Dynamic Boundary Fuzzy Control Design of Semilinear Parabolic PDE Systems With Spatially Noncollocated Discrete Observation

Fuzzy Boundary Sampled-Data Control for Nonlinear Parabolic DPSs

For a nonlinear parabolic distributed parameter system (DPS), a fuzzy boundary sampled-data (SD) control method is introduced in this article, where distributed SD measurement and boundary SD measurement are respected. Initially, this nonlinear parabolic DPS is represented precisely by a Takagi-Sugeno (T-S) fuzzy parabolic partial differential equation (PDE) model. Subsequently, under distributed SD measurement and boundary SD measurement, a fuzzy boundary SD control design is obtained via linear matrix inequalities (LMIs) on the basis of the T-S fuzzy parabolic PDE model to guarantee exponential stability for closed-loop parabolic DPS by using inequality techniques and a acrlong LF. Furthermore, respecting the property of membership functions, we present some LMI-based fuzzy boundary SD control design conditions. Finally, the effectiveness of the designed fuzzy boundary SD controller is demonstrated via two simulation examples.

Backstepping Boundary Control for a Class of Gantry Crane Systems

In this article, two boundary feedback controllers are designed via the backstepping approach for a class of gantry crane systems. To provide an accurate and concise representation of the dynamic behavior, the gantry crane with a flexible cable is described by a hybrid system. The hybrid system is formed by an ordinary differential equation coupled with a partial differential equation. In the first control strategy, a backstepping-based boundary state-feedback controller is proposed for the gantry crane to transport a payload to an expected position with less shaking. In the second control strategy, a boundary output-feedback controller is explored with an observer estimating the inaccessible states. By using the backstepping technique and kernel functions, the original systems with different control strategies are transformed into target systems. By using the operator semigroup and Lyapunov stability theories, the target system is proven to be well-posed and exponentially stable, respectively. Finally, numerical simulations and comparisons are provided to illustrate the efficiency and the advantages of the proposed methods.

Fuzzy Boundary Control for Nonlinear Delayed DPSs Under Boundary Measurements

For nonlinear delayed distributed parameter systems (DDPSs), this article considers a fuzzy boundary control (FBC) under boundary measurements (BMs). Initially, we accurately describe the nonlinear DDPS through a Takagi-Sugeno (T-S) fuzzy partial differential-difference equation (PDDE). Then, in accordance with the T-S fuzzy PDDE model, an FBC design under BMs ensuring the exponential stability for closed-loop DDPS is subsequently presented by spatial linear matrix inequalities (SLMIs) via using Wirtinger's inequality, Halanay's inequality, and the Lyapunov direct method, which respects the fast-varying and slow-varying delays. Moreover, we formulate SLMIs as LMIs for solving the fuzzy boundary controller design of nonlinear DDPSs under BMs. Finally, the effectiveness of the proposed FBC strategy is presented via simulation examples.

Spatial Decomposition-Based Fault Detection Framework for Parabolic-Distributed Parameter Processes

Fault detection for distributed parameter processes (heat processes, fluid processes, etc.) is vital for safe and efficient operation. On one hand, the existing data-driven methods neglect the evolution dynamics of the processes and cannot guarantee that they work for highly dynamic or transient processes; on the other hand, model-based methods reported so far are mostly based on the backstepping technique, which does not possess enough redundancy for fault detection since only the boundary measurement is considered. Motivated by these considerations, we intend to investigate the robust fault detection problem for distributed parameter processes in a model-based perspective covering both boundary and in-domain measurement cases. A real-time fault detection filter (FDF) is presented, which gets rid of a large amount of data collection and offline training procedures. Rigorous theoretic analysis is presented for guiding the parameters selection and threshold computation. A time-varying threshold is designed such that the false alarm in the transient stage can be avoided. Successful application results on a hot strip mill cooling system demonstrate the potential for real industrial applications.

