Fuzzy Output Feedback Control Research Articles

Observer-Based Adaptive Fuzzy Control for Intelligent Ship Autopilot with Input Saturation

In this paper, the design problem of intelligent ship autopilot with unmeasured yaw rate and input saturation is investigated based on adaptive fuzzy control. First, an adaptive fuzzy output feedback controller is proposed, then, to improve the convergence speed of the tracking error in the sense of finite time, a finite-time adaptive fuzzy output feedback controller is also designed to improve the control performance. By employing fuzzy logic system (FLS) to estimate the unknown nonlinear function, an adaptive fuzzy state observer is designed to estimate the unmeasured state. An adaptation auxiliary signal for input saturation is also established to compensate the mismatch between the controller signal and the actuator signal. Combining state observer model with backstepping method, two different adaptive fuzzy output-feedback controllers with composite parameter adaptive laws are constructed, respectively. Based on Lyapunov theory, it is proved that all signals in the closed-loop systems are bounded. Finally, the simulation results are conducted to demonstrate the effectiveness of the proposed schemes.

Robust H∞ Takagi–Sugeno fuzzy output-feedback control for differential speed steering vehicles

This paper studied the modelling and control of four-wheel independently driven electric vehicles using differential speed steering. The Takagi–Sugeno fuzzy modelling approach represents the nonlinearities of the four-wheel independently driven electric vehicle state variables in several system models. The proposed controller design is a robust Takagi–Sugeno fuzzy output-feedback control based on a fuzzy Lyapunov function approach. More precisely, the Lyapunov function is chosen to be dependent on the membership functions. Sufficient conditions for the existence of the robust Takagi–Sugeno fuzzy controller are given in terms of linear matrix inequality constraints. The designed parameters are tested by simulating the four-wheel independently driven electric vehicles under varying operating conditions. The simulation results underscore the robustness and disturbance rejection importance of the proposed controller, which is then contrasted to better highlight the improved performance of the proposed approach over a fixed robust controller design.

Improved Adaptive Fuzzy Output-Feedback Dynamic Surface Control of Nonlinear Systems With Unknown Dead-Zone Output

This article presents an adaptive fuzzy output-feedback dynamic surface control (DSC) for the nonlinear systems with dead-zone output nonlinearity. First, a novel smooth approximation of the output dead zone is given to conveniently fuse with the backstepping technique. After that a nonlinear fuzzy state observer is constructed to estimate the unmeasurable states, by employing the fuzzy logic systems for identifying the unknown compounded nonlinear functions, which releases the limitation in the existing references that the state observer needs to be linear in the presence of dead-zone output nonlinearity. Then, to reduce the effect of unknown dead-zone coefficients, an adaptive compensation mechanism is introduced by using the characteristic of hyperbolic tangent function, which can replace the widely used Nussbaum-type function-based control strategy. Furthermore, a novel DSC method based on the nonlinear filters is proposed, which not only avoids the issue of explosion of complexity inherent in the backstepping procedure, but also improves the system control performance. Under the certain assumptions, the stability of the closed-loop system is proved by use of Lyapunov function stability theory. Finally, the applicability of the proposed control method is rigorously verified by a single-link robot arm simulation example.

Nonsingular Finite-Time Event-Triggered Fuzzy Control for Large-Scale Nonlinear Systems

This article investigates the problem of event-based decentralized adaptive fuzzy output-feedback finite-time control for the large-scale nonlinear systems. The full-state tracking error constraints, unmeasured states, and external disturbances are simultaneously considered in the controlled systems. The unknown auxiliary functions are modeled by using fuzzy logic systems, and a state observer is established to estimate unmeasured states. By taking a new error transformation method based on prescribed performance functions and constructing corresponding barrier Lyapunov functions, the predefined system error dynamic performance is ensured. Then, on the basis of the event-triggered control technique and the backstepping recursive design technique, a new event-based adaptive fuzzy nonsingular finite-time control strategy is proposed, and the “singularity” problem existing in backstepping design procedure is avoided. Moreover, by using the finite-time stability criterion, it is proven that the proposed control strategy can ensure the boundedness of the whole system variables and achieve all the state tracking errors evolve within the predesigned performance regions in finite time. Finally, the effectiveness of the proposed control strategy is verified by using some simulation results.

