Non-parallel Distributed Compensation Research Articles

Fuzzy Modeling Framework Using Sector Non-Linearity Techniques for Fixed-Wing Aircrafts

This paper presents a mathematical modeling approach utilizing a fuzzy modeling framework for fixed-wing aircraft systems with the goal of creating a highly desirable mathematical representation for model-based control design applications. The starting point is a mathematical model comprising fifteen non-linear ordinary differential equations representing the dynamic and kinematic behavior applicable to a wide range of fixed-wing aircraft systems. Here, the proposed mathematical modeling framework is applied to the AIRBUS A310 model developed by ONERA. The proposed fuzzy modeling framework takes advantage of sector non-linearity red techniques to recast all the non-linear terms from the original model to a set of combined fuzzy rules. The result of this fuzzification is a more suitable mathematical description from the control system design point of view. Therefore, the combination of this fuzzy model and the wide range of control techniques available in the literature for such kind of models, like parallel and non-parallel distributed compensation control laws using linear matrix inequality optimization, enables the development of control algorithms that guarantee stability conditions for a wide range of operations points, avoiding the classical gain scheduling schemes, where the stability issues can be extremely challenging.

Composite Anti-Disturbance Control for Nonlinear Hidden Markov Jump Systems Under Replay Attacks: A Dynamic Output-Feedback Method.

This article is dedicated to researching the problem of composite anti-disturbance control for nonlinear hidden Markov jump systems, described by the interval type-2 Takagi-Sugeno fuzzy method, under replay attacks in the continuous-time domain. Based on dynamic output feedback control and disturbance observer, a fuzzy composite controller, following the core idea of nonparallel distribution compensation, is designed to compensate for the impact of multiple disturbances. For replay attacks, a multisensor scheme with the detection mechanism is introduced, enabling the studied systems to remain stable even under attacks. Afterward, with the aid of the Lyapunov stability theory, sufficient conditions for ensuring the stability of the resulting systems are deduced, and then the gains of the desired controller and disturbance observer are obtained. Finally, the rationality and effectiveness of the established method are demonstrated through simulation, as well as its superiority over the traditional H∞ control method.

Active Adaptive Observer-Based Fault-Tolerant Control Strategy for a Class of T–S Fuzzy Systems With Unmeasurable Premise Variables

This paper addresses the problem of fault-tolerant output tracking control for a class of Takagi-Sugeno (T-S) fuzzy systems with unmeasurable premise variables subject to additive and multiplicative actuator faults and external disturbances. In nominal conditions, utilizing a quadratic Lyapunov function and non-parallel distributed compensation (non-PDC) technique, the suggested strategy delivers linear matrix inequality (LMI)-based constraints. Simultaneously design of the proportional-integral (PI)-like state feedback controller and fuzzy anti-windup compensator is achieved with the aim of output tracking. In the faulty case, by considering the nominal system as a reference model, a direct adaptive projection-based approach is developed using the T-S fuzzy modeling and control techniques to supply the adaptive fault-tolerant controller components. An enhanced proportional-integral (PI) state/fault observer with unmeasurable premise variables is introduced only to provide the estimation of states to be used in the proposed controller. The overall closed-loop system ensures the uniformly ultimately bounded (u.u.b) solutions for error dynamics. Two examples, subsuming an inverted pendulum and a chaotic power system, have been used to present the merits and efficiency of the suggested approach persuasively.

Observer and fault reconstruction-based control design for interval type-2 fuzzy systems

