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This paper pays attention to the non-fragile observer-based H ∞ control problem of switched Takagi-Sugeno (T–S) fuzzy systems, where every subsystem is described by the T–S fuzzy model with local nonlinear terms. Different from the existing observer-based control strategy, a distinguishing feature of this paper is that constructed observers can make full use of current and past output measurements to enhance the performance of the observers in state estimation. However, the introduction of past output measurements has brought challenges to stability analysis and controller design. To tackle these difficulties and design a set of non-fragile fuzzy controllers to stabilize the systems, a new augmented state vector is constructed. First, a new non-fragile observer-based H ∞ control criterion is deduced based on the fuzzy Lyapunov function method. Then, the method of simultaneously solving observer and controller gains is obtained by introducing free matrix variables and using the linear matrix inequality approach. This solving method is more efficient than the traditional two-step method. Finally, two confirmatory instances are given. [ABSTRACT FROM AUTHOR]

ABSTRACT This article studies the finite‐time control problem for a class of nonlinear chaotic semi‐Markov jump systems with incomplete transition rates described by the T‐S fuzzy model approach. As a means to depict the dynamical properties pertaining to the examined system, parametric uncertainties, faults, external disturbances and input saturation are taken into consideration. The foremost objective of this study is to come up with a composite control mechanism that effectively rejects and attenuates the repercussions of faults and disturbances. In particular, we primarily built a disturbance observer in order to obtain a precise estimation of the external disturbances. After which, the fault diagnosis observer is designated to effectively estimate the faults. Specifically, a composite reliable control mechanism is developed by fusing the output of the constructed observers with the mode‐dependent fuzzy‐rule based state feedback controller. By employing suitable Lyapunov functions in conjunction with the linear matrix inequality technique, a set of mode‐dependent conditions is derived to ensure the finite‐time stochastic boundedness of the underlying closed‐loop and estimation error systems. Following this, the anticipated controller and observer gain matrices are elicited by resolving the established linear matrix inequalities. Thereafter, intending to ascertain the efficacy and usefulness of accrued theoretical findings, simulation results performed on Chua's circuit system is endowed. [ABSTRACT FROM AUTHOR]

ABSTRACT This article studies the problem of fault estimation (FE) and dynamic output fault‐tolerant control (DOFTC) for a class of Takagi–Sugeno (T–S) fuzzy singularly perturbed systems (SPSs) which subject to time delay, external disturbance and actuator fault. A new fault estimation and fault‐tolerant control scheme was proposed and designed for the influence of the change of perturbation parameter ε$$ \varepsilon $$ on the singularly perturbed system. This scheme adopts the Takagi–Sugeno (T–S) fuzzy model, learning observer and dynamic output feedback fault‐tolerant mechanism, so that the system has multi‐time‐scale dynamic stability. The results show that this method has more accurate estimation effect, faster convergence speed, and very fast steady‐state response of fault‐tolerant control when faults occur. Furthermore, when constructing the Lyapunov function, the improved matrix P(ε)$$ P\left(\varepsilon \right) $$ was selected to ensure that the closed‐loop system is stable for all ε∈(0,ε‾]$$ \varepsilon \in \left(0,\overline{\varepsilon}\right] $$, and at the same time, the conservativeness of the results was reduced. Finally, the feasibility and correctness of the proposed design method were illustrated through two numerical examples. [ABSTRACT FROM AUTHOR]

In this article, an adaptive switching controller is designed for the stabilization control and the tracking control of nonlinear systems suffering from full state constraints, unknown control directions, and system uncertainties. Featured with changing signs and unbounded increasing magnitudes, a switching control structure is proposed to deal with the unknown control direction problem. In order to explore and finally fix the correct control direction, an adaptive switching rule, a switching function, and a reference function are constructed. An integral Lyapunov function is adopted for the design of the control law, which ensures that full state constraints will not be violated. Using this method, the nonlinear system can be properly controlled without extra estimations or approximations. The boundedness of all the states and the stability of the system are analyzed and guaranteed. Finally, simulations are conducted to validate the proposed method, and the results illustrate its effectiveness. [ABSTRACT FROM AUTHOR]

Summary: As the nonlinearities of many real physical controlled systems become stronger and stronger, they are difficult to be described by accurate mathematical models. For a class of nonlinear single‐input single‐output systems with all‐state constraints and actuator faults, an event‐triggered adaptive fuzzy ABLF function fixed‐time tracking control method is proposed. The asymmetric barrier Lyapunov function (ABLF) combined with backward step technique is used to ensure the boundedness of the closed‐loop system output. In order to solve the problem of limited bandwidth resources, this paper adopts the event trigger mechanism and fuzzy control technology to approximate the unknown function to ensure the convergence of the system in a fixed time. After theoretical analysis, it is proved that the tracking error of the system converges in the small neighborhood of the origin, and it still has good tracking performance when the actuator faults. Finally, by comparing the proposed method with the asymmetric barrier Lyapunov function, which verifies the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This study focuses on addressing the challenge of adaptive fuzzy tracking control for stochastic nonlinear systems while considering full-state constraints. To tackle this issue, we introduce a fuzzy logic system to approximate the unknown nonlinear terms in the system. Additionally, a barrier Lyapunov function is utilized to confine the system state within a specific range. In order to design a novel tracking controller, the backstepping design method and the fuzzy control approach are combined. To optimize system performance, a hysteresis quantizer is integrated. To evaluate the effectiveness of the proposed control strategy, two simulation examples are presented. The simulation results demonstrate that the proposed control strategy effectively limits all state variables to a predefined range. Additionally, the tracking error of the system steadily converges to a negligible range near zero. [ABSTRACT FROM AUTHOR]

