Fuzzy Static Output Feedback Research Articles

Static Output Feedback Control for Positive Takagi–Sugeno Fuzzy Systems: A Successive Linear Programming Approach

This article considers the control synthesis for positive nonlinear systems modeled by Takagi–Sugeno (T–S) fuzzy characterizations. A fuzzy static output feedback (SOF) controller is sought to assure the closed-loop stability and positivity with a guaranteed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal{l}_{1}$</tex-math> </inline-formula> performance level. The favorable positivity enables us to adopt a linear co-positive function as the Lyapunov candidate, and we construct the essential conditions for the existence of fuzzy SOF controllers in the form of bilinear programming (BP) problem. To provide a direct and generic algorithm for solving the BP problem, we propose a vital approximation strategy by which the general bilinear constraints are replaced with a sequence of convex surrogate ones. Recognizing the fact that a fundamental promise of the proposed successive linear programming algorithm is a feasible initial solution, we also develop an iterative procedure to calculate an initial controller gain. Finally, we clarify the applicability of the developed scheme with two examples.

Reliable fuzzy control of uncertain nonlinear networked systems under actuator faults

This study investigates a reliable fuzzy static-output feedback control (SOFC) scheme for uncertain Takagi–Sugeno fuzzy model (TSFM)-based nonlinear systems under the networked induced delays, information package losses and actuator faults, simultaneously. For this purpose, firstly, a comprehensive model for the actuator fault is suggested to enhance the performance of the actuator in the networked control systems (NCSs). More precisely, the suggested model contains an additive stochastic perturbation term in the actuator to further realize the control scheme. Besides, the Markov chain (MC) is employed to model the networked induced arbitrary delays and the information package losses. Hence, the corresponding closed-loop system lies in the Markovian jump systems (MJS). Then, based on the Lyapunov theory, the stochastic robust stability of the obtained system is studied and necessary conditions are extracted in new offline linear matrix inequalities (LMIs). Since the accurate value of the transition probabilities (TP) of the MC is not definite and even the identification is difficult, in view of practical applications in our control strategy, partly unknown TPs are assumed. Finally, to validate the superiorities of the suggested control approach, a truck-trailer system is adopted and simulated. The simulation results confirm the superiorities of the suggested control approach.

Quantized-Output-Based Exponential Stabilization of Fuzzy DPSs With Time-Varying Delay and Nonlinearities

The exponential stabilization of nonlinear distributed parameter systems (DPSs) with time-varying delay is studied in this paper. With the employment of the Takagi-Sugeno (T-S) fuzzy model, the nonlinear DPSs are described as a fuzzy parabolic partial differential equation (PDE). Then, with the consideration of the measurement output and control input information quantized by a kind of dynamic quantizers, fuzzy static and dynamic output feedback controllers are proposed. The time-delayed feedback controllers are also provided in the forms of static and dynamic. On the basis of the derived T-S fuzzy PDE model, Lyapunov-based control design strategies are proposed with respect to the effect of quantization. Moreover, by constructing appropriate Lyapunov functionals, sufficient conditions for designing the output feedback control gains and the quantizers' adjusting parameters which guarantee the exponential stability of the fuzzy closed-loop system are provided in terms of standard linear matrix inequalities (LMIs). Finally, we explore the output feedback controllers into the FitzHugh-Nagumo (FHN) equation and Fisher equation as applications. The efficiency of the design strategies is indicated through the simulation results.

𝑯∞ reliable fuzzy control for vehicle dynamics stability

This article introduces a reliable control scheme for a four-wheel vehicle. This scheme assumes that actuators fail and external disturbances occur to the system. In contrast to existing results, this study assumes the actuator fault model includes linear and nonlinear terms, and an output feedback controller is designed to improve vehicle stability and handling when actuators fail. Using Takagi-Sugeno (T-S) fuzzy models, a reliable fuzzy static output feedback (SOF) controller is designed to address the nonlinear aspect of the system. Based on the non-quadratic Lyapunov function with auxiliary matrices, less conservative sufficient conditions are established such that the closed-loop system is stable with a γ level of H_∞ performance against external disturbances. Furthermore, using an appropriate model transformation, a set of linear matrix inequalities (LMIs) is formulated to synthesize the controller gains. The proposed scheme is then tested using numerical experiments to demonstrate potential applications and validate its effectiveness.