In this study, the finite-time stabilization and multiple faults reconstruction issues are scrutinized for nonlinear control systems in the presence of time-varying state delay, actuator faults and sensor faults in which the underlying system is approximated by dint of fuzzy approach. To be specific, the interval type-2 (IT2) fuzzy technique is deployed in tandem with a non-parallel distribution compensation scheme to linearize such a faulty system. Further, the existence of unknown inputs in both the system and its output are effectively reconstructed with the aid of IT2 fuzzy-based observer, namely the IT2 fuzzy unknown input (UI) observer. Simultaneously, the designed observer also ensures the reconstruction of system state vectors that are not able to be measured. With the help of this reconstruction information, a fault-tolerant control scheme is established to maintain the performance of the addressed system even in the occurrence of unknown faults. Particularly, in this work, the sampling strategy is incorporated with the developed controller design. Overall, the proposed IT2 fuzzy UI observer-based sampled fault-tolerant controller guarantees the stability of the resulting system within a finite-time duration. Furthermore, the Lyapunov stability theory enables to formulate the delay-dependent adequate constraints in the framework of linear matrix inequalities. On the grounds of established criteria, the relations are also constructed for obtaining the controller and observer gain matrices. Eventually, the simulation study is conducted with two numerical examples to validate the theoretical and practical significance of the developed control procedure.

A model reconstruction approach for control synthesis of Takagi-Sugeno fuzzy systems

This paper investigates the control synthesis for Takagi-Sugeno (TS) fuzzy systems via a model reconstruction approach. Firstly, based on a nonparallel distributed compensation (NPDC) control scheme and a fuzzy Lyapunov function candidate (FLF), LMI-based synthesis conditions are derived to guarantee the asymptotic stability of the closed-loop TS fuzzy system. Then the operation domain of the premise variables is divided into several subregions to provide more flexibility in control design. And a new local model reconstruction method is proposed to transform the time-derivative of the FLF into new fuzzy forms with transformed membership functions in each subregion. This enables better exploitation of information on membership functions, resulting in relaxed conditions for both stabilization and robust H∞ control. Two simulation examples are provided to verify the advantages of the proposed TS fuzzy control approach.

Sliding-Mode Control for IT2 Fuzzy Nonlinear Singularly Perturbed Systems and Its Application to Electric Circuits: A Dynamic Event-Triggered Mechanism

This work is devoted to an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty}$</tex-math> </inline-formula> sliding-mode control for nonlinear singularly perturbed system under a network control framework. Aiming at describing the nonlinearities with parameter uncertainties in the studied system, the idea of interval type-2 (IT2) fuzzy method is employed in the system modeling. A disturbance observer is developed to acquire the unknown disturbance, and the estimated value is implemented into the controller for neutralizing the influence of the disturbance. To further reduce the occupation of network resources, an event-triggered communication protocol with a dynamic threshold parameter is adopted, where the triggered condition can be adjusted adaptively as the evolution of the system states. Then, an appropriate fuzzy integral sliding motion is constructed based on the constructed system model and disturbance estimation. It is worth noting that the constructed fuzzy controller follows the idea of nonparallel distribution compensation, which improves the designed flexibility. In terms of fuzzy processing, by introducing the membership functions dependent method into the stability analysis, a series of relaxed criteria are established to ensure the global asymptotic stability for the closed-loop systems with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty}$</tex-math> </inline-formula> performance level. Finally, two classical examples of circuit model and inverted pendulum model are extended to IT2 fuzzy idea, showing the rationality of the proposed approach.

Active observer-based T-S fuzzy control scheme for maximum power point tracking in PV systems

This paper addresses the problem of maximum power point tracking of photovoltaic (PV) systems in the presence of model uncertainty as well as varying load and atmospheric conditions using techniques based on a Takagi–Sugeno fuzzy model. The proposed approach relies on the linear matrix inequality tool, Lambert W function, and the Newton–Raphson method. First, adopting a quadratic Lyapunov function, an active observer-based fuzzy non-parallel distributed compensation (non-PDC) controller is designed for asymptotic tracking of the desired reference input. Next, to subdue the impact of uncertainty on the PV system, the closed-loop nominal system is regarded as a reference model, and then the main control law is developed using an online lumped uncertainty estimator and keeping the nominal control law within the staple controller. This control law does not require that the bounds on uncertainties be known. The reference voltage is determined by a novel maximum power point-seeking algorithm that is organized based on the one-diode model of PV panel, Lambert W function, and Newton–Raphson method. Finally, simulations are performed for three scenarios to point out the merits and effectiveness of the proposed methodology in the presence of system uncertainties, environmental changes, and load variations.

