Fuzzy State Observer Research Articles

Fuzzy Control Based on Reinforcement Learning and Subsystem Error Derivatives for Strict-Feedback Systems With an Observer

In this paper, a novel optimized fuzzy adaptive control method based on tracking error derivatives of subsystems is proposed for strict-feedback systems with unmeasurable states. A cost function based on the tracking error derivative is used. It not only solves the problem that the traditional input quadratic cost function at the infinite time is unbounded, but also solves the problem that the optimal control input derived from the cost function with exponential discount factor cannot make the error asymptotically stable. Considering the case where the states are unmeasurable, a fuzzy state observer is designed which removes the restriction of the Hurwitz equation for the gain parameters. Based on reinforcement learning, the observer and error derivative cost function, an improved optimized backstepping control method is given. Using observed information and actor-critic structure to train fuzzy logic systems online, the control inputs are obtained to achieve approximate optimal control. Finally, all closed-loop signals are proved to be bounded by the Lyapunov method, and the effectiveness and advantages of the proposed algorithm are verified through two examples.

Fixed-time formation fault tolerant control for unmanned surface vehicle systems with intermittent actuator faults

This article studies the fixed-time fuzzy formation tracking control problem for multiple unmanned surface vehicle (USV) systems with intermittent actuator faults. Since each USV is subject to unknown motion dynamics and the external disturbances. The fuzzy state observers are developed to estimate the positions and velocity in multiple USV systems, and disturbance observers are developed to estimate the external disturbances, and fuzzy logic systems are utilized to identify the unknown motion dynamics. Then, to compensate for the influence of intermittent actuator faults, the novel fixed-time adaptive output-feedback formation fault-tolerant controllers are constructed by constructing the integral type Lyapunov function and co-designing the last virtual controller. The presented formation control method can guarantee all the signals in multiple USV systems are bounded in fixed-time. Finally, simulation results and comprehensive comparisons are provided to verify the effectiveness of the presented formation control method.

Observer‐based finite‐time adaptive fault‐tolerant control for nonlinear system with input delay and prescribed performance

SummaryThis paper focuses on the issue of the adaptive fuzzy fault‐tolerant control for a type of nonlinear system with input delay and disturbances. Fuzzy logic systems (FLSs) are used to estimate the unknown nonlinear quantities of the system. The Pade approximation is applied to counteract the negative effects of input delay on the system. The prescribed performance control based on error transformation helps to guarantee the transient performance of system errors. A fuzzy state observer is established to estimate the unmeasurable states of the system. Then, in presence of disturbances and actuator faults, a finite‐time control scheme is designed using the Lyapunov function and the backstepping technique. Based on Lyapunov stability, it is proved that the tracking error can converge to a specified range in a finite time, and all signals in the system are bounded in the controller design. In the end, the simulations of a second‐order system and a multi‐area interconnected power system certify the feasibility and effectiveness of the control strategy.

Adaptive Fuzzy Output Feedback Tracking Control for Uncertain Nonstrict Feedback Systems With Variable Disturbances via Event-Triggered Mechanism

This article studies the adaptive fuzzy event-triggered output feedback control for nonlinear systems. The systems have the nonstrict feedback structure and variable disturbances simultaneously. A fuzzy state observer with an adaptive parameter is first proposed, and a less conservative condition to solve the observer gains is obtained. By constructing the command filter, the compensator, the fuzzy controller, the event-triggered mechanism, and the adaptive parameter, the adaptive fuzzy output feedback control scheme is built to guarantee that all the signals of the closed-loop systems are bounded, and the tracking errors are less than a prescribed accuracy in finite time. Simulation examples confirm the effectiveness of the proposed method.

