Adaptive Fuzzy Tracking Control Scheme Research Articles

Adaptive fuzzy control design for nonlinear systems with actuation and state constraints: An approach with no feasibility condition

In this article, an adaptive fuzzy tracking control scheme is developed for a class of pure-feedback uncertain nonlinear systems in the presence of time-varying full-state constraints (TFSCs), actuators’ nonlinearities and external disturbances. Fuzzy logic systems (FLSs) are employed as universal approximators to online estimate unknown nonlinear functions A barrier Lyapunov function (BLF) is used to deal with the state constraint problem. In contrast to numerous adjacent studies, this research diligently tackles the open problem relating to the virtual control laws (VCLs) feasibility in the BLF-based backstepping control design. The resolution to this problem involves formulating VCLs with predefined bounds. The utilization of disturbance observers within a backstepping framework allows for effective compensation of estimation errors arising from the implementation of a predefined bounded VCL. This approach also helps prevent the occurrence of the ”complexity explosion”, making it a practical solution. The control strategy being proposed guarantees that the output tracking error will effectively approach a small region near the origin. Additionally, all signals of the closed-loop system will remain uniformly ultimately bounded (UUB), and there will be adherence to all state-constraints, ensuring no violations occur. Ultimately, an illustrative simulation example is provided to demonstrate the efficacy of the theoretical findings.

Observer-Based Adaptive Fuzzy Control of Nonstrict Feedback Nonlinear Systems With Function Constraints

In this paper, an adaptive fuzzy tracking control scheme based on fuzzy state observer is proposed for a class of uncertain non-strict feedback nonlinear systems with function constraints. In the first place, based on the approximation characteristic of fuzzy logic systems (FLSs), a fuzzy state observer is designed to estimate the immeasurable state variables in the controlled system. Next, under the framework of adaptive backstepping control technology, FLSs are selected not only to approximate unknown nonlinear functions, but also to avoid algebraic loop problem caused by non-strict feedback structure. At the same time, asymmetric Barrier Lyapunov functions (BLFs) are selected to solve the problem that system states are subject to function constraints, which are related to states and time. Then, Lyapunov stability theory is utilized to prove the stability of the controlled system, the realizability of function constraints and the convergence of output tracking errors. Finally, a simulation is given to check the effectiveness of the proposed control scheme.

Disturbance-Observer-Based Adaptive Fuzzy Tracking Control for Unmanned Autonomous Helicopter With Flight Boundary Constraints

In this article, a disturbance-observer-based adaptive fuzzy tracking control scheme is proposed for a medium-scale unmanned helicopter of six degrees of freedom in the presence of system uncertainties, flight boundary constraints, and external disturbances. A flight boundary protection algorithm is proposed to ensure its flight trajectory within the given safety range. A fuzzy logic system is utilized to estimate the system uncertainties and a nonlinear disturbance observer is adopted to handle the unknown compound terms of the external disturbances and the estimation errors resulting from the fuzzy logic system. An inverse optimal control approach is then used to avoid solving the Hamilton–Jacobi–Bellman equation in minimizing a cost function in the attitude loop. It is shown via the Lyapunov method that the desired safe tracking performance of the position loop and attitude loop of the controlled unmanned helicopter can be achieved. Simulations are provided to illustrate the effectiveness of the proposed control scheme.

Adaptive fuzzy control of a quadrotor using disturbance observer

In this paper, an adaptive fuzzy tracking control scheme by combining Lyapunov stability theory and backstepping technique is proposed for a quadrotor unmanned aerial vehicle. First, a fuzzy logic system is used to approximate the unmodeled dynamics of the quadrotor system. Second, command filtering is utilized to compute the derivatives of the virtual control signals to avoid the complex analytic derivation of these derivatives. Third, a nonlinear disturbance observer is applied to compensate for external disturbance and approximation error of the fuzzy logic system. Lyapunov stability analysis shows that the quadrotor system can be stabilized by the proposed controller with high control accuracy. Finally, the experimental results are given to verify the effectiveness of the proposed control strategy.

Reduced-Order Observer-Based Adaptive Fuzzy Tracking Control Scheme of Stochastic Switched Nonlinear Systems

In this article, an adaptive approximation-based output-feedback tracking control scheme is presented for a class of stochastic switched lower-triangular nonlinear systems with input saturation and unmeasurable state variables. First, to overcome the design obstacle caused by the nondifferential saturation nonlinearity, a carefully selected nonlinear function of the control input signal is applied to estimate the saturation function. Then, a reduced-order state observer is designed to model the unmeasured system states, which also means the error system can be established. Furthermore, the fuzzy-logic systems are utilized to approximate the unknown system nonlinearities in the adaptive backstepping-based controller design procedure. It is ensured that all the closed-loop system variables are bounded in probability and the error signal belongs to a compact set in the mean square sense. Finally, the effectiveness and the practicability of the proposed control scheme are shown by two examples.

