Observer-based Fuzzy Control Research Articles

A developed observer-based type-2 fuzzy control for chaotic systems

This study presents a novel observer-based fuzzy control for chaotic systems (CSs). A class of CSs with unmeasurable states, unknown input constraints and unknown dynamics is taken to account. A generalised type-2 (GT2) fuzzy logic system (FLS) is formulated to approximate the uncertainties. The parameters of GT2-FLS are adjusted through the tuning rules that are extracted from robustness investigation. The proposed method is applied on CSs and it is demonstrated that the suggested observer and control system result in good performance in versus of disturbances, uncertainties, unknown and time-varying input nonlinearities, unmeasurable states and noisy faults. Comparison with other type of fuzzy systems demonstrates that the proposed GT2-FLS based controller is more effective.

Observer-Based Fuzzy Controller Design for Nonlinear Discrete-Time Singular Systems via Proportional Derivative Feedback Scheme

This paper investigates the observer-based fuzzy controller design method for nonlinear discrete-time singular systems that are represented by Takagi-Sugeno (T-S) fuzzy models. At first, the nonlinearity can be well-approximated with several local linear input-output relationships. The parallel distributed compensation (PDC) technology and the proportional derivative (PD) feedback scheme are then employed to construct the observer-based fuzzy controller. To solve the problem of unmeasured states, the impulsive phenomenon of singular systems, and the PD scheme’s reasonableness, a novel observer-based fuzzy controller is developed. By using the Lyapunov theory and projection lemma, the stability criteria are built in terms of linear matrix inequalities (LMI). Moreover, the gains of fuzzy controller and fuzzy observer can be calculated synchronously by using convex optimization algorithms. Finally, a biological economic system is provided to verify the effectiveness of the proposed fuzzy control method.

Observer-based Adaptive Fuzzy Control for Strict-feedback Nonlinear Systems with Prescribed Performance and Dead Zone

This paper proposes an observer-based fuzzy controller for strict-feedback nonlinear systems. A fuzzy state observer is designed to estimate unmeasurable system states via a fuzzy logic system to approximate the unknown nonlinear functions of the system. A tangent prescribed performance function is utilized to gather the tracking error in a small neighborhood of the origin. The control input is designed to deal with the dead-zone property of the system. The proposed controller can guarantee that all the signals in the closed-loop system are semi-globally, uniformly, and ultimately bounded. Simulation results demonstrate the effectiveness of the proposed controller.

Humanoid Lower Limb: Design, Analysis, Observer-Based Fuzzy Adaptive Control and Experiment

With flexibility similar to human muscles, pneumatic artificial muscles (PAMs) are widely used in bionic robots. They have a high power-mass ratio and are only affected by single-acting pneumatic pressure. Some robots are actuated by a pair of PAMs in the form of antagonistic muscles or joints through a parallel mechanism. The pneumatic pressure and length of PAMs should be measured simultaneously for feedback using a pressure transducer and draw-wire displacement sensor. The PAM designed by the FESTO (10 mm diameter) is too small to install a draw-wire displacement sensor coaxially and cannot measure muscle length change directly. To solve this problem, an angular transducer is adopted to measure joint angles as a whole. Then, the inertia of the lower limb is identified, and observer-based fuzzy adaptive control is introduced to combine with integrated control of the angular transducer. The parameters of the fuzzy control are optimized by the Gaussian basis neural network function, and an observer is developed to estimate the unmeasured angular accelerations. Finally, two experiments are conducted to confirm the effectiveness of the method. It is demonstrated that piriformis and musculi obturator internus act as agonistic muscle and antagonistic muscles alternatively, and iliopsoas is mainly responsible for strengthening because of the constant output force. Piriformis has a greater influence on yaw and roll angles, while musculi obturator internus is the one that influences the pitch angle the most. Due to joint friction, the dead zone of the high-speed on-off valve, lag of compressed air in the trachea, and coupling among angles are very difficult to realize precise trajectory tracking of the pitch, yaw, and roll angles simultaneously.

Adaptive Fuzzy Output Feedback Fault-Tolerant Compensation for Uncertain Nonlinear Systems With Infinite Number of Time-Varying Actuator Failures and Full-State Constraints.

This paper focuses on the observer-based fuzzy adaptive fault-tolerant tracking control problem for uncertain nonlinear systems subject to unmeasured states and unmatched external disturbances. By designing a high gain state observer and a disturbance observer, unmeasured states and unmatched external disturbances are estimated and robust tracking performance is improved. Moreover, the barrier-type functions are introduced to the backstepping design procedure to address the problem that all states do not violate their constraint bounds. Finally, a novel fault-tolerant control scheme for output feedback is proposed by combining with the projection technique. By designing appropriate Lyapunov functions, it is concluded that all signals of the plant are bounded and the desired tracking error can be regulated to a small neighborhood around the origin. The simulation results show the effectiveness of the designed control scheme.