This paper is devoted to adaptive trajectory tracking of quadrotor systems with full-state constraints and random disturbances. The command-filtering technology combined with error compensation mechanisms is proposed to deal with the "explosion of complexity" problem in traditional backstepping design and reduction of the filtering errors. The Barrier Lyapunov functions (BLFs) are constructed to ensure that all system states do not violate the boundary of its constraints. The command-filtered adaptive fuzzy controller is designed such that the state constraints are not breached almost surely, all signals in the closed-loop system are bounded almost surely, and the first-order moment of the tracking error converges to an arbitrarily small neighborhood of zero by parameters tuning. Finally, the effectiveness of the proposed control method is illustrated by simulation results. [ABSTRACT FROM AUTHOR]

This paper presents a new method for regional stabilization of discrete-time nonlinear systems by static output feedback based on polynomial Lyapunov functions. The considered class of nonlinear systems subject to time-varying parameters can be described by difference-algebraic representation and an equivalent polytopic model is obtained, making it possible to apply Lyapunov theory and linear matrix inequality-based tool. In this sense, a convex optimization problem in terms of LMI is provided to guarantee the closed-loop system's robust stabilization and to enlarge the estimated domain of attraction (DoA). The proposed control design is a one-step approach that can be applied to systems with nonlinear output matrices. It requires no iterative algorithms or congruence transformation, and auxiliary decision variables are introduced only aiming at less conservative results. Besides that, the use of polynomial Lyapunov functions allows us to obtain asymmetric and non-convex estimated DoA, reducing the conservativeness. Numerical examples are provided to illustrate the effectiveness and advantages of the proposed approach. [ABSTRACT FROM AUTHOR]

The paper focuses on the issue of predefined‐time adaptive fuzzy tracking control for switched nonlinear systems. The complicated unknown nonlinear function is approximated by utilizing the fuzzy logic system. A novel adaptive fuzzy control scheme is proposed by using the common Lyapunov function and backstepping technology on the basis of the definition of predefined‐time stability, which can preset the setting time of tracking errors. The findings indicate that the presented controller can ensure that all signals remain bounded in the closed‐loop system under arbitrary switching conditions, and the tracking error can converge to the neighborhood near the origin within a predefined time. The feasibility of the developed control approach is further proved through an example of numerical simulation. [ABSTRACT FROM AUTHOR]

This paper examines a nonlinear Networked Control System (NCS) incorporating Takagi–Sugeno (T–S) fuzzy models to address the output tracking control problem in the presence of input state delay. The paper introduces a strategy based on an event-triggered scheme to reduce bandwidth utilization in the NCS by leveraging inherent constraints, including communication time delays and data transmission limitations. The presence of communication time delay leads to an asynchronous interaction between the designed control algorithm for T–S fuzzy systems, which utilizes novel LMI–based conditions, and the proposed T–S fuzzy controller. Additionally, this paper proposes a model of operation based on synchronous behaviour, enabling the design of a linear controller that is more easily implementable. In comparison to recent literature results, these results are obtained by using an associate Lyapunov Krasovskii Function (LKF) with fuzzy properties, in addition to different forms of integral inequalities as alternatives. A fuzzy model for NCSs is illustrated through an example of tracking control for output response. [ABSTRACT FROM AUTHOR]

This article realizes an adaptive finite‐time sampled‐data output‐feedback stabilization for a class of fractional‐order nonlinear systems with unmodeled dynamics and unavailable states. K‐filters are constructed to estimate unavailable states, a dynamic signal is introduced to handle unmodeled dynamics and neural networks were used to approximate uncertain nonlinearities existed in stabilizer construction. With the help of backstepping technique, an adaptive sampled‐data output‐feedback stabilizer is exported, and such stabilizer with allowable design parameters and sampling period can render the corresponding closed‐loop system reaches practically finite‐time stable, which can be demonstrated by means of selected Lyapunov function candidates. In the end, two simulations with a numerical and an engineering examples are presented to verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, a Lyapunov-based design method for event-triggered control with self-triggered sampling is proposed. In the proposed method, update of the control input and sampling of the state are individually determined based on two kinds of upper bounds of the Lyapunov function. By the proposed method, a non-monotonic Lyapunov function can be constructed. By non-monotonic decrease of a Lyapunov function, the number of communications can be reduced. In the neighborhood of the origin, we consider a control method such that the state stays in a certain set. As a result, it is guaranteed that the closed-loop system is uniformly ultimately bounded. Through a numerical example, we demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: This article investigates an adaptive fast finite‐time tracking control problem for a class of uncertain nonlinear systems with output hysteresis. The idea of output hysteresis compensation is skillfully extended to adaptive design by employing a hysteresis inverse transformation and barrier Lyapunov function. The backstepping technique is adopted to establish the fast finite‐time control strategy, which can realize finite‐time convergence of the closed‐loop system. A rigorous theoretical analysis is performed to illustrate that the signals in the closed‐loop systems are bounded in finite time, and the tracking error can converge into a compact set with sufficient accuracy. Finally, a numerical simulation is given to confirm the effectiveness of the presented strategy. [ABSTRACT FROM AUTHOR]