New Relaxed Static Output Feedback Stabilization of T–S Fuzzy Systems with Time-Varying Delays

This paper investigates the imperfect premise matching-based (IPMB) static output feedback (SOF) controller for T–S fuzzy systems with time-varying delays. Firstly, by employing integral inequality techniques, the membership-function-independent fuzzy SOF design methods in terms of LMIs are presented based on imperfect premise matching (IPM) strategy. The obtained stabilization conditions do not contain equality constraints, and the output matrices do not have rank constraints. Secondly, some suitable relaxation variables are employed, and more relaxed membership-function-dependent (MFD) stabilization conditions are obtained by considering the local boundary information of membership functions (MFs). Finally, two simulation examples are given to show the progressiveness of the proposed methods in this paper.

Robust Set-Invariance Based Fuzzy Output Tracking Control for Vehicle Autonomous Driving Under Uncertain Lateral Forces and Steering Constraints

This paper is concerned with a new control method for path tracking of autonomous ground vehicles. We exploit the fuzzy model-based control framework to deal with the time-varying feature of the vehicle speed and the highly uncertain behaviors of the tire-road forces involved in the nonlinear vehicle dynamics. To avoid using costly vehicle sensors for feedback control while favoring the simplest control structure for real-time implementation, a new fuzzy static output feedback (SOF) scheme is proposed. In particular, though the robust set-invariance property and Lyapunov-based arguments, the physical constraints on the steering input saturation and the vehicle state can be taken into account in the control design to improve the driving safety and comfort. The theoretical development relies on the use of fuzzy Lyapunov functions and the non-parallel distributed compensation control concept to reduce the design conservatism. Exploiting some specific convexification techniques, the control design is reformulated as an optimization problem under linear matrix inequalities with a single line search, which are efficiently solved via semidefinite programming techniques. The proposed fuzzy path tracking controller is evaluated through various dynamic driving tests conducted with high-fidelity CarSim/Matlab co-simulations. Moreover, to emphasize the advantages of the new fuzzy SOF controller, a performance comparison with the CarSim driver model is also performed.

Constrained Output-Feedback Control for Discrete-Time Fuzzy Systems With Local Nonlinear Models Subject to State and Input Constraints.

This article presents a new approach to design static output-feedback (SOF) controllers for constrained Takagi-Sugeno fuzzy systems with nonlinear consequents. The proposed SOF fuzzy control framework is established via the absolute stability theory with appropriate sector-bounded properties of the local state and input nonlinearities. Moreover, both state and input constraints are explicitly taken into account in the control design using set-invariance arguments. Especially, we include the local sector-bounded nonlinearities of the fuzzy systems in the construction of both the nonlinear controller and the nonquadratic Lyapunov function. Within the considered local control context, the new class of nonquadratic Lyapunov functions provides an effective solution to estimate the closed-loop domain of attraction, which can be nonconvex and even disconnected. The convexification procedure is performed using specific congruence transformations in accordance with the special structures of the proposed SOF controllers and nonquadratic Lyapunov functions. Consequently, the fuzzy SOF control design can be reformulated as an optimization problem under strict linear matrix inequality constraints with a linear search parameter. Compared to existing fuzzy SOF control schemes, the new structures of the control law and the Lyapunov function are more general and offer additional degrees of freedom for the control design. Both theoretical arguments and numerical illustrations are provided to demonstrate the effectiveness of the proposed approach in reducing the design conservatism.

Design of Static Output Feedback Controller for Fractional-Order T-S Fuzzy System

This paper studies the design of fuzzy static output feedback controllers for two kinds of fractional-order T-S fuzzy systems. The fractional order α satisfies 0&lt;α&lt;1 and 1≤α&lt;2. Based on the fractional order theory, matrix decomposition technique, and projection theorem, four new sufficient conditions for the asymptotic stability of the system and the corresponding controller design methods are given. All the results can be expressed by linear matrix inequalities, and the relationship between fuzzy subsystems is also considered. These have great advantages in solving the results and reducing the conservatism. Finally, a simulation example is given to show the effectiveness of the proposed method.

Fuzzy Static Output Feedback Control for Path Following of Autonomous Vehicles With Transient Performance Improvements

This paper provides a new solution for path following control of autonomous ground vehicles. $\mathcal {H}_{2}$ control problem is considered to attenuate the effect of the road curvature disturbance. To this end, we formulate a standard model from the road-vehicle dynamics, the a priori knowledge on the road curvature, and the path following specifications. This standard model is then represented in a Takagi–Sugeno fuzzy form to deal with the time-varying nature of the vehicle speed. Based on a static output feedback scheme, the proposed method allows avoiding expensive vehicle sensors while keeping the simplest control structure for real-time implementation. The concept of $\mathcal {D}-$ stability is exploited using Lyapunov stability arguments to improve the transient behaviors of the closed-loop vehicle system. In particular, the physical upper and lower bounds of the vehicle acceleration are explicitly considered in the design procedure via a parameter-dependent Lyapunov function to reduce drastically the design conservatism. The proposed $\mathcal {H}_{2}$ design conditions are expressed in terms of linear matrix inequalities (LMIs) with a single line search parameter. The effectiveness of the new path following control method is clearly demonstrated with both theoretical illustrations and hardware experiments under real-world driving situations.

