Fuzzy Output Feedback Control Research Articles

Adaptive fuzzy output feedback control for a class of uncertain nonlinear systems in the presence of sensor attacks

In this paper, an adaptive fuzzy output feedback control scheme is proposed for a class of unknown nonlinear systems with sensor attacks. The fuzzy logic systems are employed to approximate the uncertain nonlinearities, and the backstepping technique is implemented to construct controllers. The unknown output feedback coefficient is handled by using a Nussbaum function in the first step of backstepping design, eventually developing an adaptive controller to accommodate sensor attacks. Compared to the current control schemes for nonlinear systems under sensor attacks, the benefit of the proposed adaptive controller is that it can apply to nonlinear systems with both uncertainty and unmeasurable states. Finally, two examples validate the efficacy of the proposed control scheme.

Observer-Based Finite-Time Inverse Optimal Output Regulation for Uncertain Nonlinear Systems

This paper deals with the finite-time inverse optimal output regulation problem for a class of uncertain nonlinear systems that are subjected to an exosystem. The nonlinear systems not only contain external disturbances in the exosystem but also take the unknown nonlinear functions and unmeasured states into account. The output regulation problem is first converted into a stabilization problem through the internal model. Then, fuzzy logic systems (FLSs) are employed to approximate the unknown nonlinear functions. An auxiliary system is constructed and, based on the auxiliary system, a fuzzy state observer is designed to estimate the unmeasured states. Furthermore, a novel adaptive fuzzy finite-time inverse optimal output feedback controller and adaptive law are designed by combining backstepping technology, adaptive control technology, finite-time stability theory, and the inverse optimal control method. The control algorithm ensures that all the signals of the closed-loop system are semiglobally practical finite-time stable (SGPFS), so the newly well-defined cost function that is connected with the auxiliary system can be minimized. Finally, the validity of the approach is confirmed by virtue of the simulation results.

Command-Filter-Based Adaptive Fuzzy Finite-Time Output Feedback Control for State-Constrained Nonlinear Systems With Input Saturation

In this article, an adaptive fuzzy finite-time tracking control method is investigated for a class of state-constrained nontriangular nonlinear systems with input saturation. First, the fuzzy logic system is introduced to process the unknown functions, and the immeasurable system states are estimated accurately via the fuzzy state observer. To handle the saturation nonlinearity, the function approximation method is applied for the system transformation. Second, the “explosion of complexity” problem inherent in backstepping is solved through the command filter. Meanwhile, the barrier Lyapunov function is designed to guarantee that the constraints of states are not violated. Third, an adaptive fuzzy finite-time output feedback controller is developed to render the closed-loop system semiglobally practically finite-time stable. Eventually, simulation examples are included to illustrate the effectiveness of the theoretical results.

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.

Distributed adaptive fuzzy control for multi-agent systems with full state constraints and unmeasured states

This article proposes a fuzzy adaptive output feedback control method for multi-agent systems with uncertainties and nonlinearities, considering both full state constraints and unmeasurable states. Aiming at the problem that the state of followers in nonlinear multi-agent systems is unmeasured, an observer is constructed by applying the characteristics of fuzzy logic systems to achieve the output feedback control scheme. The state constraint of multi-agent systems is also a great challenge. Based on a backstepping technique and integral barrier Lyapunov functions (iBLFs), all states are constrained, and an adaptive controller is designed. Compared with imposing constraints on the error and then constraining the state, the method in this article compensates for defects in the constraint conditions. Furthermore, under the Lyapunov stability theorem, we can prove that all signals of closed-loop systems are cooperative semi-global uniformly ultimately bounded (CSUUB). A simulation validates the effectiveness of the proposed control scheme.