Design of an Adaptive Fuzzy Observer-Based Fault Tolerant Controller for Pneumatic Active Suspension With Displacement Constraint

This paper proposes an adaptive fuzzy observer based fault tolerant controller for a pneumatic active suspension system considering unknown parameters, actuator failures, and displacement constraints. A pneumatic spring is used for a quarter car model to enhance the vibration attenuation performance. Since the pneumatic system contains uncertain nonlinearities, fuzzy logic systems are utilized to approximate unknown nonlinear functions of unmodeled dynamics and various masses of passengers. Besides, a nonlinear disturbance observer is proposed to estimate the effects of the actuator failures, approximation errors, and external disturbances. By utilizing the disturbance estimation and fuzzy approximation techniques, an adaptive fault tolerant control (FTC) is designed to enhance the output performance of the vehicle suspension. Meanwhile, the command filtered scheme is introduced to solve the explosion of complexity problem in the traditional backstepping approach by avoiding virtual controller derivatives. In contrast to previous results, the proposed control can handle the fault tolerant problem and ensure the tracking error of vertical displacement converges into a small-predefined boundary by introducing the prescribed performance function. Moreover, the stability of the closed-loop system is analyzed according to the Lyapunov theory. Finally, comparative simulation examples and experimental studies are performed on the active pneumatic suspension test bench to verify the feasibility of the proposed scheme.

Fuzzy Observer-Based Control for the Traction Dual Rectifiers in High-Speed Train

This paper proposes a fuzzy-observer-based control algorithm to improve the efficiency of traction dual rectifiers of high-speed trains and address the low-frequency oscillation issue induced by the interaction of the DC-link voltage controller with the traction dual rectifiers circuit parameters. The proposed observer checks for the errors in the system model by estimating the system premise variables, and the fuzzy controller then accurately compensates the estimated variables. The method is deduced from the Takagi-Sugeno fuzzy logic model, which is described by a class of IF-THEN fuzzy systems. Fast computation with high precision is what makes them superior to proportional-integral-derivatives controllers. Their capability to deal with nonlinearity in time-varying systems makes them a suitable choice for traction dual rectifier control. The simulation model is formed in SIMULINK, and the waveforms are checked with a conventional fuzzy controller, predictive control, and conventional proportional-integral control. The proposed method can achieve better performance, such as fast transient, more damping, and small overshoot. Furthermore, the method can maintain stability when the system is subjected to external disturbance. In the end, hardware-in-the-loop experiments are performed to validate the proposed control algorithm.

Adaptive Fuzzy Tracking Control for a Class of Singular Systems via Output Feedback Scheme

The problem of adaptive fuzzy observer-based tracking control for nonlinear singular systems is considered in this article. The nonlinear singular systems are composed of two kinds of subsystems, differential subsystem and algebraic subsystem, which are coupled to each other. The systems can be nonstrict feedback structures. Through designing a new state observer and a linear controller, an error system with a tunable parameter is obtained. By constructing new one-sided Lipschitz conditions, the regularization and impulse-free conditions are proposed for the error system. With the help of the tunable parameter in the observer, we design an output feedback controller for the nonlinear singular systems to ensure that all states of the closed-loop system are bounded and the tracking observer errors remain in a neighborhood of the origin. Two examples are provided to illustrate the effectiveness of the presented method.

TS Fuzzy Observer-Based Controller Design for a Class of Discrete-Time Nonlinear Systems

This article presents an observer-based control design approach for a class of nonlinear discrete-time systems. The model nonlinearities are handled in two ways: 1) A Takagi–Sugeno fuzzy representation is used for nonlinearities that depend on measured states, and 2) nonlinearities that depend on unmeasured states are kept in their original form and handled using a slope-bound condition. The observer-based controller design conditions are given as linear matrix inequalities. The approach we propose significantly improves results in the literature by providing less restrictive design conditions. These improvements are illustrated in a detailed analytical and numerical comparison on a synthetic example; while a pendulum-on-a-cart example shows that the approach works both in simulation and in real-time experiments.

Fuzzy adaptive dynamic surface control for strict-feedback nonlinear systems with unknown control gain functions

In this work, the fuzzy adaptive output feedback control is investigated for single-input single-output (SISO) uncertain nonlinear systems in strict-feedback form. The controlled systems under consideration of this work contain the immeasurable states and unknown control gain functions. The immeasurable states are estimated by constructing a fuzzy state observer, and the uncertain nonlinear functions are approximated by fuzzy logic systems. In order to settle the issue of ‘explosion of complexity’ inherent in the conventional backstepping design process, the ‘dynamic surface control’ (DSC) method is introduced. An observer-based fuzzy adaptive control algorithm is proposed by employing the adaptive backstepping control design technique and constructing the Logarithm Lyapunov functions. The designed fuzzy adaptive control scheme can settle the complexity problem of control scheme and insure that the closed-loop system is semi-globally uniformly ultimately boundedness (SGUUB), a simulation example is considered to illustrate the availability of the designed controller.