Fuzzy finite-frequency output feedback control for nonlinear active suspension systems with time delay and output constraints

• The T-S fuzzy method is used to approximate the nonlinear uncertain dynamics. • A finite frequency control criterion is formulated based on the Lyapunov theory. • A parallel-distributed compensation strategy is used in the fuzzy SOF controller. This paper investigates the problem of fuzzy finite-frequency output feedback control for nonlinear active suspension systems with time delay and output constraints. Firstly, as the physical suspension systems always exist the phenomenon of sprung and un-sprung mass variation and time delay, the Takagi-Sugeno (T-S) fuzzy model is adopted to represent the nonlinear uncertain active suspension system with uncertainties and time delay. Secondly, since the human body is much more sensitive to vertical vibrations between 4 and 8 Hz, a finite-frequency control criterion is formulated for the controller deign with consideration of time delay and output constraints. Other mechanical constraints such as suspension travel, tire dynamic deflection and actuator saturation are also considered. Thirdly, on a practical point of view, not all the states are online measurable. Hence, a novel fuzzy static output feedback (SOF) controller is proposed by applying the parallel-distributed compensation (PDC) scheme. The sufficient conditions for deriving the fuzzy SOF controller are obtained in terms of linear matrix inequalities (LMIs). Finally, numerical simulations on a quarter-car suspension model are conducted to validate the effectiveness and applicability of the proposed fuzzy SOF controller.

Fuzzy Static Output Feedback Control for Discrete-time Nonlinear Time-varying Delay Systems in a Network Environment

This paper studies the problem of fuzzy output control of discrete-time nonlinear systems with immeasurable state variables, time-varying delay, and data packet dropout. A T–S fuzzy model is used to represent the original nonlinear systems with time-varying delay, and the Bernoulli distribution is employed to describe the dropout process of the random packet. The two uncertainties of time delay and data packet dropout are considered in the system design. By constructing a fuzzy Lyapunov–Krasovskii functional and introducing a summation inequality based on Cauchy–Schwartz form, the existence condition of fuzzy static output feedback controller is established by using linear matrix inequalities (LMIs). The simulation example verifies the effectiveness of the proposed method.

Polynomial static output feedback H∞ control via homogeneous Lyapunov functions

SummaryIn this paper, we study a polynomial static output feedback (SOF) stabilization problem with H∞ performance via a homogeneous polynomial Lyapunov function (HPLF). It is shown that the quadratic stability ascertaining the existence of a single constant Lyapunov function becomes a special case. With the HPLF, the proposal is based on a relaxed two‐step sum of square (SOS) construction where a stabilizing polynomial state feedback gain K(x) is returned at the first stage and then the obtained K(x) gain is fed back to the second stage, achieving the SOF closed‐loop stabilization of the underlying polynomial fuzzy control systems. The SOS equations obtained thus effectively serve as a sufficient condition for synthesizing the SOF controllers that guarantee polynomial fuzzy systems stabilization. To demonstrate the effectiveness of the proposed polynomial fuzzy SOF H∞ control, benchmark examples are provided for the new approach.

Output feedback stabilization of two-dimensional fuzzy systems

This paper is concerned with the output feedback stabilization of two-dimensional discrete fuzzy systems described by the Fornasini–Marchesini second model. Based on the fuzzy-basis-dependent Lyapunov function, a new criterion is proposed for the fuzzy static output feedback (SOF) controller, which is expressed as strict linear matrix inequalities and hence numerically tractable. The main advantage of the developed SOF control scheme is that no constraints are imposed on system matrices, which is expected to have a wider range of applications. The applicability and the advantage of the proposed results are shown through two numerical examples.

Networked fuzzy output feedback control for discrete-time Takagi–Sugeno fuzzy systems with sensor saturation and measurement noise

This paper deals with the problem of networked fuzzy static output feedback control for discrete-time Takagi–Sugeno fuzzy systems with sensor saturation and measurement noise. First, by taking network-induced delays and packet dropouts into account, the resulting closed-loop fuzzy system is modeled as an asynchronous discrete-time T–S fuzzy system subject to both interval-like delays and sector nonlinearity. Second, an augmented fuzzy-basis-dependent Lyapunov functional is introduced. By employing a matrix-based quadratic convex method, an interval-delay-dependent bounded real lemma is derived such that the closed-loop system has a prescribed H∞ performance level. Third, a fuzzy controller design method is presented by using a cone complementarity linearization algorithm. Finally, a nonlinear inverted pendulum system via networked fuzzy control is provided to show that the proposed results are of less conservatism and exhibit satisfactory adaptability to sensor saturation.