Parallel robot systems are increasingly important and widely applied due to their superior advantages such as high speed and accuracy. To improve the accuracy of these systems, recent research has focused on developing advanced control methods. However, this remains a significant challenge due to the complex mathematical model of parallel robots. This study introduces a control system based on a fuzzy cerebellar model articulation controller (FCMAC) to control parallel robots. The proposed control system includes FCMAC as the main tracking controller used to estimate the ideal control. A robust controller is employed to compensate for the error between FCMAC and the ideal controller. The parameters of FCMAC are adjusted online based on adaptive laws derived from Lyapunov functions. Finally, a five-bar parallel robot is selected to experiment with the FCMAC algorithm to demonstrate the effectiveness of the proposed controller. The results show that the accuracy of FCMAC is better than that of other algorithms. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of feedback control for a class of affine T–S fuzzy models using piece-wise Lyapunov functions. Although a large number of works on the issue have been published, several crucial problems still remain open. First, the paper shows what problems arise when using the affine T–S fuzzy model to design a controller, and in turn by employing the S-procedure, what kind of quadratic inequalities are required to help solve the resulting LMIs. It turns out that by partitioning the state space into certain cells based on the information of the antecedents of fuzzy rules, the required quadratic inequalities can be formularised. Taking advantage of the cell partition, a fuzzy controller is proposed using piece-wise Lyapunov functions, in which ensuing problems such as continuity functions used in the piece-wise Lyapunov functions and control input chattering also are addressed. Finally, examples are provided to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive output feedback aperiodic sampling control for a class of switched nonlinear systems under asynchronous switching. A novel model-dependent dynamic aperiodic sampling rule is proposed to solve problems of potential asynchronous lengthening and transmission overburdening. Blending with the sampling information, the time-schedule Lyapunov functions (TSLFs) are recreated to analyze the stability in different control situations. Meanwhile, the switched time-schedule observers and adaptive laws are designed to deal with the estimation problem of unknown system states and nonlinear function. The obtained switched sampling controllers and switching rule guarantee the closed-loop system to be uniformly ultimately bounded. Compared with the existing results, the asynchronous time in this paper does not change with the increasing sampling period. Depending on the sampled data, the time-varying observers and adaptive laws make the application of the given dynamic output feedback control design more extensive and flexible. Finally, the effectiveness of the proposed method is demonstrated by a ship steering system and a mass-spring-damper system. [ABSTRACT FROM AUTHOR]

A novel adaptive fuzzy predefined-time inverse approach is presented in this study, which enhances practical predefined-time stability to predefined-time stability. Unlike the existing optimal predefined-time control approaches, this method realizes the optimal performance without resolving the Hamilton–Jacobi–Bellman (HJB) equation, which simplifies the design and learning process. Firstly, by combining a Sontag-type function and a series of singularity-avoidance functions, an auxiliary controller is devised. Based upon this auxiliary controller, an inverse optimal predefined-time controller is set up. Secondly, based upon the method of two Lyapunov functions, it is demonstrated that the tracking error converges asymptotically to a predetermined interval within a predefined time and the inverse optimal stabilization is attained. Lastly, the availability of this method is testified through an example of the electromechanical system. [ABSTRACT FROM AUTHOR]

The predefined-time fuzzy adaptive output feedback control problem is considered for non-strict feedback stochastic nonlinear systems with state constraints. Since the controlled plant contains unknown nonlinear dynamics and unmeasured states, the unknown nonlinear dynamics are handled by using fuzzy approximation technique, and a fuzzy state observer is established to estimate unmeasured states. Then, under the frameworks of a predefined-time stability theory and backstepping control design technique, a new fuzzy adaptive output feedback control method is proposed. It is proved that the controlled system is semi-global practically predefined-time stable in probability by constructing suitable barrier Lyapunov functions. Finally, the spring–mass–damper system is given to confirm the effectiveness of the presented control method. [ABSTRACT FROM AUTHOR]

In this paper, the output feedback problem is studied for a class of nonlinear cascade systems with integral input to state stability (iISS) inverse dynamics and an unknown control direction. The tan-type barrier Lyapunov function (UBLF) is introduced for an asymmetric time-varying output constraint, which can be equal to the standard Lyapunov function of an unconstrained system, thereby solving the requirement for the asymmetric time-varying output constraint. A design strategy based on backstepping is proposed to construct a dynamic output feedback control law, and an output feedback controller is designed using the barrier function. The proposed strategy satisfies the constraint condition while keeping all other closed-loop signals bounded. Finally, the effectiveness of the proposed strategy is proven by the simulation results. [ABSTRACT FROM AUTHOR]

Based on a line-of-sight (LOS) guidance law for a curve parametrized path, a finite-time backstepping control is proposed for the kinematic path-following of an underactuated autonomous surface vehicle (ASV). Finite-time observer is utilized to estimate the unknown external disturbances accurately. The first-order Levant differentiator is introduced into the finite-time filter technique, such that the output of filter can not only approximate the derivative of the virtual control, but also avoid the singularity problem of real heading control. The integral terminal sliding mode is employed to improve the tracking performance and converging rate in the surging velocity control. By virtue of Lyapunov function, all the signals in the closed-loop system can be guaranteed uniformly ultimate boundedness, and accurate path-following task can be fulfilled in finite time. The simulation results and comparative analysis validate the effectiveness and robustness of the proposed control approach. [ABSTRACT FROM AUTHOR]

This paper deals with the application of a fuzzy-logic-based controller for a drive with a BLDC motor. Two main aspects of the work are presented in this paper. The first of them is focused on the design process of the fuzzy model. For this purpose, the rules of the applied fuzzy system are defined according to the Lyapunov function. The gain coefficients of the controller are optimized using the Chameleon Swarm Algorithm. Various issues and aspects were analyzed in the simulation tests (robustness against parameter changes, the influence of the controller parameters on the precision of control, stages of optimization, etc.). The presented work confirms the assumptions regarding precision and stable operation (also in the presence of changes in the object parameters—the mechanical time constants of the engine) in connection with the applied fuzzy speed controller. Moreover, the second part of the manuscript presents the low-cost power electronic device developed for laboratory tests. It uses STM32 ARM-based microcontrollers (state variable measurement, control algorithm calculation, control signal generation) and a Raspberry Pi 4B microcomputer (control application—reference value and parameter definition). The experiment performed for the control structure—an electric drive with a BLDC motor—verified the theoretical considerations. [ABSTRACT FROM AUTHOR]