Dynamic positioning of ships based on robust fuzzy observer

In this study, the robust fuzzy observer-based control scheme for the dynamic positioning of marine vessels is presented. The proposed controller assumes that the environmental disturbances are unknown but bounded with known upper limit. First, the authors apply the Takagi–Sugeno fuzzy model to approximate the ship model. Using formulated fuzzy model, the robust fuzzy observer is developed to approximate the unknown states. Then, by employing optimal H ∞ disturbance attenuation technique, the effects of the environmental disturbances can be attenuated to least value. Finally, the linear matrix inequality technique is hired for solving the optimal robust problem. Model ship is used for simulation, and results are given to prove the validity of the presented controller.

Fuzzy Observer-Based Transitional Path-Tracking Control for Autonomous Vehicles

This study addresses the path-tracking control issue of autonomous vehicles (AVs) when the GPS measurement is temporarily unavailable. In such a case, the vehicle states, location or the curvature of the reference path might be unobtainable, while the camera can be potentially used to detect the path-tracking states. To this end, this paper proposes a fuzzy-observer-based composite nonlinear feedback (CNF) controller with a Takagi-Sugeno (T-S) vehicle lateral dynamic model to guarantee the normal path-tracking maneuver and improve the transient performance. A parallel distributed compensation (PDC)-based CNF control method is developed to realize the control objective with the T-S vehicle model considering the transient performance and actuator saturation. The closed-loop stability and ${H} _{ \boldsymbol {\infty }}$ index performance integrating the tracking and estimation errors have been proved with a Lyapunov approach. The observer-based controller design has been implemented based on the formulation of the linear matrix inequalities (LMIs). High-fidelity simulations using CarSim-Matlab/Simulink have demonstrated the validity of the proposed approach in terms of enhancing the tracking performance under the input saturation and disturbances in GPS-denied environments.

Observer-Based Fuzzy Adaptive Inverse Optimal Output Feedback Control for Uncertain Nonlinear Systems

In this article, an observer-based fuzzy adaptive inverse optimal output feedback control problem is studied for a class of nonlinear systems in strict-feedback form. The considered nonlinear systems contain unknown nonlinear dynamics and their states are not measured directly. Fuzzy logic systems are applied to identify the unknown nonlinear dynamics and an auxiliary nonlinear system is constructed. Based on this auxiliary system, a fuzzy state observer is first designed to estimate the immeasurable states. By using the inverse optimal principle and adaptive backstepping design theory, an observer-based fuzzy adaptive inverse optimal output feedback control scheme is then developed. The proposed inverse optimal control scheme need not assume that the states are measurable. It also guarantees that the closed-loop system is semiglobally uniformly ultimately bounded, and achieves the optimal control objective as well. Finally, two simulation examples are provided to check the validity of the presented control method.

Fuzzy observer‐based tracking control of an underactuated underwater vehicle with linear velocity estimation

In the presence of the unmodelled dynamics and external time-varying disturbances, letting an underactuated underwater vehicle track a reference trajectory correctly without knowledge of the vehicle's linear velocity is a challenging problem. This study reports a solution to this problem by proposing a linear velocity observer that is based on available states. Furthermore, a fuzzy observer-based tracking controller is designed, where fuzzy logic systems are resorted to approximate the model uncertainties and disturbances. Theoretical analysis demonstrates that the vehicle can converge to a neighbourhood of the reference smooth trajectory, hence achieving a global state that is uniformly and ultimately bounded. In order to validate the performance of the proposed controller, numerical examples are presented. They show that the linear velocity observer can be used to estimate the actual linear velocity and the underwater vehicle is able to track the reference trajectory closely.

Observer-based output feedback fuzzy control for nonlinear parabolic PDE-ODE coupled systems

This paper employs observer-based feedback control technique to discuss the design problem of output feedback fuzzy controllers for a class of nonlinear coupled systems of a parabolic partial differential equation (PDE) and an ordinary differential equation (ODE), where both ODE output and pointwise PDE observation output (i.e., only PDE state information at some specified positions of the spatial domain) are available. Initially, a Takagi-Sugeno (T-S) fuzzy PDE-ODE model is constructed to exactly represent the nonlinear coupled system via the local sector nonlinearity approach. Then, based on the T-S fuzzy PDE-ODE model, a Lunberger-type fuzzy observer is constructed by the ODE output and the pointwise PDE observation output to estimate the nonlinear coupled system state. A fuzzy controller is proposed by the estimated state. Sufficient conditions for existence of the proposed observer-based fuzzy controller are developed such that the exponential stability of the augmented closed-loop system is ensured, and presented in terms of bilinear matrix inequalities (BMIs). A local algorithm via the convex optimization technique is proposed to solve these BMIs. Finally, numerical simulation results are provided to support the proposed design method.