Nonfragile Fuzzy Output Feedback Synchronization of a New Chaotic System: Design and Implementation

A new three-dimensional (3D) chaotic system is proposed with four nonlinear terms which include two quadratic terms. To analyze the dynamical properties of the new system, mathematical tools such as Lyapunov exponents (LEs), Kaplan–York dimensions, observability constants, and bifurcation diagram have been exploited. The results of these calculations verify the specific features of the new system and further determine the effect of different system parameters on its dynamics. The proposed system has been experimentally implemented as an analog circuit which practically confirms its predicted chaotic behavior. Moreover, the problem of master–slave synchronization of the proposed chaotic system is considered. To solve this problem, we propose a new method for designing a nonfragile Takagi–Sugeno (T–S) fuzzy static output feedback synchronizing controller for a general chaotic T–S system and applied the method to the proposed system. Some practical advantages are achieved employing the new nonlinear controller as well as using system output data instead of the full-state data and considering gain variations because of the uncertainty in values of practical components used in implementation the controller. Then, the designed controller has been realized using analog devices to synchronize two circuits with the proposed chaotic dynamics. Experimental results show that the proposed nonfragile controller successfully synchronizes the chaotic circuits even with inexact analog devices.

DR-Admissibility With Static Output Feedback For Uncertain Descriptor Fuzzy System

In this paper, the issue of DR-admissibility analysis and synthesis for a class of uncertain continuous fuzzy descriptor systems is investigated. The descriptor Takagi-sugeno T-S fuzzy model with parameter uncertainties is adopted for admissibility analysis and control design. Using linear matrix inequality approach and introducing some free matrices, sufficient criterion is established to guarantee the admissibility and DR-stability of the considered class of nonlinear systems. From this new characterization, fuzzy static output feedback controller is designed not only to ensure the admissibility of the closed loop descriptor systems but also the transient performances in a specified LMI region. An example is introduced to illustrate the effectiveness of the proposed condition.

Fuzzy Static Output Feedback H∞ Control for Nonlinear Systems Subject to Parameter Uncertainties

This study is concerned with the stabilization issue of nonlinear systems subject to parameter uncertainties. An interval type-2 T-S fuzzy model is used to represent the nonlinear systems subject to parameter uncertainties. An interval type-2 fuzzy static output feedback controller is designed to synthesize the interval type-2 T-S fuzzy systems. The membership-function-dependent stability conditions are derived by utilizing the information of upper and lower membership functions. The proposed stability conditions are presented in the form of linear matrix inequalities (LMIs). LMI-based stability conditions for interval type-2 fuzzy static output feedback H∞ control synthesis are also developed. Several simulation examples are given to show the superiority of the proposed approach.

A design method for T–S fuzzy systems with partly immeasurable premise variables subject to actuator saturation

This study is concerned with the problem of control synthesis of T–S fuzzy systems with partly immeasurable premise variables subject to actuator saturation and external disturbances. By using measurable premise variables of fuzzy models as the premise variables of fuzzy controllers, a new fuzzy static output feedback control scheme is proposed. Different from the existing ones, the measurable premise variables can directly be used in the fuzzy controllers, which is helpful for the larger domain of attraction. A numerical example is given to illustrate the effectiveness of the proposed method.

Non-fragile static output feedback control for singular T–S fuzzy delay-dependent systems subject to Markovian jump and actuator saturation

In this paper, we consider the problem of non-fragile static output feedback control for singular T–S fuzzy delay-dependent systems subject to Markovian jump and actuator saturation. Sufficient conditions are presented to guarantee the resulted closed-loop system to be stochastically admissible and dissipative. Then, the non-fragile fuzzy static output feedback controller can be obtained by solving the LMIs. And the estimation of the largest domain of attraction for the system is formulated and solved as an optimization problem. Finally, some numerical examples are provided to show the effectiveness of the proposed approaches.

Fuzzy PID control synthesis for Takagi–Sugeno fuzzy systems

This study proposes a kind of H ∞ fuzzy proportional–integral–derivative (PID) control synthesis method for Takagi–Sugeno (T–S) fuzzy systems. The basic idea of the presented method is to transform the fuzzy PID controller design problem into that of the fuzzy static output feedback (SOF) controller design. On the basis of an iterative linear matrix inequality algorithm, the fuzzy SOF control laws can be obtained. After that, the fuzzy PID controller is recovered from the fuzzy SOF controller. Simulation examples are given to show the effectiveness of the proposed method.