A delayed Takagi–Sugeno fuzzy control approach with uncertain measurements using an extended sliding mode observer

In this study, a sliding mode observer (SMO) is implemented on a T–S fuzzy system with multiple time–varying delays over continuous time. Because state data may not be fully available in practice, state observers are used to estimate state information. A system based on observers is implemented with non–parallel distribution compensation (N-PDC). Moreover, the concept of dissipative control provides a framework for analyzing the performance of H∞, L2−L∞, and dissipativeness. In order to design two sliding surfaces using the SMO gain matrix, first two integral–type sliding surfaces must be constructed. Then, we define a few additional parameters using fuzzy Lyapunov stability and SMO theory, resulting in asymptotically stable closed–loop performances. On the basis of the new error system, convex optimization is used to generate the sliding mode controller and the gained weight matrices. Following is an example of the power system (ship electric propulsion) to demonstrate the potential scheme.

Observer-Based Non-PDC Control Design for PMSG-Based Wind Energy Conversion Systems

In this study, the nonparallel distribution compensation (PDC) control is proposed for permanent magnet synchronous generator (PMSG)-based wind energy conversion systems (WECS). To do this, the nonlinear PMSG-based WECS is expressed by Takagi-Sugeno (T-S) fuzzy systems. Based on the imperfect premise matching, the T-S fuzzy observer is delineated for estimating the unmeasurable states of the proposed WECS. Unlike the traditional PDC control, a general non-PDC control strategy is designed via the T-S fuzzy observer. The designed control scheme indicates that it is not required to share the same membership functions as the observer and system. By constructing the Lyapunov functional with available information on the fuzzy membership function and introducing the slack variables, sufficient conditions are obtained to assure the asymptotic stability of error dynamic for the PMSG-based T-S fuzzy system and its observer. Finally, the feasibility and applicability of the derived theoretical results are validated through the numerical example.

Observer-based event-triggered non-PDC control for networked T-S fuzzy systems under actuator failures and aperiodic DoS attacks

This article addresses the observer-based event-triggered non-parallel distribution compensation (PDC) H∞ control issue for networked T-S fuzzy systems (TSFSs) under actuator failures and aperiodic denial-of-service (DoS) attacks. In order to alleviate the interference of network transmission, a fuzzy observer following the asynchronous premise variables as the system is constructed, and we design an observer-based switched fuzzy controller through a non-PDC scheme. And an event-triggered scheme (ETS) is designed to save the limited network bandwidth. Then, based on switching strategy and quantifying the DoS attacks signal indexes, the networked TSFSs can be converted into a new switched augmented system. Moreover, in virtue of piecewise Lyapunov-Krasovskii functional (LKF) method, we propose sufficient conditions to guarantee that the networked TSFS is exponential stability (ES) with a desired H∞ performance. Further, a collaborative design project is presented to obtain triggering parameters, observer gains, and controller gains, and we derive the quantitative relationship between sampling period, triggering parameters, system parameters, actuator fault matrix, and DoS attacks signal indexes. At last, two practical examples are employed to certify the effectiveness and superiority of the presented techniques.

Forecast analysis and sliding mode control on a stochastic epidemic model with alertness and vaccination

In this paper, a stochastic SEIR epidemic model is studied with alertness and vaccination. The goal is to stabilize the infectious disease system quickly. The dynamic behavior of the model is analyzed and an integral sliding mode controller with distributed compensation is designed. By using Lyapunov function method, the sufficient conditions for the existence and uniqueness of global positive solutions and the existence of ergodic stationary distributions are obtained. The stochastic center manifold and stochastic average method are used to simplify the system into a one-dimensional Markov diffusion process. The stochastic stability and Hopf bifurcation are analyzed using singular boundary theory. An integral sliding mode controller with non-parallel distributed compensation is designed by linear matrix inequality (LMI) method, which realizes the stability of system and prevents the outbreak of epidemic disease. The correction of theoretical analysis and the effectiveness of controller are validated using numerical simulation performed in MATLAB/Simulink.

