Backlash-like Hysteresis Research Articles

Finite-time adaptive switched gain control for non-strict feedback nonlinear systems via nonlinear command filter

This paper is aimed at developing a finite-time adaptive control for non-strict feedback nonlinear systems with unknown backlash-like hysteresis. First, the adaptive fuzzy systems are applied to identify the unknown functions which contain all the system states. Second, based on the practical finite-time stability criteria, a novel finite-time adaptive switched gain controller via nonlinear command filter is proposed. The stability analysis shows that the tracking error converges to a small region around the origin within a finite time. Meanwhile, all the resulting closed-loop system states are bounded. Finally, simulation examples verify the effectiveness of the designed control scheme.

Design on Type-2 Fuzzy-Based Distributed Supervisory Control With Backlash-Like Hysteresis

In this article, the distributed synchronization control problem is investigated for a class of uncertain nonlinear leader-following systems on directed graph, where unknown backlash-like hysteresis exists in the actuator of each follower and the topology of the graph is fixed. Based on basic graph theory, the principle of variable structure control and Lyapunov theory, by using the unknown smooth function approximation capability of type-2 fuzzy logic systems, a new distributed adaptive supervisory control design method is proposed such that all followers asymptotically synchronize to the leader and each synchronizing error is bounded. In the control method, with the help of supervisor control strategy, it is guaranteed that the resulting closed-loop signals including system states, respectively, belong to the corresponding compact sets, which is necessary for fuzzy approximation theory because it is on a compact set that an unknown smooth function can be approximated by fuzzy logic system. Furthermore, the adaptive compensation terms of the optimal approximation errors are adopted to reduce the effects of modeling errors. Finally, simulation results demonstrate the effectiveness of the proposed new design method.

Cooperative Neuro Adaptive Control of Leader Following Uncertain Multi-Agent Systems with Unknown Hysteresis and Dead-Zone

In this paper, a cooperative adaptive control of leader-following uncertain nonlinear multiagent systems is proposed. The communication network is weighted undirected graph with fixed topology. The uncertain nonlinear model for each agent is a higher-order integrator with unknown nonlinear functions, unknown disturbances and unknown input actuators. Meanwhile, the gains of input actuators are unknown nonlinear functions with unknown sign. Two most common behaviors of input actuators in practical applications are hysteresis and dead-zone. In this paper, backlash-like hysteresis and dead-zone are used to model the input actuators. Using universal approximation theorem proved for neural networks, the unknown nonlinear functions are tackled. The unknown weights of neural networks are derived by proposing appropriate adaptive laws. To cope with modeling errors and disturbances an adaptive robust structure is proposed. Considering Lyapunov synthesis approach not only all the adaptive laws are derived but also it is proved that the closed-loop network is cooperatively semi-globally uniformly ultimately bounded (CSUUB). In order to investigate the effectiveness of the proposed method, it is applied to agents modeled with highly nonlinear mathematical equations and inverted pendulums. Simulation results demonstrate the effectiveness and applicability of the proposed method in dealing with both numerical and practical multi-agent systems.

Adaptive neural tracking control of stochastic nonaffine nonlinear switched systems with unknown backlash-like hysteresis

This paper is concerned with the tracking control problem for a class of switched nonaffine stochastic nonlinear systems in completely nonaffine form and nonlower-triangular structure, with unknown backlash-like hysteresis involved, and a novel adaptive neural tracking control scheme, based on backstepping design, is proposed. To eliminate the problem of complexity explosion, dynamic surface control (DSC) technique is incorporated into the backstepping design procedure, such that the process of controller design becomes much simpler. High-order neural networks (HONNs) are employed to approximate the lumped unknown nonlinear functions, and only one adaptive parameter is required to be updated. Stability analysis shows that the proposed scheme guarantees all the closed-loop error signals are semi-globally uniformly ultimately bounded in the 4th-moment or mean square, and the system output can converge to an arbitrary small neighbourhood of the given trajectory. Finally, simulation results are presented to verify the effectiveness of the proposed approach.