Adaptive fuzzy tracking of switched nonstrict-feedback nonlinear systems with state constraints based on event-triggered mechanism

This paper is devoted to develop an adaptive fuzzy tracking control scheme for switched nonstrict-feedback nonlinear systems (SNFNS) with state constraints based on event-triggered mechanism. All state variables are ensured to keep the predefined regions by employing barrier Lyapunov function (BLF). The fuzzy logic systems are exploited to cope with the unknown dynamics existing the SNFNS. It proposes to mitigate data transmission and save communication source whereby the event-triggered mechanism. With the aid of Lyapunov stability analysis and the average dwell time (ADT) method, it is shown that all variables of the entire SNFNS are uniformly ultimate bounded (UUB) under switching signals. Finally, simulation studies are discussed to substantiate the validity of theoretical findings.

Fuzzy Robust Constrained Control for Nonlinear Systems With Input Saturation and External Disturbances

This article proposes a high-order disturbance observer (HODO) and dynamic surface control (DSC) technique-based adaptive fuzzy control scheme for nonlinear systems subjected to input saturation and external time-varying disturbances. First, based on a Sigmoid function, the saturation input is tackled by utilizing a well-defined nonlinear smooth function. Furthermore, HODO and fuzzy logic systems are used to estimate the external disturbances and to handle the lumped unknown functions, respectively. Then, by using the backstepping method and DSC technique, a HODO-based adaptive fuzzy tracking control scheme is proposed for nonlinear systems with saturation nonlinearity, uncertainties, and external disturbances. The Lyapunov analysis method is used to prove that all signals in the entire system are semiglobally uniformly ultimately bounded (SGUUB). In addition, the tracking error converges to a compact set with a tunable error bound determined by some design parameters. Finally, a numerical simulation of two-stage chemical reactor shows the effectiveness of the developed tracking control strategy.

Finite-Time Adaptive Fuzzy Tracking Control for a Class of Nonlinear Systems With Full-State Constraints

In this article, a new command filtered backstepping based finite-time adaptive fuzzy tracking control scheme for a class of unknown nonlinear systems with full-state constraints is established. First, the proposed finite-time command filter will filtering the virtual control signal and get the intermediate control signal within finite-time, so the problem of calculating complexity will not occur in the backstepping process. Then, the fraction-power-based error compensate signal is set up, which can eliminate the influence of filtering error on the control performance. Considering that the unknown nonlinearities exist in the system, the fuzzy logic system based adaptive control technique is used to deal with them, and only one parameter needs to be estimated. It is shown that the states will not violate the prescribed constrains, all the signals in the closed-loop system are bounded in finite-time and the tracking error can converge to the desired neighborhood of the origin in finite time under the barrier Lyapunov function and fraction-power-based virtual control signals. Finally, the effectiveness of the control method is shown by the simulations.

Event-Triggered Adaptive Fuzzy Tracking Control for Pure-Feedback Stochastic Nonlinear Systems With Multiple Constraints

This article investigates the event-triggered adaptive tracking control for a class of pure-feedback stochastic nonlinear systems with full state constraints and input saturation. The saturated input is expressed as a smooth nonlinear function with bounded disturbance. The pure-feedback structure is transformed into strict-feedback case via mean value theorem, and a novel event-triggered adaptive fuzzy tracking control scheme with relative threshold is then proposed. The barrier Lyapunov function is introduced to analyze the system stability, and the state constraints are, thus, guaranteed. It is proved that the closed-loop stochastic nonlinear system is semiglobally uniformly ultimately bounded in probability, and the output tracking error converges to a small neighborhood of zero. Finally, the effectiveness of the proposed method is verified via simulation studies.

Adaptive Fuzzy Tracking Control for a Class of Uncertain Switched Nonlinear Systems With Full-State Constraints and Input Saturations.

In this article, an adaptive fuzzy tracking control scheme is developed for a class of uncertain switched nonlinear systems with input saturations and full-state constraints. First to surmount the design difficulty with respect to a saturation nonlinearity controller, a nonlinear smooth function approximating the nondifferential saturation function is introduced to establish a standard switched adaptive tracking control strategy based on the mean-value theorem and the input compensation technique. Then, invoking fuzzy-logic systems (FLSs), a novel analysis method of average dwell time for switched nonlinear systems with full-state constraints is proposed by using an artful logarithmic inequality. Furthermore, the designed adaptive controller can ensure that all the states of uncertain switched nonlinear systems are not to violate the set constraint bounds by employing barrier Lyapunov functions (BLFs), and that the system output tracking error can converge to a desired neighborhood of the origin within a suitable compact set. Finally, the simulation results are given to demonstrate the validity of the presented approach.