Fuzzy Control Design of Nonlinear Time-Delay Parabolic PDE Systems Under Mobile Collocated Actuators and Sensors

Via mobile sensing measurements, this study applies the Takagi-Sugeno (T-S) fuzzy model to deal with the mobile fuzzy control design problem for nonlinear time-delay parabolic partial differential equation (PDE) systems. Initially, we use a T-S fuzzy model to accurately represent the nonlinear time-delay parabolic PDE system. Subsequently, under the assumption that the actuators and sensors are collocated while the spatial domain is divided by several subdomains, a control scheme containing the fuzzy controllers and the guidance of mobile actuator/sensor pairs is proposed based on the obtained T-S fuzzy model, where the projection modification guidance to be designed can guarantee that each mobile actuator/sensor pair moves within the prescribed area. Then, using the Lyapunov direct method and integral inequalities, a membership-function-dependent design of fuzzy controllers plus mobile actuator/sensor guidance laws is developed to render the resulting closed-loop time-delay system exponentially stable. Moreover, the exponential decay rate can also be increased by the proposed mobile guidance laws. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed design method and the application of mobile actuator/sensor pairs contributes to accelerating the convergence speed of the closed-loop state.

Spatial-L∞-Norm-Based Finite-Time Bounded Control for Semilinear Parabolic PDE Systems With Applications to Chemical-Reaction Processes

This article investigates a spatial- L^∞ -norm-based reliable bounded control problem for a class of nonlinear partial differential equation systems in a finite-time interval. The main novelties are reflected in the following aspects: 1) inspired by the sector-nonlinearity approach, the considered nonlinear system is reconstructed by a Takagi-Sugeno fuzzy model, which provides an effective method for control design. Besides, several actuator failures, such as stuck faulty, outage faulty, and bias faulty, are taken into account and modeled by a novel Markov process; 2) partial areas' states are sampled and transmitted based on a new distributed event-triggered communication strategy, which reduces the cost of the system design and saves the limited network resources to some extent; and 3) on the basis of the first two works, a new piecewise fuzzy controller, which requires fewer actuators compared with the distributed control method, is constructed. Then, some sufficient conditions to guarantee the finite-time boundedness (in the sense of spatial L^∞ norm) and mixed L₂-L_∞/H_∞ disturbance attenuation performance are established, and a new linear matrix inequality relax technique is introduced to deal with the strict constraint that is caused by the asynchronous phenomenon between plant and controller. Finally, two simulation studies are given to illustrate the effectiveness and advantages of the developed controller.

Further Study on Observer Design for Continuous-Time Takagi-Sugeno Fuzzy Model With Unknown Premise Variables via Average Dwell Time

This article further studies the problem of observer design for the continuous-time Takagi-Sugeno (T-S) fuzzy system with unmeasurable premise variables. A membership function-dependent Lyapunov function is designed to obtain the observer-based controller. Different from the existing results, a switching method is proposed to deal with the time derivative of membership functions. Several problems such as, too many parameters, and the small local stabilization region in the existing papers are solved by applying the switching method. In addition, two algorithms are designed to obtain the controller gains and observer gains. In the end, two examples are provided to demonstrate the effectiveness of the proposed approach.

Finite-Time [Formula: see text] Asynchronous Control for Nonlinear Markov Jump Distributed Parameter Systems via Quantized Fuzzy Output-Feedback Approach

This article focuses on the asynchronous output-feedback control design for a class of nonlinear Markov jump distributed parameter systems based on a hidden Markov model. Initially, the considered systems are represented by a Takagi-Sugeno fuzzy model via a sector nonlinearity approach. Furthermore, asynchronous quantizers are introduced to save the limited communication resource in engineering applications. Then, based on the Lyapunov direct method and some inequality techniques, a series of novel stability criteria, which guarantee the finite-time boundedness and [Formula: see text] disturbance attenuation performance of the target plants, is established in the form of spatial differential linear matrix inequalities. Finally, a simulation study is provided to verify the viability of the developed approach.