A Novel Mixed Control Approach for Fuzzy Systems via Membership Functions Online Learning Policy

This article focuses on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {L}_{2}-\mathcal {L} _{\infty}/ \mathcal {H}_{\infty}$</tex-math></inline-formula> optimization control issue for a family of nonlinear plants by Takagi–Sugeno (T–S) fuzzy approach with actuator failure. First, considering unmeasurable system states, sufficient criteria for devising fuzzy imperfect premise matching dynamic output feedback controller to maintain asymptotic stability while guaranteeing a mixed performance for T–S fuzzy systems are provided. Therewith, in the light of feasible areas of dynamic output feedback controller membership functions (MFs), a new MFs online learning policy using gradient descent algorithm is proposed to learn the real-time values of MFs to acquire a better <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {L}_{2}-\mathcal {L}_{\infty}/ \mathcal {H}_{\infty}$</tex-math></inline-formula> control effect. Different from the traditional method using an imperfect premise matching scheme, under the proposed optimization algorithm, the trajectory of mixed performance index is lowered effectively. Afterward, a sufficient criterion is presented for assuring the convergence of the error of the cost function. Finally, the superiority of this online optimization learning policy is confirmed via simulations.

Prescribed Performance Fuzzy Adaptive Output Feedback Control for Nonlinear MIMO Systems in a Finite Time

This article studies the fuzzy adaptive output feedback control design problem for nonstrict feedback multi-input–multi-output nonlinear systems with full-states prescribed performance in finite time. Fuzzy logic systems are introduced to solve the problem of unknown nonlinear dynamics. And on this basis, a fuzzy-based state observer is designed to observe the unmeasurable state. Further, by combining the adaptive back-stepping control algorithm and the nonlinear filters, a novel dynamic surface control (DSC) method is proposed, which not only solves the computational complexity explosion problem inherent in the back-stepping control algorithm, but also improves the control performance, in contrast to the traditional DSC methods with linear filters. Besides, to further improve the tracking performance under the structure of full-states prescribed performance, a new Lyapunov function is designed considering the transform error constraint. Based on the Lyapunov theory, the stability of the closed-loop system is analyzed to ensure that all signals of the closed-loop system are semiglobal practical finite-time stability. Finally, to elaborate on the feasibility and effectiveness of the proposed control method, a simulation example is provided.

Membership-Function-Dependent Control Design of Interval Type-2 Sampled-Data Fuzzy-Model-Based Output-Feedback Tracking Control System

This article focuses on the stability analysis and control design of an interval type-2 sampled-data fuzzy-model-based output-feedback (IT2SDFMBOF) tracking control system, which is formed by the interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy model, the stable reference model, and the interval type-2 sampled-data output-feedback (IT2SDOF) fuzzy controller. The design goal is to establish a proper IT2SDOF fuzzy controller that is able to drive the states of the nonlinear plant subject to uncertainties to track those of the stable reference model, and the <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 index is adopted to optimize the tracking control performance. To improve the robustness of the IT2SDOF fuzzy controller against uncertainties of the nonlinear plant, IT2 fuzzy sets are utilized. Considering that the tracking control system is sampled-data (SD) type, a two-sided looped-functional-based approach exploiting the information on the interval from time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t_k$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t$</tex-math></inline-formula> and the interval from time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t_{k+1}$</tex-math></inline-formula> is applied to enhance the stability analysis. The imperfect premise matching (IPM) concept permits the number of rules and the premise membership functions of the IT2 T-S fuzzy model and the IT2SDOF fuzzy controller to be different, which can be employed to promote the design flexibility. The tracking control system with the SD type and IPM design will cause the membership grades between the IT2 T-S fuzzy model and the IT2SDOF fuzzy controller to be mismatched. In addition, the membership-function-dependent stability analysis approach that can introduce the boundary information of membership functions into the stability analysis is used to relax the stability conditions. The relaxed stability conditions subject to the <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 building on the Lyapunov stability theory are developed in terms of linear matrix inequalities. Simulation results demonstrate the effectiveness of the proposed IT2SDFMBOF tracking control system.