Finite-Time Adaptive Fuzzy Tracking Control Design for Parallel Manipulators with Unbounded Uncertainties

In this paper, a finite-time adaptive fuzzy tracking control scheme is proposed for parallel manipulators with unbounded uncertainties. The proposed approach is based on fuzzy logic systems (FLS), nonsingular fast terminal sliding mode control (NFTSMC) and adaptive sliding compensation from nonlinearities in output feedback. FLS are adopted to handle system uncertainties and external disturbances. This learning approach does not require knowledge of parallel manipulator dynamics. The proposed control scheme can possess several advantages over other state-of-the-art approaches such as rapid response, robustness, higher precision, nonsingular, and finite-time converge. Besides, since the proposed approach is a hybrid scheme of NFTSMC and FLS, the proposed controller can have much better tracking control performance. The finite-time convergence and stability of the closed-loop robotic system are ensured by the Lyapunov theory. Finally, from the simulation results, it is clearly evident that the proposed approach can indeed outperform previous existing methods.

Adaptive Output Fuzzy Fault Accommodation for a Class of Uncertain Nonlinear Systems With Multiple Time Delays

This paper is concerned with the problem of robust adaptive output fuzzy tracking control for a class of uncertain nonlinear time-delayed systems with actuator failures, which include loss of effectiveness, outage, and stuck modes. First, a novel disturbance rejection filter is designed to estimate the unmeasured states and the external disturbances. Then, by using fuzzy logic systems to approximate the suitable nonlinear compound functions, the corresponding adaptive fuzzy fault-tolerant controller with the adjustable parameter updated laws is established based on back-stepping method. Furthermore, it is shown that all the closed-loop signals are bounded, and the system output tracking error can converge to a small neighborhood in the presence of parameter uncertainty, mismatched disturbance, multiple time delays, and actuator faults. Finally, simulation results are provided to illustrate the efficiency of the proposed adaptive fuzzy tracking control scheme.

Adaptive Fuzzy Backstepping Tracking Control for Strict-Feedback Systems With Input Delay

This paper investigates the problem of adaptive fuzzy tracking control for nonlinear strict-feedback systems with input delay and output constraint. Input delay is handled based on the information of Pade approximation and output constraint problem is solved by barrier Lypaunov function. Some adaptive parameters of the controller need to be updated online through considering the norm of membership function vector instead of all sub-vectors. A novel adaptive fuzzy tracking control scheme is developed to guarantee all variables of the closed-loop systems are semiglobally uniformly ultimately bounded, and the tracking error can be adjusted around the origin with a small neighborhood. The stability of the closed-loop systems is proved and simulation results are given to demonstrate the effectiveness of the proposed control approach.

Adaptive fuzzy tracking control for a class of pure-feedback nonlinear systems with time-varying delay and unknown dead zone

This paper investigates the problem of adaptive fuzzy tracking control for a category of pure-feedback nonlinear systems with time-varying delay and unknown dead zone. Fuzzy logic systems are used to identify unknown functions existing in systems. Mean-value theorem is introduced to overcome the difficulty arising from the pure-feedback structure in designing controller. Based on the information of dead-zone slopes, dead zone is handled. Only one adaptive parameter needs updating online by considering the norm of membership function vectors rather than all sub-vectors. Moreover, utilizing the adaptive backstepping technique, a novel adaptive fuzzy tracking control scheme is developed to guarantee all signals of the closed-loop systems are semi-globally uniformly ultimately bounded, and the tracking error can be regulated to the origin with a small neighborhood. The stability of the closed-loop system is proved and simulation results are given to demonstrate the effectiveness of the proposed control approach.

Adaptive quantized fuzzy control of stochastic nonlinear systems with actuator dead-zone

This paper studies a tracking issue of stochastic nonlinear quantized systems with actuator dead zone. By combing a sector-bounded property of a hysteretic quantizer and a simplified dead zone model, a novel connection between control signal and system input is established. Based on this connection, the stochastic nonlinear quantized control is transformed into the conventional stochastic nonlinear control with unknown control gain and bounded perturbation. Therefore, the control difficulty is overcome, which results from the coexistence of the unknown actuator dead zone and the quantization effect of the control signal. Then, fuzzy logic systems are utilized to cope with the unknown composite nonlinear functions including the bounded perturbation, and an adaptive learning mechanism is set up to compensate the unknown control gain. Hence, a refreshing adaptive fuzzy tracking control scheme is formed to achieve a desired tracking performance.