Modeling Backlash-Like Hysteresis of Tendon Sheath Mechanism-Pair

Abstract Tendon sheath mechanism (TSM) is an effective power transmission system to access remote locations through tortuous channels, and it is widely used in endoscopic surgical robots. However, owing to deformation of TSM during power transmission, the input–output hysteresis is expressed in the form of backlash-like hysteresis. This paper is premised on the idea that sheath deformation can occur if the sheath is fixed only at certain points rather than being fully fixed at all points. Based on our hypothesis, a new TSM-pair backlash-like hysteresis model was derived, which considers the deformation property of the sheath. Experimental setups were designed to validate the new model, and its mechanical parameters were identified. The experimental results revealed that the sheath significantly deforms and that such deformation produces backlash-like hysteresis together with the tendon deformation. This model can be used to provide accurate prediction and control of TSM.

Event-Triggered Adaptive Fuzzy Control for Stochastic Nonlinear Systems With Unmeasured States and Unknown Backlash-Like Hysteresis

This article investigates the event-triggered control problem for stochastic nonlinear systems with unmeasured states and unknown backlash-like hysteresis. Based on the fuzzy logic systems, the unknown nonlinear functions can be identified. Then, by utilizing a fuzzy state observer, the unmeasured states of the considered system can be estimated. Moreover, by introducing an event-triggered mechanism, the communication load can be largely reduced. By employing the backstepping control strategy and the adaptive control method, a novel adaptive fuzzy event-triggered control method is constructed. It is shown that whole signals in the closed-loop systems are, ultimately, semiglobally and uniformly bounded in probability. Moreover, the tracking errors and the observer errors are located in a small neighborhood around the origin. Finally, a numerical example is given to confirm the effectiveness of the design scheme.

BLF-based adaptive DSC for a class of stochastic nonlinear systems of full state constraints with time delay and hysteresis input

This paper is concerned about barrier Lyapunov function(BLF)-based adaptive dynamic surface control(DSC) for a class of stochastic nonlinear systems of full state constraints with hysteresis input and time delay. All states of the system are guaranteed to be constrained in bounded compact set. The pure feedback nonlinear system is transformed into a strictly feedback nonlinear system with nonaffine nonlinear terms by using the mean value theorem. By using backstepping design of BLF combine with DSC technique, the explosion of complexity is avoided. Based on the neural network with the finite covering lemma, the time-delay functions are solved. Simultaneously, the backlash-like hysteresis input control in this paper is considered. The two cases of symmetric and asymmetric BLFs are discussed separately. An adaptive controller is designed to ensure that the output tracking error converges on a small region of the origin. Finally, the control scheme ensures that all signals in the closed-loop systems are semi-global uniformly ultimately bounded. Results of two simulation cases are presented to prove the effectivity of the theoretical analysis.

Robust neural tracking control for switched nonaffine stochastic nonlinear systems with unknown control directions and backlash-like hysteresis

This paper is concerned with the tracking control problem for a class of switched stochastic nonlinear systems in nonaffine form with both unknown control directions and unknown backlash-like hysteresis, and a novel neural tracking control scheme is proposed based on backstepping technique and Nussbaum function. Dynamic surface control (DSC) is adopted to overcome the problem of complexity explosion of the traditional backstepping design. High-order neural networks (HONNs) are utilized to approximate the lumped unknown nonlinear functions, and only one adaptive parameter needs to be updated. Stability analysis shows all closed-loop error signals are semi-globally uniformly ultimately bounded in the fourth-moment (or mean square), and the system tracking error is ensured to converge to a small neighborhood of zero. Finally, simulation results illustrate the effectiveness of the proposed scheme.

Time-varying Barrier Lyapunov Function Based Adaptive Neural Controller Design for Nonlinear Pure-feedback Systems with Unknown Hysteresis

This paper deals with the adaptive neural network (NN) control problem for a class of pure-feedback systems with time-varying constrained states and unknown backlash-like hysteresis. First of all, the considered plant is transferred into a strict feedback system on account of the implicit function theorem and mean value theorem. Then, the time-varying Barrier Lyapunov functions (BLFs) are integrated into the backstepping techniques so that all the states do not transgress the corresponding constraint boundary. This approach avoids the procedure of finding inverse, and therefore greatly improves the robustness of controller. At the same time, the radial basis function (RBF) NNs are employed to identify the unknown internal dynamics, which is a key operation in each step. Based on the Lyapunov stability analysis scheme, all the closed-loop signals are proved to be uniformly ultimately bounded (UUB), and the tracking error converges to a small neighborhood of the origin. Finally, two simulation examples are developed to further verify the proposed control strategy.