Adaptive Event-Triggered Output Feedback Control for Nonlinear Switched Systems Based on Full State Constraints

Aiming at the research content of tracking control for a class of nonlinear uncertain switched systems including full state constraints, a novel event-triggered adaptive fuzzy output feedback control scheme is given. The systems studied need to use the approximation principle of fuzzy logic systems (FLSs) to solve the nonlinear smooth function with unknown terms. For ensuring that all states of the systems are within the time-varying constraint limits, the stability of the switched systems is verified by utilizing tangent barrier Lyapunov function (Tan-BLF). Based on the potential barrier Lyapunov function (BLF) and backstepping recursive construction method, the adaptive law, controller and event-triggered mechanism of the subsystem are designed. The proposed method will make that the signal is bounded. Moreover, the tracking error can be adjusted to the neighborhood closed to the origin. Simulation examples indicate the feasibility of the method.

Dynamic event-triggered security control for networked T-S fuzzy system with non-uniform sampling

This paper is focused on the security control problem for the dynamic event-triggered networked T-S fuzzy control system with non-uniform sampling and stochastic network attacks. Different from existing research, the signals from sensor are sampled in a non-uniform period. To improve communication, a novel dynamic event-triggered method is proposed, which can adjust the trigger parameters dynamically according to the changes of external output. Then, a T-S fuzzy dynamic output feedback control model with event-triggered mechanism and network attacks is constructed. Furthermore, by introducing a set of slack matrix, the asynchronous premise variable problem caused by event-triggered method is solved, and some sufficient conditions that insure the asymptotic stability with an H∞ performance requirement of the established closed-loop system can be obtained by utilizing Lyapunov function method and stochastic analysis technique. Moreover, the gains of the fuzzy dynamic output feedback controllers are found by solving the linear matrix inequalities (LMIs). Finally, two practical examples are given to support the merits and effectiveness of the proposed method.

A T-S fuzzy state observer-based model predictive reset control for a class of fuzzy nonlinear systems with event-triggered mechanism

In this study, the problem of observer-based control for a class of nonlinear systems using Takagi-Sugeno (T-S) fuzzy models is investigated. The observer-based model predictive event-triggered fuzzy reset controller is constructed by a T-S fuzzy state observer, an event-triggered fuzzy reset controller, and a model predictive mechanism. First, the proposed controller utilizes the T-S fuzzy model and is constructed based on state observations and discrete sampling output, which can greatly reduce the occupation of communication resources. Then, the model predictive strategy for reset law design is designed in this paper. With a reasonable reset of the controller state at certain instants, the performance of the reset control systems is improved. Finally, the validity of the proposed method is illustrated by simulation. The merits of the proposed controller in improving transient performance and reducing the communication occupation are demonstrated by comparing its results with the output feedback fuzzy controller and the first-order fuzzy reset controller.

Adaptive Fuzzy Output-Feedback Control for Switched Uncertain Nonlinear Systems With Full-State Constraints.

This article investigates an adaptive fuzzy tracking control approach via output feedback for a class of switched uncertain nonlinear systems with full-state constraints under arbitrary switchings. The adaptive observer and controller are designed based on fuzzy approximation. The main characteristic of discussed systems is that the state variables are not available for measurement and need to be kept within the constraint set. In order to estimate the unmeasured states, the adaptive fuzzy state observer is constructed. To guarantee that all the states do not violate the time-varying bounds, the tangent barrier Lyapunov functions (BLF-Tans) are selected in the design procedure. Based on the common Lyapunov function method, the stability of considered systems is analyzed. It is demonstrated that all the signals in the resulting system are bounded, and all the states are limited in their constrained sets. Furthermore, the simulation example is used to validate the effectiveness of the presented control strategy.