Adaptive fuzzy output feedback inverse optimal control for vehicle active suspension systems

In this paper, the adaptive fuzzy inverse optimal output feedback control problem for vehicular active suspension systems (ASSs) is addressed. The considered vehicular active suspension system (ASS) is a quarter-car model with electromagnetic actuators and contains unknown nonlinear characteristics. The fuzzy logic systems (FLSs) are used to approximate unknown nonlinearities, and an auxiliary system model is constructed. Based on auxiliary system model, a fuzzy state observer is designed to estimate immeasurable states. By using adaptive backstepping design technique and inverse optimal principle, an adaptive fuzzy output feedback inverse optimal strategy is proposed. The developed adaptive fuzzy inverse optimal output feedback control method not only guarantees that the attitude of the vehicle is stabilized, but also achieves inverse optimization in relation to the cost functional. Finally, the simulation studies are given in the cases of both bump road and sinusoid road displacement input, and the simulation results show the validity of the proposed control method.

Output Feedback and Stability Analysis of Positive Polynomial Fuzzy Systems

This article investigates the polynomial fuzzy output feedback (PFOF) control synthesis problem for positive polynomial fuzzy systems. When the states of a positive system cannot be fully obtained, the output feedback control strategy is a good method to stabilize the control system. From fuzzy control point of view, we employ the polynomial fuzzy model rather than the Takagi–Sugeno fuzzy model, and this kind of models can express a wider range of nonlinear positive systems. However, the polynomials in the system matrices and the feedback control gain matrices will make the nonconvex stability conditions more difficult to deal with. Thereby, in order to crack the hard nut, a nonzero transformation vector is introduced in this article to deal with the nonconvex problem skillfully. Furthermore, the imperfect premise matching technique is taken into account so that the implement of the controller is more simple and money-saving. In addition, the augmented dynamic of the positive polynomial fuzzy-model-based (PPFMB) control system is investigated to facilitate the stability and positivity analysis, and the basic conditions in the light of sum of squares (SOSs) are derived. Besides, the advanced membership function dependent (MFD) technique is used so that a great of useful information of MFs is extracted to improve the relaxation of the results. Finally, the effectiveness of the theoretical findings is illustrated by a simulation example.

Observer-Based Adaptive Fuzzy Tracking Control for Strict-Feedback Nonlinear Systems With Unknown Control Gain Functions.

This article investigates the adaptive fuzzy output-feedback backstepping control design problem for uncertain strict-feedback nonlinear systems in the presence of unknown virtual and actual control gain functions and unmeasurable states. A fuzzy state observer is designed via fuzzy-logic systems, thus the unmeasurable states are estimated based on the designed fuzzy state observer. By constructing the logarithm Lyapunov functions and incorporating the property of the fuzzy basis functions and bounded control design technique into the adaptive backstepping recursive design, a novel observer-based adaptive fuzzy output-feedback control method is developed. The proposed fuzzy adaptive output-feedback backstepping control scheme can remove the restrictive assumptions in the previous literature that the virtual control gains and actual control gain functions must be constants. Furthermore, it can make the control system be semiglobally uniformly ultimately boundedness (SGUUB) and keep the observer and tracking errors to remain in a small neighborhood of the origin. The numerical simulation example is presented to validate the effectiveness of the proposed control scheme and theory.

H-infinity stability analysis and output feedback control for fuzzy stochastic networked control systems with time-varying communication delays and multipath packet dropouts

The H-infinity stability analysis and delay-dependent Takagi–Sugeno (T–S) fuzzy dynamic output feedback control are proposed for the T–S fuzzy discrete networked control systems with time-varying communication delay and multipath packet dropouts. T–S fuzzy model is employed to approximate the discrete networked control system with time-varying state delay and external disturbance. Stochastic system theory and Bernoulli probability distribution are employed to describe the time-varying communication delay and multipath packet dropouts. Delay-dependent T–S fuzzy dynamic output feedback controller is designed. The delay-dependent T–S fuzzy dynamic output feedback controller is employed to relax the design conditions and enhance the design flexibility. The delay-dependent Lyapunov–Krasovskii functional, stochastic system theory and Bernoulli probability distribution are introduced to guarantee the stochastic mean-square stability and prescribed H-infinity performance. Some slack matrices are introduced to reduce the computation complexity. Finally, simulation examples are presented to show the effectiveness and advantages of the proposed methods.

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.