Date-Driven Tracking Control via Fuzzy-State Observer for AUV under Uncertain Disturbance and Time-Delay

This paper focuses on developing a data-driven trajectory tracking control approach for autonomous underwater vehicles (AUV) under uncertain external disturbance and time-delay. A novel model-free adaptive predictive control (MFAPC) approach based on a fuzzy state observer (FSO) was designed to achieve high precision. Concretely, the mathematical model of AUV motion was analyzed, and simplified via model decoupling, thus providing the model basis with an explicit physical explanation for the controller. Second, the MFAPC scheme for a multiple-inputs and multiple-outputs (MIMO) discrete time system was derived, that estimates system external disturbance. The controller can online estimate and predictive time-varying parameter pseudo-Jacobian matrix (PJM) to establish equivalent state space data-model for AUV motion system. Third, the Takagi–Sugeno (T–S) fuzzy model based state observer was designed to combine with the MFAPC scheme for the first time, which was used to online decline the state error generated by system uncertain time-delay. In addition, the stability of the proposed control scheme was analyzed. Finally, two trajectory tracking scenarios were designed to verify the effectiveness and robustness of the proposed FMFAPC scheme, and the simulations are implemented using the realistic parameters of T-SEA AUV.

Adaptive Event-Triggered Control of Stochastic Nonlinear Systems With Unknown Dead Zone

We consider the tracking control problem for a class of stochastic nonlinear systems in strict-feedback structure via output feedback signal in this article. The controlled plant is assumed subject to unknown dead-zone input. By utilizing the fact that the unknown dead-zone input function can be modeled as a time-varying nonlinear function and a bounded disturbance, and selecting appropriate design parameters, we show that the effect of unknown dead zone can be compensated. We design a fuzzy state observer via fuzzy logic modeling technique to estimate the unknown system states. Then, we prove, via Lyapunov stability analysis, that the controlled plant is bounded in probability. In addition, all the signals in the closed-loop system are guaranteed to be globally bounded in probability. The tracking errors are also ensured to converge to a small neighborhood of the origin. Finally, to show the effectiveness of the proposed control strategy, a simulation example of one-link manipulator is presented in the simulation section.

Adaptive inverse optimal backstepping control strategy for longitudinal vibration of high-speed elevator system based on fuzzy observer

To effectively suppress the longitudinal vibration of the car under the conditions of high-speed operation and emergency braking, and improve the ride comfort of the car system, this paper proposes an adaptive fuzzy inverse optimal output feedback control strategy. Firstly, the dynamic model of the high-speed elevator system is established and the nonlinear dynamic model is approximated by the fuzzy logic system, and the auxiliary system model is established. Fuzzy state observer is designed to estimate the unmeasurable state. Furthermore, an adaptive inverse optimal output feedback controller based on fuzzy observer is designed by using adaptive backstepping technology and inverse optimal control principle. The stability analysis shows that the proposed adaptive fuzzy inverse optimal output feedback control strategy not only ensures the stability of the car attitude of high-speed elevator but also realizes the inverse optimization of the target cost function. Finally, the acceleration time–frequency response analysis of the two typical stages of high-speed elevator uniform running and emergency braking is carried out, and the numerical results are compared with the linear quadratic controller optimized by stepping quantum genetic algorithm (GA-LQR) and controller based on the state-dependent Ricatti equation (SDRE). The analysis verifies the effectiveness of the controller.

Saturation-Tolerant Prescribed Control for a Class of MIMO Nonlinear Systems.

This article proposes a saturation-tolerant prescribed control (SPC) for a class of multiinput and multioutput (MIMO) nonlinear systems simultaneously considering user-specified performance, unmeasurable system states, and actuator faults. To simplify the control design and decrease the conservatism, tunnel prescribed performance (TPP) is proposed not only with concise form but also smaller overshoot performance. By introducing non-negative modified signals into TPP as saturation-tolerant prescribed performance (SPP), we propose SPC to guarantee tracking errors not to violate SPP constraints despite the existence of saturation and actuator faults. Namely, SPP possesses the ability of enlarging or recovering the performance boundaries flexibly when saturations occur or disappear with the help of these non-negative signals. A novel auxiliary system is then constructed for these signals, which bridges the associations between input saturation errors and performance constraints. Considering nonlinearities and uncertainties in systems, a fuzzy state observer is utilized to approximate the unmeasurable system states under saturations and unknown actuator faults. Dynamic surface control is employed to avoid tedious computations incurred by the backstepping procedures. Furthermore, the closed-loop state errors are guaranteed to a small neighborhood around the equilibrium in finite time and evolved within SPP constraints although input saturations and actuator faults occur. Finally, comparative simulations are presented to demonstrate the feasibility and effectiveness of the proposed control scheme.

