are established in the form of linear matrix inequalities (LMIs), which ensure the global asymptotic stability of T-S fuzzy systems under the designed control technique. Finally, the applicability and superiority of developed reliable sampled-data control techniques were validated by three practical systems.

Improved Nonlinear Extended State Observer-Based Sliding-Mode Rotary Control for the Rotation System of a Hydraulic Roofbolter

This paper develops a sliding-mode control with an improved nonlinear extended state observer (SMC-INESO) for the rotation system of a hydraulic roofbolter with dead-zones, uncertain gain, and disturbances, with the purpose of improving tracking performance. Firstly, the rotation system is modeled to compensate for dead-zone nonlinearity. Then, we present an improved nonlinear extended state observer to estimate disturbances of the rotation system in real time. Moreover, a proportional-integral-differential sliding-mode surface is introduced and an improved sliding-mode reaching law is designed. Based on this, a sliding-mode control law is developed. In order to eliminate the influence of estimation error and uncertain gain, we design two adaptation laws based on the sliding-mode surface and the estimated states. Finally, the effectiveness of the proposed SMC-INESO is verified through comparative simulation studies.

Approximation of Fuzzy Sets by Interval Type-2 Trapezoidal Fuzzy Sets

In this paper, we propose a gradient-based method to approximate a fuzzy set through a trapezoidal fuzzy set (TFS). By adding some constraints in the formulated optimization problem, the major characteristics of the fuzzy set such as the core, the major part of the support, and the shape of the membership function could be preserved; also the form of the optimized result as a TFS is guaranteed. We regard the optimized TFS as the "skeleton" (blueprint) of the original fuzzy set. Based on this skeleton, we further extend the TFS to a higher type, that is, an interval type-2 TFS (IT2 TFS), so that more information about the original fuzzy set could be captured but the number of the parameters used to describe the original fuzzy set is still maintained low (nine parameters are required for an IT2 TFS). The principle of justifiable granularity is used to ensure that the formed type-2 information granule exhibits a sound interpretation. Both synthetic fuzzy sets and those constructed by the fuzzy C -means algorithm applied to the publicly available data have been used to demonstrate the usefulness of the proposed approximation methods.

Event-Triggered Adaptive Control of Saturated Nonlinear Systems With Time-Varying Partial State Constraints

This paper investigates the problem of event-triggered adaptive control for a class of nonlinear systems subject to asymmetric input saturation and time-varying partial state constraints. To facilitate analyzing the influence of asymmetric input saturation, the saturation function is converted into a linear form with respect to control input. To achieve the objective that partial states do not exceed the constraints, a more general form of Lyapunov function is offered. Different from some existing results about output/full state constraints, the proposed scheme only requires that the partial states satisfy the time-varying constraints. Moreover, an event-triggered scheme with a varying threshold is designed to reduce the communication burden. With the time-varying asymmetric barrier Lyapunov functions, a novel event-triggered control scheme is developed, which ensures that partial states are without violation of required constraints and the tracking error converges to a small neighborhood of the origin despite appearing as saturated phenomenon. Eventually, the theoretic results are confirmed by two examples.