Robust H∞ dynamic output feedback control for interval type-2 T-S fuzzy multiple time-varying delays systems with external disturbance

This research focuses on the H∞ stability analysis and fuzzy dynamic output feedback control for a class of interval type-2 T-S fuzzy systems. Interval type-2 T-S fuzzy model is employed to approximate the uncertain system with multiple time-varying delays and external disturbance. Interval type-2 T-S fuzzy dynamic output feedback controller is designed by employing the interval type-2 T-S fuzzy model. Some stability criterions in terms of linear matrix inequalities (LMIs) are presented by introducing the fuzzy Lyapunov function. The closed-loop system is described as a descriptor system by employing the descriptor redundancy approach. Some less conservative stability criterions un-including the product terms between system gains and controller gains are presented and the fuzzy-basis-dependent matrix with system gains transformation is introduced. The stability criterions are extended to a finite set of LMIs constraints. Finally, simulation examples and comparison figures are presented to show the effectiveness of the proposed approach.

Event-Triggered Adaptive Fuzzy Output-Feedback Control for Nonstrict-Feedback Nonlinear Systems With Asymmetric Output Constraint.

This article addresses the event-triggered adaptive fuzzy output-feedback control problem for a class of nonstrict-feedback nonlinear systems with asymmetric and time-varying output constraints, as well as unknown nonlinear functions. By designing a linear observer to estimate the unmeasurable states, a novel event-triggered adaptive fuzzy output-feedback control scheme is proposed. The barrier Lyapunov function (BLF) and the error transformation technique are used to handle the output constraint under a completely unknown initial tracking condition. It is shown that with the proposed control scheme, all the solutions of the closed-loop system are semiglobally bounded, and the tracking error converges to a small set near zero, while the output constraint is satisfied within a predetermined finite time, even when the constraint condition is violated initially. Moreover, with the proposed event-triggering mechanism (ETM), the Zeno behavior can be strictly ruled out. An example is finally provided to demonstrate the effectiveness of the proposed control method.

Adaptive Prescribed Performance Output Regulation of Nonlinear Systems with Nonlinear Exosystems

The paper studies the prescribed performance output regulation problem for a class of nonlinear uncertain strict-feedback systems which are driven by nonlinear exosystems. Fuzzy logic systems (FLSs) are used to approximate the unknown functions. A fuzzy adaptive observer is designed to estimate the system state. A fuzzy internal model is designed to reject disturbance. Simultaneously, a parameter-type Lyapunov function and L function are designed to ensure the prescribed performance of the system. As illustrated by example, the proposed prescribed performance fuzzy adaptive output feedback control scheme is shown to guarantee semi-globally uniformly ultimately bounded, and the dynamic performance and steady-state performance of the tracking error are dependent on the prescribed performance functions.

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.

Adaptive-Event-Trigger-Based Fuzzy Nonlinear Lateral Dynamic Control for Autonomous Electric Vehicles Under Insecure Communication Networks

This article presents a novel adaptive-event-trigger-based fuzzy nonlinear lateral dynamic control algorithm for autonomous electric vehicles under insecure communication networks. The integration of path following control and direct yaw moment control is considered to acquire a better lateral dynamic performance. To effectively tackle inherent nonlinearities of lateral dynamics, the Takagi-Sugeno fuzzy model approach is employed to approximate the nonlinear lateral dynamics. To avoid the infeasibility of state-feedback control due to the immeasurability of sideslip angle, a fuzzy output feedback control strategy is proposed via a useful transformation. To improve resource utilization of the band-limited communication networks, an adaptive event-triggered communication mechanism is proposed to save communication resource. Moreover, to enhance the robustness of the proposed controller, the insecure communication link is considered, which is described by the Bernoulli random distributed process. Finally, simulation results show the proposed adaptive-event-trigger-based fuzzy controller not only can save communication resource, but also achieve the perfect control performance.

Finite-time dynamic output-feedback dissipative control for singular uncertainty T–S fuzzy systems with actuator saturation and output constraints

This paper studies the problem of finite-time dynamic output-feedback control for singular uncertainty T–S time-varying delay fuzzy systems with actuator saturation and output constraints. Through a dynamic parallel distributed compensator, the (U,V,R)−α− dissipative output-feedback fuzzy controller is designed. Furthermore, by employing reciprocally convex approach and a new lemma, the sufficient conditions are obtained to guarantee that the systems are finite-time bounded subject to (U,V,R)−α− dissipative performance level. Then, the desired fuzzy state-feedback controller and dynamic output feedback controller are derived by solving the linear matrix inequalities (LMIs). Finally, the feasibility and effectiveness of the proposed method can be validated by some simulations.