Robust adaptive fault-tolerant control for a class of uncertain nonlinear systems with multiple time delays

This study is concerned with the problem of robust adaptive fuzzy fault-tolerant control for a class of uncertain nonlinear systems with mismatching parameter uncertainties, external disturbances, multiple state time delays perturbations and actuator failures, which include loss of effectiveness, outage and stuck modes. A novel direct adaptive fuzzy tracking control scheme is developed to achieve the fault-tolerant control objective. First, by introducing a positive nonlinear control gain function, the effects of state time delays and actuator failures are effectively compensated. Then, a suitable fuzzy logic system (FLS), which is used to approximate the corresponding nonlinear function, is constructed to eliminate the influences on mismatched parameter uncertainty and external disturbance. Moreover, it is shown that all the closed-loop system signals are uniformly bounded and that the tracking error converges to a small neighborhood of the origin via Lyapunov–Krasovskii stability analysis. Finally, the proposed adaptive fuzzy fault-tolerant tracking design approach is illustrated on a two stage chemical reactor system with delayed recycle streams.

Robust tracking observer-based adaptive fuzzy control design for uncertain nonlinear MIMO systems with time delayed states

This paper addresses the problem of designing robust observer-based adaptive fuzzy tracking control scheme for a class of MIMO nonlinear systems with plant uncertainties, time delayed uncertainties, and external disturbances. A fuzzy logic system (FLS) is utilized to approximate the unknown nonlinear functions and an adaptive fuzzy observer is introduced for state estimations. The proposed control law is based on indirect adaptive fuzzy control and uses two on-line estimations. This allows for the simultaneous inclusion of identifying gains of the delayed state uncertainties and training of the weights of the fuzzy system by introducing estimated error vectors. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear system functions with online update laws. The adaptive fuzzy tracking control using Variable Structure (VS) control technique is derived based on Lyapunov criterion and the Riccati-inequality to resolve system uncertainties, time delayed uncertainties, and external disturbances. This is done in such a way that all states of the system are bounded and the H∞ tracking performance is achieved. Finally, a two-connected inverted pendulums on carts system (Liu et al., 2011) [29] is used for simulation purposes and some comparisons are given to illustrate the validity and effectiveness of the proposed method.

구동기 동역학을 가지는 이동 로봇에 대한 FBFN을 이용한 강인 적응 퍼지 추종 제어

This paper proposes a robust adaptive fuzzy tracking control scheme for a nonholonomic mobile robot with external disturbances as well as parameter uncertainties in the robot kinematics, the robot dynamics, and the actuator dynamics. In modeling a mobile robot, the actuator dynamics is integrated with the robot kinematics and dynamics so that the actuator input voltages are the control inputs. The presented controller is designed based on a FBFN (Fuzzy Basis Function Network) to approximate an unknown nonlinear dynamic function with the uncertainties, and a robust adaptive input to overcome the uncertainties. When the controller is designed, the different parameters for two actuator models in the actuator dynamics are taken into account. The proposed control scheme does not require the kinematic and dynamic parameters of the robot and actuators accurately. It can also alleviate the input chattering and overcome the unknown friction force. The stability of the closed-loop control system including the kinematic control system is guaranteed by using the Lyapunov stability theory and the presented adaptive laws. The validity and robustness of the proposed control scheme are shown through a computer simulation.

Adaptive Fuzzy Tracking Control of a Class of Stochastic Nonlinear Systems with Unknown Dead-Zone Input

In this paper, a direct adaptive fuzzy tracking control scheme is presented for a class of stochastic uncertain nonlinear systems with unknown dead-zone input. A direct adaptive fuzzy tracking controller is developed by using the backstepping approach. It is proved that the design scheme ensures that all the error variables are bounded in probability while the mean square tracking error becomes semiglobally uniformly ultimately bounded (SGUUB) in an arbitrarily small area around the origin. Simulation results show the effectiveness of the control scheme.

Direct Fuzzy Tracking Control of a Class of Nonaffine Stochastic Nonlinear Systems with Unknown Dead-Zone Input

In this paper, a direct adaptive fuzzy tracking control scheme is presented for a class of stochastic nonaffine uncertain nonlinear systems with unknown dead-zone input. Based on the first-type fuzzy logic system's online approximation capability, a direct adaptive fuzzy tracking controller is developed by using the backstepping approach. It is proved that the design scheme ensures that all the error variables are bounded in probability while the mean square tracking error becomes semiglobally uniformly ultimately bounded(SGUUB) in an arbitrarily small area around the origin. Simulation results show the effectiveness of the control scheme.