Finite-Time Dynamic Event-Triggered Fuzzy Output Fault-Tolerant Control for Interval Type-2 Fuzzy Systems

The finite-time dynamic event-triggered fuzzy output feedback fault-tolerant control problem is studied in this article for the interval type-2 (IT2) Takagi–Sugeno fuzzy system with parameter uncertainties and actuator faults. A fuzzy state observer is first developed to solve the immeasurable state problem. Second, by using the sampled estimating states and measured output signals, a dynamic event-triggered mechanism is formulated via integrating sensor-to-observer with observer-to-controller. Third, an observer-based finite-time event-triggered fuzzy fault-tolerant controller is synthesized via the nonparallel distribution compensation design principle. Consequently, the finite-time stable conditions of the addressed IT2 fuzzy system are established by constructing an appropriate Lyapunov function. Furthermore, an output feedback control design algorithm of solving control and observer gains is given in terms of the established sufficient finite-time stable conditions. Finally, a practical example of a nonlinear tunnel diode circuit system is provided to verify the effectiveness of the proposed IT2 fuzzy control scheme.

Extended Dissipative Control for Interval Type-2 T-S Fuzzy Markov Jump Systems Subject to Actuator Faults

In this paper, the issue of extended dissipative control for interval type-2 fuzzy Markov jump systems subject to actuator faults is investigated. It is different from the traditional T-S fuzzy method, the interval type-2 fuzzy set is introduced to model the system, and the nonlinearity with parameter uncertainty is captured using the interval type-2 Takagi-Sugeno fuzzy model. During the implementation of the control process, the possible actuator failures are fully considered when designing a controller, and a fault-tolerant control strategy is employed to enhance the elasticity of the designed controller. It is worth noting that, in order to better adapt to the characteristics of interval type-2 fuzzy system, the designed controller follows non-parallel distribution compensation rules, that is, the designed controller does not have the same premise structure and fuzzy rules as the system model, which further improves the flexibility of controller design. Some sufficient conditions ensuring the stability with the extended dissipative performance of the systems are established. In the meanwhile, the obtained results with less conservatism are ensured owing to the boundary information of membership functions considered in the stability analysis. Finally, two numerical examples are provided to indicate the effectiveness of the proposed method.

Membership-function-dependent memory controller design for interval type-2 fuzzy systems under fading channels

This paper studies the problem of membership-function-dependent memory output feedback (MOF) controller design for interval type-2 (IT2) fuzzy systems under fading channels. A time-varying stochastic process is introduced to model the unpredictable channel fading phenomenon. Taking the impact of channel fading into consideration, a non-parallel distribution compensation (non-PDC) strategy is employed to construct a class of memory output feedback fuzzy controllers. By fully exploiting the membership functions, the membership-function-dependent performance analysis and controller synthesis results have been obtained, such that the closed-loop system can be guaranteed with mean-square exponential stability and performance γ. Finally, simulation studies have been presented to demonstrate the effectiveness of the proposed approach.

Event-Triggered Non-PDC Filter Design of Fuzzy Markovian Jump Systems under Mismatch Phenomena

This paper focuses on dealing with the problem of co-designing a fuzzy-basis-dependent event generator and an asynchronous filter of fuzzy Markovian jump systems via event-triggered non-parallel distribution compensation (non-PDC) scheme. The introduction of the event-triggered non-PDC scheme can reduce the number of real-time filter gain design operations with a large computational load. Furthermore, to perform an effective relaxation process, several kinds of time-varying parameters in filter design conditions are simultaneously relaxed by utilizing two zero equalities of transition probabilities and mismatch errors. In addition, to improve the considered performance, the event generation function is established based on fuzzy-basis-dependent event weighting matrices.