Fuzzy Adaptive Output Feedback Control for MIMO Switched Nontriangular Structure Nonlinear Systems With Unknown Control Directions

This paper investigates an adaptive fuzzy output feedback control design problem for the switched multiple-input and multiple-output (MIMO) nontriangular structure nonlinear systems. The discussed system contains the unknown nonlinear dynamics, the unknown backlash hysteresis, the immeasurable states, and the unknown control directions under a class of switching signals. The fuzzy logic systems are utilized to learn the unknown nonlinear dynamics and construct an MIMO fuzzy switched nonlinear observer. By combining the property of the Nussbaum gain function with the Prandtl-Ishlinskii models, a novel observer-based fuzzy adaptive backstepping schematic design algorithm is presented. Furthermore, the stability of the whole controlled system is proved via Lyapunov stability theory and the average dwell time method. The simulation results are presented to verify the validity of the proposed control scheme.

Adaptive Fuzzy Output-Feedback Control for Nonaffine MIMO Nonlinear Systems With Prescribed Performance

This article proposes an adaptive fuzzy output-feedback control approach for a class of nonaffine multi-input multi-output nonlinear systems with prescribed performance and immeasurable states. For most of the existing fuzzy approximation-based approaches, there are many parameters in the fuzzy systems that need to be estimated online with adaptive laws. To overcome this difficulty, we propose a new fuzzy system; the remarkable advantage of this fuzzy system is that only one parameter needs to be estimated online. The fuzzy system is used to approximate the unknown nonlinear function, and an adaptive fuzzy state observer is developed to estimate the unmeasured states. By utilizing the state observer and the prescribed performance control scheme, an adaptive fuzzy prescribed performance output-feedback control method is developed. The number of the adaptive laws both for the state observer and the controller is reduced to the number of subsystems. It is proved that all the signals in the closed-loop systems are semiglobally uniformly ultimately bounded, and that the prescribed performance error constraints can be achieved. Simulation examples are provided to highlight the effectiveness of the proposed approach.

Finite-time fuzzy output-feedback control for $ p $-norm stochastic nonlinear systems with output constraints

<abstract> <p>This paper investigates the finite-time control problem of $ p $-norm stochastic nonlinear systems subject to output constraint. Combining a tan-type barrier Lyapunov function (BLF) with the adding a power integrator technique, a fuzzy state-feedback controller is constructed. Then, an output-feedback controller design scheme is developed by the constructed state-feedback controller and a reduce-order observer. Finally, both the rigorous analysis and the simulation results demonstrate that the designed output-feedback controller not only guarantees that the output constraint is not violated, but also ensures that the system is semi-global finite-time stable in probability (SGFSP).</p> </abstract>

Stabilization Control with Optimal L1-Gain and L∞-Gain for Positive T-S Fuzzy Systems

In this paper, the problem of stabilization with optimal L1-gain for positive T-S fuzzy systems is investigated with the use of linear Lyapunov function. A T-S fuzzy model for positive nonlinear system is established to study the stabilization control for the positive system. Sufficient condition for stabilization is presented in term of linear programming. The static output-feedback fuzzy controller is constructed to guarantee that the closed-loop system is controlled positive, asymptotically stable and the L1-gains from the exogenous inputs to the regulated output is minimized, respectively. Moreover, the stabilization problem with optimal L∞-gain for positive T-S fuzzy systems is solved. Finally, three examples are presented to show the effectiveness of the theoretical results.

Reduced-Order Observer-Based Adaptive Backstepping Control for Fractional-Order Uncertain Nonlinear Systems

This article presents two adaptive fuzzy output-feedback dynamic surface control schemes for single-input-single-output (SISO) strict-feedback fractional-order uncertain nonlinear systems under the complete smooth nonlinearity and partial piecewise-smooth nonlinearity, respectively. For the former, complete smooth nonlinear functions are approximated by employing fuzzy logic systems, based on which a novel fractional-order reduced-order observer is constructed to estimate the unmeasurable states. For the latter, a new switched approximation and estimate strategy is proposed to deal with the problem of piecewise-smooth nonlinearity. Meanwhile, fuzzy basis function property is utilized to eliminate the assumption requirement that the nonlinear functions must satisfy the Lipschitz condition inherent in the output-feedback control, which is suitable for two cases. Under certain assumptions, the stability of two closed-loop systems are proved via fractional-order Lyapunov function stability criterion. Specifically, the stability proof of the second case is built on the foundation of the common Lyapunov function method. Finally, two diverse Chua's circuit simulation examples are provided to, respectively, validate the effectiveness of the proposed two control strategy.