This paper introduces an H ∞ robust constrained event-triggered fuzzy controller for discrete-time nonlinear systems in the presence of system parameter uncertainties, the parameter uncertainties of the output matrices and the disturbances, simultaneously. To reduce the communication resources and improve the robust performance, the event-triggered mechanism is incorporated with the H ∞ robust fuzzy controller design. Moreover, by employing the fuzzy modeling of the actuator saturation and a nonquadratic Lyapunov function (NQLF), the ultimate bounded stability (UBS) of the closed-loop system is guaranteed subject to the amplitude limitations of the control signal. This means, a new linear matrix inequality (LMI) problem is derived to ensure the robustness and constraints in an offline scheme based on the event-triggered strategy. Besides, to meet the practical problem to further improve the controlled system performance, the control input rate constraint is also considered and a new LMI condition is provided with no online computational burden. Therefore, the computational burden of the proposed controller is greatly reduced with less conservatism. Two simulation examples including a numerical dynamic system and a truck–trailer system are employed to illustrate the less conservatism and computational complexity of the proposed method compared with the existing approaches. [ABSTRACT FROM AUTHOR]

Summary: In this article, we study the problem of robust fault estimation for a class of T‐S fuzzy systems with time delays and external disturbances based on the finite information learning observer. The learning observer with intermittent sampling is constructed and the change rate of output estimation error is introduced to estimate the system fault effectively. At the same time, by introducing a generalized inverse matrix to the designed observer, a sufficient condition for the stability of the error estimation system is given by using fuzzy Lyapunov function, which not only solves the problem of system fault and external disturbance estimation, but also reduces the conservatism of the obtained conclusion. Finally, the results described by LMI are solved numerically and simulated to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the problem of adaptive fuzzy tracking control for a class of uncertain switched nonlinear systems with unknown control direction is studied. Aiming at the problem, an adaptive control scheme with Nussbaum gain technology is constructed by using the average dwell time (ADT) method and the backstepping method to overcome the unknown control direction, and time‐varying asymmetric barrier Lyapunov functions (ABLFs) are adopted to ensure the full‐state constraints satisfaction. The proposed control scheme guarantees that all closed‐loop signals remain bounded under a class of switching signals with ADT, while the output tracking error converges to a small neighborhood of the zero. An important innovation of this design method is that the unknown control direction, asymmetric time‐varying full state constraints, and predefined time‐varying output requirements are simultaneously considered in uncertain switched nonlinear systems for the first time. We set a moment in advance, and make the systems comply with the constraint conditions before running the moment by the shift function nested in the first time‐varying ABLF. Finally, a simulation example verifies the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper focuses on the topic of adaptive neural tracking control for flexible‐joint manipulator systems with output restrictions and input saturation. With the aid of the error compensation mechanism, command filter‐based adaptive neural control is proposed for robotic systems driven by permanent magnet synchronous machine (PMSM). An auxiliary signal produced by the first‐order linear system designed by the property of unmodeled dynamics is used to erase the dynamical uncertainties. The input saturation of system is estimated by tanh$$ \tanh $$‐function with mathematical transformation. Using barrier Lyapunov function (BLF), each component constraint of output is tackled. During the virtual control design phase, radial basis function neural networks (RBFNNs) may reliably assess the unknown nonlinear continuous function. All the variables in the closed‐loop system are proved to be semiglobally uniform ultimate bounded (SGUUB) by integrating all compensation signals into the overall Lyapunov function and using the defined compact set in the stability analysis of dynamic surface control (DSC). An applied example on robotic system is used to verify the effectiveness of the constructed design idea. [ABSTRACT FROM AUTHOR]

In this work, a novel disturbance rejection controller based on a nonlinear fractional order proportional integral derivative with fuzzy (NLFOPIDF) approximation and an adaptive law technique for a 160 kW two horizontal axis parts tidal turbine model is proposed. The tidal turbine system encounters gigantic unknown uncertainties with external and internal disturbances induced by fatigue forces and non-uniform operative thrust and turbulence deviations caused by the effect of wind and wave movements. The main working purpose of the tidal turbine system is to extract the maximum power generated by obtaining and tracking the optimal turbine speed. To track the optimal speed turbine, two controller loops are synthesized for the tidal turbine dynamics (outer loop) and current dynamics in the q-axis component (inner loop). The stability and convergence are verified for the outer and inner loops using a candidate Lyapunov function. An approximation fuzzy function is proposed to estimate the nonlinear dynamics of the tidal turbine system, and an adaptive technique is applied to adapt the tidal turbine system against the variation in nonlinear dynamics. The results demonstrate that the NLFOPIDF controller is superior to other works in optimal power generation and optimal turbine speed tracking. Moreover, this controller can be used to achieve the maximum power coefficients to get the optimal power generation. [ABSTRACT FROM AUTHOR]

