Observer-based Fuzzy Control Research Articles

Observer-Based Fuzzy Adaptive Dynamic Surface Control of Uncertain Nonstrict Feedback Systems With Unknown Control Direction and Unknown Dead-Zone

In this paper, an observer-based fuzzy adaptive controller for a class of uncertain nonstrict nonlinear systems with unknown control direction and unknown dead-zone is presented. First, by using equivalence dead-zone inverse and a linear state transformation, the original system is converted to a new one. Then, by using fuzzy logic systems, the unknown nonlinearities are approximated based on an adaptive mechanism, and a nonlinear fuzzy state observer is designed to estimate immeasurable states. The dynamic surface control technique is employed to solve the problem of explosion of complexity in the traditional backstepping approach, and then, this method is combined with Nussbaum gain function to address the problem of unknown control direction. Besides, barrier Lyapunov function is employed to overcome the violation of system output. The proposed controller guarantees that the closed-loop system is stable; all the system states are bounded, and tracking errors converge to a neighborhood of the origin. A numerical simulation is provided to confirm the usefulness of the proposed control design.

Power Optimization of wind energy conversion system using T-S Fuzzy approach

This paper presents a maximum power point tracking control for a wind energy conversion system (WECS) using a squirrel cage induction generator (SCIG) which supplies a DC load through AC/DC converter. The goal of the developed fuzzy control law is to track the reference signals corresponding to the maximum power generation that leads to an optimal operation of the induction generator. First, the dynamics behaviour of the WECS is represented by a Takagi-Sugeno (T-S) fuzzy model. Then, a H∞ observer-based fuzzy controller is proposed to achieve a maximum power point tracking even when we consider a varying wind speed profile. The controller and observer gains are calculated by solving linear matrix inequalities (LMIs). Finally, simulation results are presented to illustrate the effectiveness of the proposed approach.

Model-based robust suppression of epileptic seizures without sensory measurements.

Uncontrolled seizures may lead to irreversible damages in the brain and various limitations in the patient's life. There exist experimental studies to stabilize the patient seizures. However, the experimental setups have many sensory devices to measure the dynamics of the brain cortex. These equipments prevent to produce small portable stabilizers for patients in everyday life. Recently, a comprehensive cortex model is introduced to apply model-based observers and controllers. However, this cortex model can be uncertain and have time-varying parameters. Therefore, in this paper, a robust Takagi-Sugeno (TS) controller and observer are designed to suppress the epileptic seizures without sensory measurements. The unavailable sensory measurements are provided by the designed nonlinear observer. The exponential convergence of the observer and controller is satisfied by the feedback parameter design using linear matrix inequalities. In addition, TS fuzzy observer-controller design has been compared with the conventional PID method in terms of control performance and design problem. The numerical computations show that the epileptic seizures are more effectively suppressed by the TS fuzzy observer-based controller under uncertain membrane potential dynamics.

Fuzzy Observer-Based Repetitive Tracking Control for Nonlinear Systems

This article is concerned with the periodic tracking control problem for nonlinear systems. First, the Takagi-Sugeno (T-S) fuzzy model is employed to describe the nonlinear control systems. Second, considering the partly unmeasurable states of the system, a novel fuzzy observer-based repetitive controller, which is the mixed controller of the fuzzy observer-based controller and the fuzzy repetitive controller, is designed to deal with the periodic tracking control problem. To reduce the conservatism and increase the feasible solution space of the stabilization conditions, a new fuzzy relaxed matrix technique is developed by introducing some relaxed matrices in the derivative of the fuzzy normalized membership function. Then, the fuzzy Lyapunov functional with an additional separation parameter and the augmented fuzzy matrix technique (the interactions of fuzzy observer subsystems) are proposed such that the delay-dependent stability condition of the closed-loop system in the form of linear matrix inequality is obtained with less conservatism. It is worth noting that due to introducing an additional parameter in the fuzzy Lyapunov functional, the fuzzy controller and fuzzy observer can be separately designed, which largely enhances the flexibility of design with low computational complexity. Finally, three examples are provided to illustrate the effectiveness and less conservatism of the proposed method.