Observer-Based Fuzzy Fault-Tolerant Control for Nonlinear Parabolic PDEs

This paper investigates fault-tolerant control design for a class of nonlinear parabolic distributed parameter systems (DPSs) with actuator faults. Under the averaged measurements, an observer-based fuzzy fault-tolerant control law is constructed. Sufficient conditions in terms of bilinear matrix inequalities conditions are derived to ensure internal exponential stability and disturbance attenuation performance of system simultaneously by using Lyapunov–Krasovskii method. An iterative optimization algorithm is proposed to find feasible solutions. An example is given to illustrate the efficiency of main results.

Fuzzy Observer-Based Dynamic Surface Control for Input-Saturated Nonlinear Systems and its Application to Missile Guidance

In this paper, a fuzzy observer-based tracking control scheme is proposed for a class of strict-feedback uncertain nonlinear system with input saturation. To facilitate the fuzzy logic system (FLS) design, the original uncertain nonlinear system is transformed into an output feedback system firstly. Then, an adaptive state observer is constructed. In order to efficiently tackle the input saturation, an auxiliary system (AS) is introduced. Using the estimated states and AS, the dynamic surface control (DSC) strategy is developed based on backstepping method. Under the DSC scheme, the tracking control problem is reduced to optimal regulation problem of an affine system. Subsequently, an adaptive dynamic programming (ADP) based optimal control scheme is proposed. The stability of the overall system is guaranteed by Lyapunov theory. Finally, guidance simulation is made to confirm the effectiveness of the developed control method.

Event-Triggered Dissipative Observer-Based Control for Delay Dependent T–S Fuzzy Singular Systems

This paper investigates the problem of event-triggered dissipative observer-based output feedback control for a class of Takagi-Sugeno (T-S) fuzzy singular systems with unavailable states, time-varying delays, and imprecise membership functions. The considered singular system is presented as a T-S fuzzy singular system which gives a more realistic presentation for a variety of non-linear dynamical systems than conventional state space representation. The general framework we designed is based on a fuzzy observer-based controller with time varying delay along with extended dissipativity, which provides the H∞, L2-L∞ and dissipative performance indices and is robust against the disturbances and time-varying delay. Moreover, a novel Lyapunov-Krasovskii functional is adopted to analyze the closed loop stability of the fuzzy system. The solvability of Lyapunov-Krasovskii functional results in the formation of linear matrix inequalities. The controller and observer gains can be obtained by solving the linear matrix inequalities. Simulations are performed to validate the proposed scheme.

Event-Triggered Observer-Based Fuzzy Control for Coal-Fired Power Generation Systems Based on Singularly Perturbed Theory

The fuzzy controller design method for coal-fired power generation systems (CFPGSs) based on the singular perturbation theory is proposed in this paper. By analyzing the characteristics of two-time-scale, nonlinearity and input saturation for CFPGSs and using the singular perturbation theory and fuzzy control theory, the CFPGSs are modeled as fuzzy singularly perturbed systems with actuator saturation. In addition, considering the factors of the unavailable information on some state variables (such as inlet steam mass flow) and the limited bandwidth of network, an event-triggered observer-based controller structure is constructed. Then, by establishing an Lyapunov-Krasovskii functional based on the parameter $\varepsilon $ and the upper bound of time-delay, a design method of event-triggered observer-based anti-windup controller is proposed, such that the closed-loop systems are asymptotically stable. And, the ill-conditioned numerical problems and Zeno phenomenon are avoided in the design process. Finally, a simulation verifies the effectiveness of the proposed method, that is, the system outputs (electric power and main steam pressure) tend to the reference value.

Observer-Based Fuzzy Control for Four-Wheel Independently Driven Electric Vehicles with Active Steering Systems

This paper presents an observer-based control strategy to improve the maneuverability and stability performance of four-wheel independently driven electric vehicles with active front-wheel steering systems. Since the system states are difficult to be measured directly, a novel observer is designed to estimate the vehicle yaw rate and lateral velocity simultaneously. Takagi–Sugeno fuzzy model is used to handle the time-varying parameters of the vehicle model. Based on Lyapunov function theory, stability conditions of the closed-loop system are derived. The fuzzy $$H_{\infty }$$ controller is designed to make the resulting T–S fuzzy system asymptotically stable and satisfy $$H_{\infty }$$ performance under given constraints. Simulation results are given to demonstrate the validity of the presented control method.