Dynamic-output-feedback based interval type-2 fuzzy control for nonlinear active suspension systems with actuator saturation and delay

This paper proposes a fuzzy dynamic output feedback (DOF) controller for uncertain nonlinear active suspension systems (ASSs) with actuator saturation and time-varying delay. Firstly, given the time-delay and nonlinear characteristics of the suspension systems, an interval type-2 (IT-2) Takagi-Sugeno (T-S) fuzzy model is introduced to characterize the uncertain nonlinear ASSs with actuator saturation. Secondly, with the Lyapunov-Krasovskii function and the reciprocally convex technique, a series of sufficient delay-dependent conditions are derived to make sure that the control system with optimized H∞ performance and mechanical constraints is asymptotically stable. Thirdly, a DOF controller is designed to estimate the unmeasurable parameters of the system. Finally, the performance evaluation of the proposed controller is conducted through numerical and experimental tests.

Event-triggered output feedback dissipative control of nonlinear systems under DoS attacks and actuator saturation

This paper presents a novel event-triggered dynamic output feedback dissipative control of nonlinear systems under intermittent denial-of-service (DoS) attacks and actuator saturation. Firstly, based on attack information, a secure event-triggered mechanism (ETM) is introduced, which not only saves systems resources but also is Zeno-free and resilient to DoS attacks. Secondly, a switched T–S fuzzy closed-loop system model is built, which unifies the parameters of nonlinear plant, noises, ETM, DoS attacks, switched output feedback fuzzy controller, and actuator saturation all in one framework. Thirdly, low conservative exponential stability criteria are derived while guaranteeing strict , , -dissipativity, and hence the relationships between system performance and factors such as DoS attacks, secure ETM, noises and actuator saturation are established. Further, sufficient conditions are given for the co-design of the switched output-based fuzzy controller and the secure ETM. Finally, the effectiveness of the proposed method is confirmed by numerical examples, achieving over 92% system resources.

Stability analysis and robust controller design for systems with mixed time-delays and stochastic nonlinearity via cone complementarity linearization

The stochastic Takagi-Sugeno (T-S) fuzzy discrete dynamic output feedback control is investigated for a class of stochastic T-S fuzzy discrete networked control systems. Firstly, the T-S fuzzy model and stochastic Bernoulli theory are employed to approximate the discrete system plant. Secondly, the T-S fuzzy model and stochastic Bernoulli theory are employed to design the stochastic T-S fuzzy discrete dynamic output feedback controller. Thirdly, the stochastic Bernoulli theory is employed to describe the characteristics of random occurrence for multipath packet dropouts. The delay-dependent discrete Lyapunov functional and Schur complement are employed, the closed-loop system is stochastically finite-time bounded stable subject to (c1,c2,ω¯,N,R). The Schur complement and congruence transformation matrix are introduced to determine controller gain matrices. The cone complementarity linearization is applied to convert controller design into nonlinear minimization constraints for solving the nonconvex problem caused by fuzzy-basis-dependent LMIs. Simulations are given to show the effectiveness of proposed methods.

Designing an Optimal Reset Controller for TS Fuzzy Systems

This study considers the problem of designing a reset dynamic output feedback controller (R-DOFC) for continuous-time nonlinear dynamics modeled by a Takagi-Sugeno (TS) fuzzy form. The exponential convergence of the closed-loop system state trajectories to the equilibrium point is satisfied by designing the fuzzy dynamic output feedback controller (DOFC) without reset action via the linear matrix inequality (LMI) technique. After that, by developing an optimization problem, the after-reset value is designed by using system output measurements at each reset time. In this approach, a genetic algorithm is adopted to minimize the proposed cost function of certain transient performances to achieve the best reset time instants. Moreover, sufficient conditions for choosing the DOFC after-reset value are formulated in the form of LMIs. The proposed reset fuzzy DOFC is applied to two nonlinear systems. The merits of the proposed reset DOFC are demonstrated by comparing the obtained results with those of other approaches.