In this paper, a non-quadratic Lyapunov function is employed to reduce conservatism in a nonlinear observer designed for a class of continuous-time Takagi–Sugeno fuzzy systems with unmeasurable premise variables. This structure presents greater challenges compared to systems with measured variables. To overcome this issue, we utilize the mean value theorem and the sector nonlinearity transformation to convert the nonlinear error dynamics into a linear parameter-varying system. Moreover, we introduce the line integral Lyapunov function, which based on the integral of the membership functions, in order to ensure the global stability of the fuzzy systems under consideration. The use of this function offers several notable advantages over conventional quadratic forms, including a reduction in conservatism. Additionally, this type of functions constructed in a manner that eliminates the need for generating time derivatives of the membership functions, thereby simplifying calculations and analysis in comparison to other nonquadratic functions. Furthermore, it also enables capturing the system's behavior along a trajectory. The stability conditions are more relaxed and expressed as linear matrix inequalities, which can be solved using a linear programming approach through specialized software tools. To validate the effectiveness of the proposed methodology, we conducted a hardware-in-the-loop test using a flexible joint robot. The obtained results clearly underscore the success of the proposed approach. • A new observer is designed for a nonlinear system described by a Takagi–Sugeno fuzzy model obtained via the nonlinear sector transformation. • Thanks to the mean value theorem and the LILF the observer is constructed. • The obtained stability constraints are more relaxed compared to those obtained with the quadratic function. • Observer gain is obtained by solving a set of linear matrix inequalities using a linear programming approach via specialized software tools. • The effectiveness and feasibility of the proposed observer have been validated via a hardware-in-the loop platform. [ABSTRACT FROM AUTHOR]

A permanent magnet synchronous motor (PMSM) is a nonlinear, strongly coupled, controlled object with time-varying, fractional-order characteristics. It is difficult to achieve the ideal control effect by using the traditional control method when motor parameter changes and load perturbations occur during the operation of the PMSM, so a fractional-order adaptive fuzzy backstepping control method is proposed to improve the system's fast response and anti-jamming ability in the case of sudden changes in rotational speed, load perturbations and other conditions. Initially, the fractional order theory is introduced, backstepping control is utilized to decompose the system into multiple subsystems, and a fractional order-based Lyapunov function is designed for each subsystem to ensure the system's stability. Suitable control laws, as well as parameter adaptive laws, are derived through rigorous mathematical derivation. Finally, a fractional order adaptive fuzzy backstepping controller (FOAB-FPID) is designed by combining the advantages of fuzzy control. Then a mechanical simulation model of the PMSM is established to verify the validity of the designed controller, followed by three sets of comparative experiments: PID, fuzzy PID (F-PID), and integer-order adaptive fuzzy backstepping (IOAB-FPID), which are selected to simulate the PMSM under the control of the four controllers. Finally, it is validated on the constructed PMSM experimental platform. Simulation and experimental results show that FOAB-FPID can adaptively adjust system parameters during sudden speed changes, achieve real-time speed tracking, and maintain speed stability under load perturbations and internal parameter uptake. Compared with the three control strategies, reached PMSM system has better acceleration, fast response performance, and better anti-disturbance ability, which proves the rationality and effectiveness of the FOAB-FPID control method. [ABSTRACT FROM AUTHOR]

In this article, an event‐triggered zero‐error adaptive output tracking controller with fixed‐time convergence mode is designed for a kind of uncertain nonlinear systems under full‐state constraints, unknown control coefficients, input dead‐zone, and saturation. The constrainedly practically fixed‐time stability is investigated for the considered high‐order nonlinear system. Then applying the barrier Lyapunov function technology and blending an error transformation into backstepping scheme, the Nussbaum‐gain‐based adaptive fuzzy control is proposed with prescribed performance. The control process consists of two phases, among which the first phase is used to render tracking error into the preset adjustable residual set within a preassigned fixed time at a prescribed decay rate, and the second phase further force the tracking error to converge to zero asymptotically. Additionally, the desired full‐state constraints are not violated in the whole control process. The simulation results are also given to show the effectiveness of the designed control method [ABSTRACT FROM AUTHOR]

For stochastic robotic systems actuated by direct current (DC) motors with full-state constraints, adaptive trajectory tracking is investigated in this paper. The main challenge is how to deal with the highly coupled terms with the stochastic disturbance and unknown nonlinear functions. First, as an approximate instrument of unknown nonlinear functions, the fuzzy logic system is adopted to tackle the uncertainty of stochastic robotic systems. Second, the command filter technique is used to solve the "complexity explosion" problem in the traditional backstepping process, and error compensation mechanisms are introduced to eliminate the error influence caused by command filters. Then, based on barrier lyapunov functions (BLFs), the adaptive fuzzy tracking controller is designed such that the state constraints are not breached almost surely, all signals in the closed-loop system are bounded almost surely and the first-order moment of the tracking error converges to an arbitrarily small neighborhood of zero. Finally, the tracking problem of the two-link planar manipulator in stochastic surroundings is analysed to demonstrate the effectiveness and advantages of the proposed control strategy. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive fuzzy tracking control method is proposed to address the issues of dead-zone and unobservable states in a flexible robotic arm system. The control design process begins with the utilization of a fuzzy logic system to approximate the nonlinear functions present in the flexible robotic arm system. To estimate the unobservable states of the system, a state observer is then designed. To alleviate the computational complexity during controller design, the command filtering technique is introduced. Additionally, the Nussbaum function is incorporated to address the unknown control gain problem. The stability of the system can be verified through the design of a Lyapunov function. This study's simulation results demonstrate that the designed control system can closely track the specified reference signals. The closed-loop system effectively controls the flexible robotic arm, as verified through experimentation. [ABSTRACT FROM AUTHOR]