Adaptive Fuzzy Output-Feedback Predefined-Time Control of Nonlinear Switched Systems With Admissible Edge-Dependent Average Dwell Time

This article investigates the adaptive fuzzy output-feedback predefined-time control of nonlinear switched systems with an admissible edge-dependent average dwell time. Different from most of the existing results on neural or fuzzy adaptive finite/fixed-time tracking control of switched systems, where the tracking error goes to a small neighborhood of the origin within finite time, the proposed one can ensure the output tracking error to reach user-defined accuracy within predefined time, which can be arbitrarily preassigned by the designers. Technically, based on the mode-dependent fuzzy state observer, an adaptive output-feedback predefined-time controller is constructed by incorporating a new state-scale transformation function into the barrier Lyapunov function, ensuring predefined transient behavior and tracking accuracy. Besides, by extending the adaptive control problem to the admissible edge-dependent average dwell time framework, the proposed adaptive control scheme can guarantee that all the closed-loop signals are bounded under switching signals with an admissible edge-dependent average dwell time property. It is less conservative than the average dwell time and mode-dependent average dwell time. Finally, two illustrative examples validate the performance of the method presented.

Observer-Based Event-Triggered Adaptive Fuzzy Control for Fractional-Order Time-Varying Delayed MIMO Systems Against Actuator Faults

This article presents the observer-based event-triggered adaptive hybrid fuzzy dynamic surface control strategy for a category of uncertain nonstrict-feedback fractional-order nonlinear multi-input multi-output systems, including unknown time-varying delays and actuator faults. First, an adaptive hybrid fuzzy state observer and a serial-parallel estimation system are constructed to estimate the unmeasured system states and incorporate them into the control design scheme, respectively, where some appropriate fuzzy logic systems are introduced to approximate the unknown nonlinear functions. According to the dynamic surface control technique, the designed adaptive fuzzy control approach can surmount the deficiency of “complexity explosion.” Then, an observer-based adaptive event-triggered control algorithm is developed by constructing the Lyapunov–Krasovskii functionals and estimating the compounded disturbances. Furthermore, it is proved that under the drive of the reference signals, all the signals in the closed-loop system are semiglobally uniformly ultimately bounded and Zeno behavior can be successfully excluded. Finally, an example with numerical simulations is utilized to exhibit the applicability of the obtained observer-based event-triggered adaptive fuzzy control approach.

Design of equivalent‐input‐disturbance estimator based modified repetitive control with adaptive periodic event‐triggered for time‐varying delay nonlinear systems

AbstractThis article addresses the problems of the disturbance rejection and the periodic signal tracking for a class of time‐varying delay nonlinear systems subjected to unknown exogenous disturbances. To approximate the nonlinearity of the system, a Takagi‐Sugeno (T‐S) fuzzy model has been used. The proposed modified repetitive controller (MRC) scheme based on the equivalent‐input‐disturbance (EID) estimator improves the performance of periodic and aperiodic unknown disturbances rejection effectively and achieves good tracking performance for periodic references. Furthermore, an adaptive periodic event triggered mechanism based fuzzy state observer (APETM‐FSO) has been utilized to reduce data transmission, energy consumption, and computational burden, save the resources of communication. With the help of a designed adaptive event triggering condition, the APETM can detect the event occurrence, which is described by exceeding the error signal to a predetermined threshold. Only when the event occurs, the current data are transmitted otherwise, data can be kept unchanged using a zero‐order hold. Hence, The MRC, EID, and APETM‐FSO based on a time‐varying delay T‐S fuzzy model construct the overall system. Then, to achieve the asymptotic stability of the overall system subjected to unknown disturbances, sufficient conditions based on the Lyapunov–Krasovskii functional stability theory and linear matrix inequalities (LMIs) are derived. In addition, the FSO and fuzzy state feedback controller gains are designed using the matrix decomposition and LMI approaches. Simulation results with comparative study are presented to demonstrate the effectiveness and feasibility of the proposed scheme.