Membership-Function-Dependent Design of $L_1$-Gain Output-Feedback Controller for Stabilization of Positive Polynomial Fuzzy Systems

This article presents the <inline-formula><tex-math notation="LaTeX">$L_1$</tex-math></inline-formula>-gain polynomial fuzzy output-feedback controller design and the stability analysis using the sum-of-squares (SOS) approach for positive polynomial fuzzy-model-based (PPFMB) control systems. The polynomials, positivity, and optimal <inline-formula><tex-math notation="LaTeX">$L_1$</tex-math></inline-formula> performance make some existing convex methods for general systems inapplicable. To overcome this problem, first, an augmented system of the PPFMB control system is constructed; then, by introducing some constraint conditions and mathematical techniques, nonconvex stability and positivity conditions are skillfully transformed into convex ones simultaneously. In addition, to control the systems flexibly and lower the implementation cost, the imperfect premise matching concept is taken into account for controller design. Besides, the high-degree-polynomial approximation method is adopted to conduct stability and positivity analysis by incorporating the information of membership functions and the boundary information of the state variables. On the basis of the Lyapunov stability theory, the relaxed stability and positivity conditions in terms of the SOS form are obtained. Finally, two simulation examples are presented to verify the feasibility of the theoretical results.

Fuzzy dynamic output feedback control for nonlinear networked multirate sampled-data systems: An integral inequality method

This paper is devoted to fuzzy dynamic output feedback control for nonlinear networked multirate sampled-data systems based on T-S fuzzy systems. Using asynchronous multirate sampled-data, a multirate fuzzy controller is designed. The resultant closed-loop system is modeled as a perturbed system with two perturbed terms which include multirate sampling and the asynchronous membership functions between the controlled plant and the controller. A novel refined integral inequality is developed, and it improves Jensen's inequality and extends Wirtinger's inequalities by considering the sawtooth structure of time-varying delays. By applying the inequality to the perturbed system and constructing a new storage function, a stability criterion and two fuzzy dynamic output feedback controller design methods are presented for the nonlinear networked multirate sampled-data systems. Finally, three illustrative examples show the effectiveness of the proposed method.

Observer-Based Adaptive Fuzzy Output Feedback Control of Fractional-Order Chaotic Systems With Input Quantization

This study investigates the adaptive fuzzy output feedback control of strict-feedback fractional-order chaotic systems with unmeasurable states and quantized input. First, the functional uncertainties are approximated by fuzzy logic systems (FLSs). Second, combining the FLS and the system output signal, an observer is constructed to estimate the unmeasurable states. A command filter is defined to cope with the “explosion of complexity” problem resulting from the repeated derivatives of virtual control inputs in each backstepping step. To compensate for quantization errors, a hyperbolic tangent function is introduced to transform the control signal, which can not only guarantee that the tracking error converges to an arbitrarily small region near the origin but also reduce the chattering phenomenon of the control input. In addition, the stability analysis is carried out relying on the fractional Lyapunov stability criterion such that all the signals keep bounded. Finally, a numerical simulation example is put forward to verify the effectiveness of our method.

Multi-objective H2/H∞ saturated non-PDC static output feedback control for path tracking of autonomous vehicle

This paper presents a new fuzzy output feedback control design for autonomous vehicle steering under actuator saturation, unavailability of the sideslip angle measurement, unknown road curvature, and lateral wind force. To take into account the actuator constraint, the saturation effect is transformed into dead-zone nonlinearity. A static output controller based on non-compensation parallel distributed technic and a Takagi-Sugeno (T-S) model of vehicle lateral dynamics is proposed to consider the unavailability of some vehicle states. To avoid the problem of imposing bounds on membership functions time derivatives resulting from the use of the fuzzy Lyapunov approach, a proper integral structure based on the non-quadratic Lyapunov approach is investigated. The mixed [Formula: see text] stabilization conditions of the augmented closed-loop system are expressed in terms of linear matrix inequalities (LMIs). Finally, the robustness and the advantages of the proposed approaches are demonstrated through different tests.