This paper addresses the asymptotic control problem of uncertain multi-input and multi-output (MIMO) nonlinear systems. The considered MIMO systems contain unknown virtual control coefficients (UVCCs) and state constraints. A creative Lyapunov function by associating with the lower bounds of UVCCs is presented to counteract the adverse effect deriving from UVCCs. The state constraints are ensured by utilising the barrier Lyapunov function. Moreover, the asymptotic tracking controller is recursively constructed by combining the backstepping technique with fuzzy logic systems. The remarkable character of the designed controller is that the asymptotic tracking performance can be achieved by introducing some smooth functions into adaptive backstepping procedure. In contrast to the existing results, the conditions on the UVCCs are relaxed. Finally, the new control design is illustrated by a practical example. [ABSTRACT FROM AUTHOR]

To improve the anti-disturbance and reliability performance for unmanned surface vehicles subject to actuator faults and external disturbances, an adaptive event-triggered observer-based output feedback control method is proposed. Firstly, a Takagi-Sugeno fuzzy system is established by considering unknown disturbances and actuator faults. Secondly, an adaptive event-triggered mechanism is designed and then the state and disturbance observers are constructed using the output of the event generator. Based on the outputs of the observers, an adaptive event-triggered observer-based output feedback dynamic positioning controller is developed and the asymptotical stability with H ∞ performance is analyzed via the Lyapunov function method. Finally, the advantages of the proposed method are demonstrated via an example. [ABSTRACT FROM AUTHOR]

In this paper, first, general dynamic modeling is proposed for multi-input/output nonlinear systems in the form of affine and non-affine systems. Then, an observer barrier function-based adaptive fuzzy scheme is suggested to estimate unknown functions. Briefly, the main contributions of the proposed scheme are: (1) the proposed modeling can be employed in various classes of nonlinear systems, e.g., Single Input–Single Output (SISO), Single Input–Multi Output (SIMO), Multi Input–Single Output (MISO), and Multi Input–Multi Output (MIMO) systems with square or non-square control gain matrix, (2) by combining an observer error signal and the barrier Lyapunov function, the proposed Observer-based Barrier Lyapunov Function (OBLF) method can be employed to solve the problems of output constraint by preventing the output from violating the constraint, and (3) a non-singular robust adaptive fuzzy approach is presented for various classes of nonlinear systems so that the uncertainties are attenuated by a robust bounded H ∞ -like control term. The proposed scheme guarantees the stability of the closed-loop system based on the Strictly Positive Real (SPR) condition and OBLF theory, but it does not need the SPR conditions to be well known. Finally, to show the usefulness of the proposed technique, the simulation examples are employed for various classes of nonlinear affine and non-affine systems with square or non-square control gains. [ABSTRACT FROM AUTHOR]

A non‐approximation‐based output feedback control strategy for a class of switched large‐scale nonlinear systems with quantized inputs and sensor uncertainties is proposed. A dynamic gain, which is shared by the state observers and controllers of all the subsystems, is designed so that the effects of sensor uncertainties, quantized inputs, unknown parameters, and external disturbances can be compensated. By constructing some common Lyapunov functions (CLFs) shared by the switched systems, it is proved that with the proposed scheme, the closed‐loop system stability can be guaranteed under arbitrary switching, and the outputs of all the subsystems can be steered to within arbitrarily small neighborhoods of the origin. [ABSTRACT FROM AUTHOR]

In this paper, the adaptive output feedback asymptotic tracking problem is investigated for nonlinear systems with dead-zone input and unknown nonlinearities, where only system output is available. First, an observer is constructed to estimate unavailable states. Then, by the observer and barrier Lyapunov function, an adaptive output feedback controller is designed, which compensates the influence of dead-zone input and unknown nonlinearities. Furthermore, based on the proposed controller and tuning function, the global boundedness of all signals in closed-loop system is achieved, and the tracking error can asymptotically converge to zero. Particularly, it should be noted that there is no need to calculate the derivatives of virtual control laws in controller design, thus reducing the computational complexity. Finally, two numerical examples are taken to verify the effectiveness of the designed controller. [ABSTRACT FROM AUTHOR]

A fuzzy integral controller with an event-triggered strategy for a class of nonlinear continuous singularly perturbed systems is proposed in this manuscript. Since the singularly perturbed systems are characterized by the parasitic parameter ɛ , which leads the systems to have multi-time-scale dynamics, a state feedback controller is proposed and designed for manipulating the effects of the parasitic parameter with the ɛ free functions by utilizing the Takagi–Sugeno fuzzy model, integral feedback, and event-triggered mechanism. As a result, we demonstrate that the proposed method maintain almost the same performance as the conventional controllers with less steady-state error while producing fewer events, which makes the communication channels between the plant system and the controller more available, through the examples of electrical engineering problems. • The nonlinear singularly perturbed system is modeled by using TS fuzzy model. • The proposed method is ɛ free function that met the H ∞ criterion. • Lyapunov function is used for stability analysis with LMI approach. • The integral feedback is used for improving the transient responses. • Event-triggered mechanism is used for reducing the communication cost. [ABSTRACT FROM AUTHOR]