Adaptive finite‐time control of multi‐agent systems with partial state constraints and input saturation via event‐triggered strategy

AbstractThis paper focuses on the finite‐time control problem of multi‐agent systems with input saturation, unknown nonlinear dynamics, external disturbances and partial state constraints via output feedback. Fuzzy logic system and fuzzy state observer are introduced to approximate the uncertain nonlinearities and estimate the unmeasurable states, respectively. The partial state constraints are dealt with by using the barrier Lyapunov function, so that all states of the system do not exceed the preset boundary values. In order to reduce the computational complexity of the virtual controller and save communication resources, a first‐order filter and an event‐triggered mechanism are introduced, respectively. It is proved that the Zeno behavior does not occur via the proposed event‐triggered controller. By stability analysis, the finite‐time convergence of tracking error to a small neighborhood of the origin is proven. The effectiveness of the theoretical results is verified by examples.

Event-triggered fuzzy finite-time reliable control for dynamic positioning of nonlinear unmanned marine vehicles

This paper studies the fuzzy finite-time reliable dynamic positioning (DP) control for nonlinear unmanned marine vehicles. Firstly, the motion dynamics of nonlinear unmanned marine vehicles is modeled by the Takagi-Sugeno (T-S) fuzzy system. Secondly, a fuzzy state observer is designed to estimate the immeasurable position and velocity of unmanned marine vehicles. In order to decrease the frequency of data transmission of actuators and sensors, a dynamic event-triggered mechanism is presented based on unmanned marine vehicles information and the estimation error. Then, a fuzzy event-triggered reliable output feedback control method is presented by finite-time theory to tackle the actuator faults problem occurring in unmanned marine vehicles. The sufficient finite-time stable conditions in the form of LMIs are established via constructing finite-time Lyapunov-Krasovskii functional. Ultimately, the computer simulation results and comparisons with the existing control methods verify the advantages of the presented control method.

Distributed finite-time performance-prescribed time-varying formation control of autonomous surface vehicles with saturated inputs

This paper studies a time-varying formation control problem of a swarm of autonomous surface vehicles (ASVs) with prescribed constraints. Every ASV suffers from unavailable velocities, saturated inputs, internal uncertainties, and external disturbances. A distributed finite-time performance-prescribed time-varying formation control method is proposed for ASVs. Specifically, an adaptive fuzzy state observer (AFSO) is firstly proposed to recover the unavailable velocity by using saturated inputs and estimated disturbances from the fuzzy logic system. Secondly, a tunnel prescribed performance (TPP) function is designed to limit tracking errors with a concise form and smaller overshoot. At the kinematic level, with TPP-based error transformation, a C1 finite-time time-varying guidance law is proposed by using the smooth switch functions and recovered velocities. Next, a finite-time command filter based on Levant differentiator is presented to smooth the guidance signals. At the kinetic level, a C1 finite-time saturated control law is developed with the estimated velocities and disturbances. Then, it proves that tracking errors of the proposed closed-loop system converge into a small neighborhood around the equilibrium within finite time while evolving under TPP constraints regardless of saturated inputs. Finally, comparison results are provided to demonstrate the effectiveness of the proposed distributed finite-time performance-prescribed time-varying formation control method.

Finite-Time Dynamic Event-Triggered Fuzzy Output Fault-Tolerant Control for Interval Type-2 Fuzzy Systems

The finite-time dynamic event-triggered fuzzy output feedback fault-tolerant control problem is studied in this article for the interval type-2 (IT2) Takagi–Sugeno fuzzy system with parameter uncertainties and actuator faults. A fuzzy state observer is first developed to solve the immeasurable state problem. Second, by using the sampled estimating states and measured output signals, a dynamic event-triggered mechanism is formulated via integrating sensor-to-observer with observer-to-controller. Third, an observer-based finite-time event-triggered fuzzy fault-tolerant controller is synthesized via the nonparallel distribution compensation design principle. Consequently, the finite-time stable conditions of the addressed IT2 fuzzy system are established by constructing an appropriate Lyapunov function. Furthermore, an output feedback control design algorithm of solving control and observer gains is given in terms of the established sufficient finite-time stable conditions. Finally, a practical example of a nonlinear tunnel diode circuit system is provided to verify the effectiveness of the proposed IT2 fuzzy control scheme.