Event‐triggered fuzzy output feedback fault‐tolerant control for interval type‐2 Takagi–Sugeno large‐scale systems with time delays

The event-triggered output feedback fault-tolerant control problem is studied in this paper for interval type-2 Takagi–Sugeno (IT2 T-S) fuzzy large-scale systems with time delays. First, a fuzzy state observer is designed to address the immeasurable states problem. Then, by introducing a discrete event-triggered mechanism, an observer-based event-triggered fuzzy decentralized controller with dynamic parameters is synthesized in the presence of actuator faults based on the nonparallel distribution compensation (PDC) design principle. The sufficient conditions of asymptotic stability for the closed-loop systems are derived by constructing an appropriate dynamic parameter based Lyapunov–Krasovskii functional candidate. Finally, a simulation example is provided to verify the feasibility of the developed fuzzy control method.

Robust Constrained Model Predictive Control for T-S Fuzzy Uncertain System with Data Loss and Data Quantization

This paper addresses the robust constrained model predictive control (MPC) for Takagi-Sugeno (T-S) fuzzy uncertain quantized system with random data loss. To deal with the quantization error and the data loss over the networks, the sector bound approach and the Bernoulli process are introduced, respectively. The fuzzy controller and new conditions for stability, which are written as the form of linear matrix inequality (LMI), are presented based on nonparallel distributed compensation (non-PDC) control law and an extended nonquadratic Lyapunov function, respectively. In addition, slack and collection matrices are provided for reducing the conservativeness. Based on the obtained stability results, a model predictive controller which explicitly considers the input and state constraints is synthesized by minimizing an upper bound of the worst-case infinite horizon quadratic cost function. The developed MPC algorithm can guarantee the recursive feasibility of the optimization problem and the stability of closed-loop system simultaneously. Finally, the simulation example is given to illustrate the effectiveness of the proposed technique.

Fault tolerant robust control with transients for over-actuated nonlinear systems

For the problem of robust fault tolerant control of over-actuated nonlinear systems, a new robust synthesis method is investigated. The nonlinear system is modeled via a T–S fuzzy system approach with actuators layout. Based on a designed non-parallel distributed compensation form controller, the closed loop system is obtained. Then a more generalized performance index is introduced by involving the system transients and actuator faults. With a newly proposed nonlinear approximation method, a series of linear matrix inequalities which can make the system robust stable are listed. Finally, based on a dynamic positioning vessel control task, the validity of the proposed method is verified.

Parallel and Nonparallel Distributed Compensation Controller Design for T-S Fuzzy Discrete Singular Systems With Distinct Difference Item Matrices

The issues of admissibility and controller design for a class of extended T-S fuzzy discrete singular systems (FDSSs) with distinct difference item matrices are discussed in this article. A new augmented system which is the equivalent of the original system is introduced to convert these distinct difference item matrices into the easy treatment form. On this basis, using the fuzzy Lyapunov function (FLF), relaxed sufficient condition is given to ensure the admissibility of unforced systems. This condition is described via strict linear matrix inequalities (LMIs), which facilitates to analyze the admissibility. Meanwhile, the design methods of parallel and nonparallel distributed compensation (PDC and Non-PDC) controllers are also proposed. Finally, the advantages of the developed admissibility and controller design approach are illustrated by three examples.

Regional input-to-state stabilization of fuzzy state-delayed discrete-time systems with saturating actuators

We address the regional input-to-state stabilization of discrete-time Takagi-Sugeno fuzzy models under delayed state, saturating actuators, and external energy bounded disturbances. We propose a convex method to design state feedback-based non-parallel distributed compensation, ensuring the fuzzy closed-loop system’s regional stability. Moreover, we introduce a geometrical estimate of the region of attraction in an augmented space, allowing a more extensive set of safe initial sequences. Furthermore, the minimization of the ℓ2-gain from the external disturbance to the controlled output ensures closed-loop performance. Also, we provide optimization procedures allowing the maximization of the estimate of the region of attraction or the disturbance energy tolerance. By employing numerical examples, we compare our approach with similar ones found in the literature, showing our proposal’s efficacy, and its outperform concerning the compared methods.