Fuzzy Observer Based Control for Nonlinear Coupled Hyperbolic PDE-ODE Systems

In this work, the fuzzy observer-based control problem is investigated for a class of nonlinear coupled systems, which consists of a hyperbolic partial differential equation (PDE) containing nonlinearities and a nonlinear ordinary differential equation (ODE). The nonlinear coupled system is represented as a Takagi–Sugeno (T–S) fuzzy coupled hyperbolic PDE-ODE model. Based on the T–S fuzzy model, a novel Lyapunov functional approach is proposed to design a fuzzy observer based control strategy. More specifically, a fuzzy observer is presented to estimate the state variables of the fuzzy coupled PDE-ODE system with the measurements of the PDE, and the exponential convergence of the observer error is proved. Then, a fuzzy controller is given utilizing the estimated states as feedback variables, and it is proved that the evolution profiles of the PDE and the trajectory of the ODE in the closed-loop fuzzy system converge exponentially to the desired values, respectively. The sufficient existence conditions of the fuzzy observer based controller are formulated in terms of a set of space differential linear matrix inequalities (SDLMIs). A recursive algorithm based on the finite-difference approximation and the linear matrix inequality techniques are provided to solve the SDLMIs. Finally, the results are applied to case study of a predator–prey system, and the simulations are performed to illustrate the effectiveness of the proposed observer based control law.

Adaptive fuzzy observer-based cooperative control of unknown fractional-order multi-agent systems with uncertain dynamics

In our paper, a new cooperative control for unknown fractional-order multi-agent systems is proposed. In addition to unknown dynamics, for the first time, the values of the fractional orders are also assumed to be unknown, and a new robust observer-based cooperative method for consensus issue of multi-agent systems (MASs) is presented. The unknown functions in the dynamics of the systems in all agents are estimated with the proposed interval type 2 fuzzy self-structuring radial basis function neural network (IT2F-SRBFNN). The free parameters of all IT2F-SRBFNN in all agents are adjusted using the adaptation laws which can be derived from the Lyapunov stability analysis. The strength of the proposed strategy is verified by a number of simulation examples.

Mode-dependent non-fragile observer-based controller design for fractional-order T–S fuzzy systems with Markovian jump via non-PDC scheme

In this paper, controller synthesis problem based on non-fragile observer is investigated for a class of fractional-order nonlinear systems subject to abrupt changes under the fractional-order T–S fuzzy model with Markovian jump. By utilizing non-parallel-distributed-compensation (non-PDC) scheme, the model-dependent observer and the observer-based fuzzy controller are designed under imperfect premise matching to enhance design flexibility. Moreover, the multiplicative random sensor noise over the measurement output is considered. Then, based on the matrix singular value decomposition method (SVD) and the membership-function-shape-dependent (MFSD) analysis approach, new less-conservative sufficient conditions in term of LMIs are derived to guarantee the closed-loop fractional-order fuzzy system robustly stochastically stable. Finally, two examples are provided to illustrate the effectiveness of the new design techniques for fractional-order systems.

Fuzzy Adaptive Practical Finite-Time Control for Time Delays Nonlinear Systems

This paper focuses on fuzzy adaptive practical finite-time output feedback control problem for a class of single-input and single-output nonlinear system with time-varying delays in nonstrict feedback form. Fuzzy logic systems are adopted to approximate the unknown nonlinear functions, and state observer is constructed to estimate the unmeasured states. By combining practical finite-time Lyapunov stability theory with the backstepping design, an observer-based fuzzy adaptive practical finite-time control strategy is proposed. Meanwhile, the stability of the closed-loop system is proved, which means that the output can follow the given reference signal in a finite time, and the closed-loop system is semi-global practical finite-time stability. Finally, two simulation examples are provided to elaborate the effectiveness of the presented control strategy.

Optimal fuzzy controller based on non-monotonic Lyapunov function with a case study on laboratory helicopter

ABSTRACTThis paper presents a new approach to design an observer-based optimal fuzzy state feedback controller for discrete-time Takagi–Sugeno fuzzy systems via LQR based on the non-monotonic Lyapunov function. Non-monotonic Lyapunov stability theorem proposed less conservative conditions rather than common quadratic method. To compare with optimal fuzzy feedback controller design based on common quadratic Lyapunov function, this paper proceeds reformulation of the observer-based optimal fuzzy state feedback controller based on common quadratic Lyapunov function. Also in both methodologies, the dependence of optimisation problem on initial conditions is omitted. As a practical case study, the controllers are implemented on a laboratory twin-rotor helicopter to compare the controllers' performance.