Observer-Based Finite-Time Inverse Optimal Output Regulation for Uncertain Nonlinear Systems

This paper deals with the finite-time inverse optimal output regulation problem for a class of uncertain nonlinear systems that are subjected to an exosystem. The nonlinear systems not only contain external disturbances in the exosystem but also take the unknown nonlinear functions and unmeasured states into account. The output regulation problem is first converted into a stabilization problem through the internal model. Then, fuzzy logic systems (FLSs) are employed to approximate the unknown nonlinear functions. An auxiliary system is constructed and, based on the auxiliary system, a fuzzy state observer is designed to estimate the unmeasured states. Furthermore, a novel adaptive fuzzy finite-time inverse optimal output feedback controller and adaptive law are designed by combining backstepping technology, adaptive control technology, finite-time stability theory, and the inverse optimal control method. The control algorithm ensures that all the signals of the closed-loop system are semiglobally practical finite-time stable (SGPFS), so the newly well-defined cost function that is connected with the auxiliary system can be minimized. Finally, the validity of the approach is confirmed by virtue of the simulation results.

Reinforcement learning‐based optimized output feedback control of nonlinear strict‐feedback systems with event sampled states

SummaryThis article focuses on the event‐triggered optimized output feedback control problem for nonlinear strict‐feedback systems. First, a fuzzy state observer is designed to estimate the unmeasurable states. Then, the fuzzy‐based reinforcement learning is performed under critic‐actor architecture to realize the optimized control. In addition, a novel event‐triggered mechanism is developed for the system states to greatly economize communication resources. By means of the Lyapunov stability theory, it can be proved that all signals of the closed‐loop system are bounded, and the Zeno behavior can be successfully avoided. Lastly, an inverted pendulum example is provided to confirm the effectiveness of the derived algorithm.

Command-Filter-Based Adaptive Fuzzy Finite-Time Output Feedback Control for State-Constrained Nonlinear Systems With Input Saturation

In this article, an adaptive fuzzy finite-time tracking control method is investigated for a class of state-constrained nontriangular nonlinear systems with input saturation. First, the fuzzy logic system is introduced to process the unknown functions, and the immeasurable system states are estimated accurately via the fuzzy state observer. To handle the saturation nonlinearity, the function approximation method is applied for the system transformation. Second, the “explosion of complexity” problem inherent in backstepping is solved through the command filter. Meanwhile, the barrier Lyapunov function is designed to guarantee that the constraints of states are not violated. Third, an adaptive fuzzy finite-time output feedback controller is developed to render the closed-loop system semiglobally practically finite-time stable. Eventually, simulation examples are included to illustrate the effectiveness of the theoretical results.

Distributed Output Feedback Funnel Control for Uncertain Nonlinear Multiagent Systems

Adaptive output-feedback consensus with funnel performance is studied for nonlinear uncertain multiagent systems (MASs). The nonlinear MASs contain unknown dynamics and only an output variable can be measured. The other states are not measured directly and are reconstructed via fuzzy state observers. The presence of output feedback makes the proposed design significantly different from the existing literature on control with funnel performance. In particular, appropriate adaptive laws must be defined to handle the presence of uncertain dynamics and local output information from a few neighboring nodes. Interestingly, with a suitable error transformation, it is shown that the proposed control law has a simpler structure than barrier function methods proposed in the literature to handle funnel-like performance. With respect to this point, simulation studies illustrate that the proposed method can dramatically reduce the control effort while satisfying transient and steady-state performance imposed by the funnel.

Adaptive Fuzzy Event-Triggered Tracking Control for Nonstrict Nonlinear Systems

This article addresses adaptive fuzzy event-triggered controller design for nonstrict nonlinear systems. First, for estimating the unmeasurable states, the high-gain fuzzy state observer is designed. By using backstepping technique, the adaptive fuzzy controller is designed. A new switching threshold event-triggered mechanism is given to decide when the controller needs to be updated and the Zeno behavior is avoided. Stability analysis shows that the tracking error can be arbitrarily small and all variables of the closed-loop system remain bounded. At last, the effectiveness of our control strategy is illustrated through simulation.