This article considers a fuzzy adaptive event-triggered control design problem for electro-hydraulic systems. The addressed electro-hydraulic system contains immeasurable states and unknown nonlinear dynamics. Fuzzy logic systems (FLSs) are utilized to model the controlled electro-hydraulic system, and a state observer is formulated to get the estimations of the immeasurable states. Subsequently, a novel event-triggered strategy is introduced by using first-order filter technique, which can reduce the frequent updating of the voltage input. Then, by constructing composite Lyapunov functions, an observer-based fuzzy adaptive event-triggered control method is presented. The stability of the controlled electro-hydraulic system and the convergence of the tracking error are proved. Finally, the computer-simulated studies confirm the effectiveness of the presented control method. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel controller design method for stochastic nonlinear systems with unmodeled dynamics, uncertain parameters, and unknown covariance noise. In order to deal with these uncertainties, a new event‐based small gain controller is designed. The event‐triggered scheme can reduce the computational burden caused by disturbance and noise. By combining the technique of changing supply rate with small gain condition, a stochastic input‐to‐state practically stability Lyapunov function is obtained for the subsystem. Simultaneously, the changing supply function is used to treat with unmodeled dynamics. Based on backstepping process and adaptive control approach, the influence of unknown covariance noise is overcome. It is proved that the designed state‐feedback controller can ensure the overall system is stochastic input‐to‐state practically stability. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the problem of multi‐objective robust fault estimation based on observer is addressed for T‐S fuzzy nonlinear singularly perturbed systems with time‐varying state delay and external disturbance. Under H∞$$ {H}_{\infty } $$ performance constraint, a fuzzy augmented fault estimation observer is introduced to improve the performance of actuator and sensor fault estimation simultaneously. The sufficient conditions for the existence of fault estimator are given in the form of LMIs, where ε$$ \varepsilon $$‐dependent Lyapunov function is considered. The given multi‐objective fault estimator design strategy has a good ability to suppress external disturbance and ensure the estimation accuracy and convergence rate work well for all ε∈(0,ε‾]$$ \varepsilon \in \left(0,\overline{\varepsilon}\right] $$. Then the largest stability bound and the best attenuation capacity are guaranteed by deriving a modified optimal algorithm. Finally, two examples are given to illustrate the feasibility and correctness of the proposed design method. [ABSTRACT FROM AUTHOR]

This study introduces a novel H ∞ optimal constrained integral sliding mode control (OCISMC) for nonlinear systems due to the matched/unmatched external disturbances based on Takagi–Sugeno (TS) fuzzy models. Based on the Lyapunov function, the appropriate conditions are provided to reach the sliding mode from any initial condition and robustness against the matched disturbances is guaranteed. The optimal nominal part of the proposed OCISMC is designed based on an online optimization problem. To reach robustness against the unmatched disturbances and constrained controller, the H ∞ performance and the limitations of the control signal are included in the design procedure of the suggested OCISMC. Furthermore, by considering a non-quadratic Lyapunov function (NQLF), a new linear matrix inequality problem with less conservatism is derived. Finally, two examples are simulated and compared with the existing works to illustrate the capability of the proposed OCISMC. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the design of asynchronous switched nonlinear H∞$$ {H}_{\infty } $$ filters for a class of continuous‐time nonlinear switched systems with mismatching switching laws and L2$$ {L}_2 $$ norm‐bounded disturbances. In this context, the switched nonlinear system is modelled as a switched Takagi–Sugeno (T‐S) model with nonlinear consequent parts, that is, where unmeasured nonlinear terms are kept in the nonlinear consequent parts in order to circumvent the occurrence of unmeasured premise variables, which is usually faced in conventional T‐S modeling without nonlinear consequent parts. In this framework, asynchronous switched T‐S filters with unmeasured nonlinear consequent parts are proposed to estimate unmeasured and/or disturbed system's outputs, even when the filter's switching law mismatches the switched nonlinear system's one, which can be in practice unknown or imprecisely measured. Based on a candidate multiple Lyapunov function, combined with a H∞$$ {H}_{\infty } $$ criterion, conditions are proposed in terms of Linear Matrix Inequalities for the design of the considered asynchronous switched T‐S filters with unmeasured nonlinear consequent parts. Compared with previous related works, these conditions have the advantage of being dwell‐time‐independent and less conservative, thanks to the incremental quadratic constraints employed to deal with the unmeasured nonlinear consequent parts. Furthermore, acknowledging that T‐S models are only representing nonlinear ones on subsets of their state space, an optimization procedure to estimate the filtering error's domain of attraction is developed. Two illustrative examples are considered to validate the proposed results. An academic one is presented to illustrate the improvements brought in terms of conservatism by the proposed switched T‐S filter design methodology with regards to previous related studies. Then, a case study illustrates the effectiveness of this proposal from a switched nonlinear mass‐spring system inspired from related literature. [ABSTRACT FROM AUTHOR]

This paper considers the control problem of T–S fuzzy systems with mixed time delays. Based on the time derivative data of the membership function of T–S fuzzy systems, fuzzy Lyapunov functions are designed by two methods, and observer-based switching controllers are obtained. One is to design fuzzy Lyapunov functions by loosening the requirement of positive quality of symmetric matrices. The other approach takes the controller's form into account. First, the form of the system model is adjusted by comparing each state value involved in the system with the state value of the controller. Then, the fuzzy Lyapunov function is designed using the difference value of the comparison. Both of the above observer-based switching controllers can stabilize the system. Examples are provided to demonstrate the effectiveness of the switching controllers proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of observer-based mismatched faults for switched singular fuzzy systems subject to disturbances. First, in order to obtain the estimation of unmeasurable or partially measurable states, fuzzy adaptive observer is obtained, eliminating the influence of external disturbances and mismatched faults, simultaneously. Second, by constructing appropriate piecewise Lyapunov functions and average dwell time, the switched singular fuzzy stochastic system with external parameter perturbations and faults is guaranteed to be robustly stable Further, by solving the linear matrix inequalities a sufficient condition to maintain the stability of error dynamic system is presented. Finally, to illustrate the proposed method is available, numerical examples are presented. [ABSTRACT FROM AUTHOR]