Observer-based fuzzy adaptive stabilization of uncertain switched stochastic nonlinear systems with input quantization

This paper proposes an observer-based fuzzy adaptive output feedback control scheme for a class of uncertain single-input and single-output (SISO) nonlinear stochastic systems with quantized input signals and arbitrary switchings. The SISO system under consideration contains completely unknown nonlinear functions, unmeasured system states and quantized input signals quantized by a hysteretic quantizer. By adopting a new nonlinear disposal of the quantized input, the relationship between the control input and the quantized input is established. The hysteretic quantizer that we take can effectively avoid the chattering phenomena. Furthermore, the introduction of a linear observer makes the estimation of the states possible. Based on the universal approximation ability of the fuzzy logic systems (FLSs) and backstepping recursive design with the common stochastic Lyapunov function approach, a quantized output feedback control scheme is constructed, where the dynamic surface control (DSC) is explored to alleviate the computation burden. The proposed control scheme cannot only guarantee the boundedness of signals but also make the output of the system converge to a small neighborhood of the origin. The simulation results are exhibited to demonstrate the validity of the control scheme.

Observer-based dissipative output feedback control for network T–S fuzzy systems under time delays with mismatch premise

This paper deals with the problem of non-parallel distribution compensation networked control systems (NCSs) under event-triggered strategy based on the fuzzy system for a class of nonlinear systems with time-varying delays and mismatching premise membership functions. The T–S fuzzy model under event-triggered strategy is provided in unified framework, in which (1) a delay fuzzy observer-based with the mismatch premise is employed to approximate the immeasurable states of the existing system; (2) a delay fuzzy observer-based controller is constructed, by considering the same premises as in observer; and (3) event-triggered strategy is considered to mitigate the effect of communication burden. Another derivation of this paper is to introduce the notation of extended dissipativity which provides the $$H_{\infty }$$ , $$L_{2}-L_{\infty }$$ and dissipative performances. Furthermore, in this regard, by taking into account a novel fuzzy Lyapunov–Krasovskii functional in conjunction with free weighting matrices, containing mode-dependent integral terms such that the resulting system is stable with the desired performance. Then, desired observer-based controller is presented in the account of LMI. Finally, we validate our results with a truck–trailer example.

Input-to-State Stabilization of Uncertain Parabolic PDEs Using an Observer-Based Fuzzy Control

This paper presents an observer-based fuzzy controller for one-dimensional parabolic partial differential equations with distributed bounded disturbance using discrete point measurements. Sufficient conditions are derived to guarantee the input-to-state stability of the closed-loop system in terms of linear matrix inequalities. A numerical simulation example is given to demonstrate the efficiency of the results.

Fuzzy observer-based fault tolerant control against sensor faults for proton exchange membrane fuel cells

In this paper, robust fault diagnosis problem of Proton Exchange Membrane Fuel Cells (PEMFC) is presented based on Takagi-Sugeno (TS) Fuzzy Unknown Input Observer (FUIO). TS FUIO based on Linear Matrix Equalities (LMEs) and the Linear Matrix Inequalities (LMIs) are design. Firstly, the nonlinear PEMFC system with sensor faults and disturbance is represented by TS fuzzy model. Then, a FUIO and sensor fault estimation algorithm is developed and then a model based Fuzzy Fault Tolerant Controller design uses the concept of Parallel Distributed Compensation (PDC). Sufficient stability conditions are studied based on LMIs and LMEs. In order to verify the proposed approach, a PEMFC system with return manifold pressure and hydrogen mass sensors fault and disturbance was tested to illustrate the effectiveness of the proposed strategy.

Observer-Based Fuzzy Control for Memristive Circuit Systems

This paper proposes an observer-based fuzzy control scheme for a class of memristive chaotic circuit systems. First, the Takagi-Sugeno fuzzy model is adopted to reconstruct the nonlinear chaotic circuit system. Next, based on the proposed fuzzy model, an observer-based fuzzy controller is developed to estimate the states and stabilize the origin. Third, the results are extended to explore the L∞-gain observer-based fuzzy control for the chaotic system with disturbances. Finally, simulation results are also addressed to show the effectiveness of the proposed control scheme.

Fuzzy observer-based sampled-data control for a class of pure-feedback nonlinear systems

This paper aims at the sampled-data control problem for a class of pure-feedback nonlinear systems. A fuzzy state observer is constructed to evaluate the unavailable states. In this process, fuzzy logic systems are applied to approximate the uncertain nonlinear functions. Based on the new designed state observer, a sampled-data control scheme for the pure-feedback nonlinear systems is proposed. The designed sampled-data controller ensures the boundedness of the nonlinear systems. Finally, two numerical examples are used to demonstrate that the proposed method is efficient.

Observer-based fuzzy adaptive optimal stabilization control for completely unknown nonlinear interconnected systems

Abstract Fuzzy adaptive optimal bounded control problems are first investigated for a class of nonlinear continuous-time interconnected systems whose system internal dynamics and unmatched interconnections are completely unknown, when there exist unavailable states in the subsystems of the interconnected systems. The system states and the interconnection terms of the interconnected system are approximated by using a fuzzy state observer. The decentralized optimal controllers and observer-critic structure are designed according to adaptive dynamic programming and enforcement learning technology. The presented control methods can ensure that the system states and parameter estimation errors of the interconnected systems are ultimately uniformly bounded. A simulation example validates the effectiveness of the presented scheme.

A Novel Actuator Fault-tolerant Control Strategy of DFIG-based Wind Turbines Using Takagi-Sugeno Multiple Models

In this paper, a new combined fuzzy observer-based fault-tolerant tracking control scheme is proposed for a doubly fed induction generator (DFIG) based wind turbine (WT) subject to actuator faults. The main contribution consists of the proposal of a novel fault-tolerant fuzzy tracking controller combined with a nominal control law. The control objective is to ensure good state references tracking regardless of the actuator faults effects and simultaneous system state and faults estimation. This later requires the knowledge of the occurrence of actuator faults which are estimated from a Takagi-Sugeno Fuzzy Proportional Integral Observer (T-S FPIO). Within this control scheme, a T-S FPIO has been developed to provide stability tracking error dynamics even the system is subjected to different actuator faults. A compensation term is appended to the composite controller and to ensure robustness against actuator faults. Stability and tracking analysis properties are demonstrated through a quadratic Lyapunov function, which are formulated in terms of Linear Matrix Inequalities (LMIs). The observer gains are determined based on the proposed LMIs stability conditions. A numerical simulation is carried out on a typical 1.5 MW DFIG based WT system to access the effectiveness of the proposed control scheme in comparison to the existing results.

Functional observer-based fuzzy controller design for continuous nonlinear systems

ABSTRACTThis paper presents a novel method of synthesising controllers for nonlinear systems represented by Takagi--Sugeno fuzzy model using functional observer. The proposed method uses minimum order observer for estimating the control input of each rule as a function of states. Existence conditions of the functional observer-based controller are provided in the form of rank equality conditions. The stability conditions of the observer are obtained using quadratic Lyapunov function, and the conditions are presented in the form of linear matrix inequalities. Observer parameters can be obtained by solving these inequalities. Finally, systematic synthesis procedures for constructing the observer are presented. Examples with simulation output are given to demonstrate this method and to compare its performance with a conventional full-state observer-based controller.

Fuzzy observer-based control for maximum power-point tracking of a photovoltaic system

ABSTRACTThis paper presents a novel fuzzy control design method for maximum power-point tracking (MPPT) via a Takagi and Sugeno (TS) fuzzy model-based approach. A knowledge-dynamic model of the PV system is first developed leading to a TS representation by a simple convex polytopic transformation. Then, based on this exact fuzzy representation, a H∞ observer-based fuzzy controller is proposed to achieve MPPT even when we consider varying climatic conditions. A specified TS reference model is designed to generate the optimum trajectory which must be tracked to ensure maximum power operation. The controller and observer gains are obtained in a one-step procedure by solving a set of linear matrix inequalities (LMIs). The proposed method has been compared with some classical MPPT techniques taking into account convergence speed and tracking accuracy. Finally, various simulation and experimental tests have been carried out to illustrate the effectiveness of the proposed TS fuzzy MPPT strategy.

A Novel Fuzzy Observer-Based Steering Control Approach for Path Tracking in Autonomous Vehicles

In this paper, the problem of steering control is investigated for vehicle path tracking in the presence of parametric uncertainties and nonlinearities. In practice, the vehicle mass varies due to the number of passengers or amount of payload, while the vehicle velocity also changes during normal cruising, which significantly influences vehicle dynamics. Moreover, the vehicle dynamics are strongly nonlinear caused by the tire/road forces under different road surface conditions. With fuzzy modeling method, the original nonlinear path tracking system with parameter variations is first formulated as a T–S fuzzy model with additive norm-bounded uncertainties, and then an approach to the fuzzy observer-based output feedback steering control for vehicle dynamics is proposed under a fuzzy Lyapunov function framework. By employing matrix inequality convexifying techniques, a sufficient condition is developed in the form of linear matrix inequalities such that the closed-loop path tracking error system is asymptotically stable with a guaranteed $\mathcal {H}_{\infty }$ level. Finally, the effectiveness of the proposed fuzzy observer-based output feedback controller is demonstrated in Carsim/Matlab joint simulation environment, via which the advantage of a T–S fuzzy observer-based output controller over the closed-loop driver model embedded in Carsim is also shown with parametric uncertainties and nonlinearities.