A fixed-time adaptive fuzzy second-order sliding mode (SOSM) approach has been designed to handle the problem of nonlinear systems with output constraints. According to the advantages of using fuzzy logic systems, the unknown bounds of uncertainties can be approached dynamically. The problem of output constraints has been well handled by constructing a barrier Lyapunov function. Next, with the help of adding a power integrator technique and adaptive fuzzy control, a fixed-time adaptive fuzzy SOSM controller is designed for the considered systems. In addition to the above, the controller can not only promote the sliding variables to converge to the origin in fixed time, but also stabilize the variables in the constrained range. In other words, under the proposed method, the systems can be stable in a specified time no matter how the initial value changes. Lastly, a numerical example is used to verify the performance of the proposed SOSM control tactic. [ABSTRACT FROM AUTHOR]

This paper studies the adaptive tracking control for a class of constrained high-order nonlinear systems with uncertainties. First, a type of improved asymmetric log-type barrier Lyapunov functions (LBLFs) is constructed to handle the full-state constraints. Second, fuzzy systems are built to approximate the unknown functions in the control system. An adaptive controller is designed on the basis of adding a power integrator technique. Consequently, the designed controller can ensure that the constraints are not breached, while the tracking error approaches an arbitrarily small neighborhood of the origin. The designed controller's performance can be guaranteed with the disappearance of the constraints. The computational burden of fuzzy approximation is mitigated by the adaptive gain-update law. A numerical example and a practical example are presented to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A new and efficient output-feedback adaptive backstepping control strategy is developed to realize a finite-time output tracking control task for nonlinear output-constrained systems. The main characteristic of this strategy is to construct an asymmetric barrier Lyapunov function based on the performance functions and error variable to achieve finite-time tracking control. Because the system states are unknown, fuzzy state observer is set up to reconstruct the system states. Consequently, an observer-based fuzzy adaptive output-feedback controller is presented. The proposed control strategy ensures that the output tracking error meets the preassigned precision level throughout a pre-given time period, meanwhile, the output variable complies with time-varying restrictions for all time and other closed-loop signals are bounded. Lastly, two examples are employed for numerical simulation research to reveal the feasibility and availability of the developed control strategy. [ABSTRACT FROM AUTHOR]

Learning and synthesizing stabilizing controllers for unknown nonlinear control systems is a challenging problem for real-world and industrial applications. Koopman operator theory allows one to analyze nonlinear systems through the lens of linear systems and nonlinear control systems through the lens of bilinear control systems. The key idea of these methods lies in the transformation of the coordinates of the nonlinear system into the Koopman observables, which are coordinates that allow the representation of the original system (control system) as a higher dimensional linear (bilinear control) system. However, for nonlinear control systems, the bilinear control model obtained by applying Koopman operator based learning methods is not necessarily stabilizable. Simultaneous identification of stabilizable lifted bilinear control systems as well as the associated Koopman observables is still an open problem. In this paper, we propose a framework to construct such stabilizable bilinear models and identify their associated observables from data by simultaneously learning a bilinear Koopman embedding for the underlying unknown control affine nonlinear system as well as a Control Lyapunov Function (CLF) for the Koopman based bilinear model using a learner and falsifier. Our proposed approach thereby provides provable guarantees of asymptotic stability for the Koopman based representation of the unknown control affine nonlinear control system as a bilinear system. Numerical simulations are provided to validate the efficacy of our proposed class of stabilizing feedback controllers for unknown control-affine nonlinear systems. [ABSTRACT FROM AUTHOR]

The permanent magnet synchronous motor is extensively used in robots due to its superior performances. However, robots mostly operate in unstructured and dynamically changing environments. Therefore, it is urgent and challenging to achieve high-performance control with high security and reliability. This paper investigates an accelerated adaptive fuzzy neural prescribed performance controller for the PMSM to solve chaotic oscillations, prescribed output performance constraint, full-state constraints, input constraints, uncertain time delays, and unknown external disturbances. First, for ensuring the permanent magnet synchronous motor with higher security, faster response speed, and lower tracking error simultaneously, a novel unified prescribed performance log-type barrier Lyapunov function is proposed to handle both prescribed output performance constraint and full-state constraints. Subsequently, a continuous differentiable constraint function-based model is introduced for solving input constraints nonlinearity. The Lyapunov-Krasovskii functions are utilized to compensate the uncertain time delays. Besides, a type-2 sequential fuzzy neural network is exploited to approximate unknown nonlinearities and unknown gain. For the "explosion of complexity" associated with backstepping, a tracking differentiator is integrated into this controller. Furthermore, a speed function is introduced in the backstepping technique for accelerated convergence. On the basis of above works, the accelerated adaptive backstepping controller is achieved. And the presented controller can ensure that all the closed-loop signals are ultimate boundedness, and all state variables are restricted in the prespecified regions and the permanent magnet synchronous motor successfully escapes from chaotic oscillations. Finally, the simulation results verify the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

With the excellent characteristic of intrinsic compliance, pneumatic artificial muscle can improve the interaction comfort of wearable robotic devices. This paper resolves the safety tracking control problem of a pneumatically actuated lower limb exoskeleton system. A single-parameter adaptive fuzzy control strategy is proposed with high control precision and full state constraints for the safe gait training tasks. Based on the barrier Lyapunov function, all signals in the closed-loop system can be bounded in finite time, which guarantees the deviation of the exoskeleton's moving trajectory within a bounded range. Furthermore, with the proposed single-parameter adaptive law, the computational burden and the complexity of the control are reduced significantly. Finally, numerical simulations, no-load tracking experiments, and passive and active gait training experiments with healthy subjects validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]