Bilateral coordinate boundary adaptive control for a helicopter lifting system with backlash-like hysteresis

Bilateral coordinate boundary adaptive control for a helicopter lifting system with backlash-like hysteresis

Adaptive neural control for switched nonlinear systems with unknown backlash-like hysteresis and output dead-zone

This paper investigates the problem of adaptive neural tracking control for a class of uncertain switched nonlinear systems in nonstrict-feedback structure. It should be pointed out that both the issues of unknown backlash-like hysteresis and output dead-zone are involved in the considered systems. A Nussbaum-type gain function is presented in this paper to overcome the difficulty existing in tracking the output dead-zone with unknown control direction, and the variable separation technique is applied to decompose the unknown functions containing all state variables into the sum of smooth functions with each error dynamic. Then by combining the backstepping approach and the approximation capability of radial basis function neural networks, an adaptive neural tracking control strategy is constructed, which guarantees that all the signals of the closed-loop systems are controlled to be semi-globally uniformly ultimately bound and the tracking error converges to a small region around the origin. Finally, the effectiveness of the proposed control strategy is verified by two simulation examples.

Observer-based adaptive fuzzy tracking control of MIMO switched nonlinear systems preceded by unknown backlash-like hysteresis

This paper considers the problem of adaptive fuzzy output feedback tracking control for a class of multi-input and multi-output (MIMO) switched nonlinear systems with hysteresis nonlinearities, where the hysteresis nonlinearities are described by a set of differential equations with unknown parameters. Fuzzy logic systems, as specialized function approximators, are employed to approximate the unknown nonlinear functions of the system under study. A MIMO switched fuzzy observer is constructed to tackle the problem of unmeasured states, and the dynamic surface control technique is introduced to avoid the appearance of repeated differentiations existing in most traditional backstepping designs. Based on the multiple Lyapunov function approach, an adaptive fuzzy output feedback controller is developed. The proposed control scheme can guarantee that all the signals in the resulting closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) under a class of switching signals with average dwell time, and the outputs to track given reference signals exactly. Simulation results demonstrate the validity of the control scheme.

Adaptive actuator failure compensation control for hypersonic vehicle with full state constraints

This paper addresses the longitudinal control problem of air-breathing hypersonic vehicles subject to actuator faults, full state constraints and backlash-like hysteresis. To accomplish the full state constraints, the modified nonlinear mappings are proposed to transform the altitude subsystem to a new system without state constraints. An adaptive backstepping controller is developed for this new system, in which the command filters are embedded to eliminate the problem of “explosion of terms”. Then, the controller parameters are updated to compensate the dysfunction of failed actuators and attenuate the unfavorable effects resulted from the backlash-like hysteresis. It is proved that the proposed controller can guarantee that the tracking errors converge to an arbitrarily small residual set and the full state constraints are not violated. Simulation results are carried out to demonstrate the effectiveness of the proposed control scheme.

Neural Network Identification and Sliding Mode Control for Hysteresis Nonlinear System with Backlash‐Like Model

A new neural network sliding mode control (NNSMC) is proposed for backlash‐like hysteresis nonlinear system in this paper. Firstly, only one neural network is designed to estimate the unknown system states and hysteresis section instead of multiscale neural network at former researches since that can save computation and simplify the controller design. Secondly, a new NNSMC is proposed for the hysteresis nonlinearity where it does not need tracking error transformation. Finally, the Lyapunov functions are adopted to guarantee the stabilities of the identification and control strategies semiglobally uniformly ultimately bounded (UUB). Two cases simulations are proved the effectiveness of the presented identification approach and the performance of the NNSMC.

Neural network based adaptive dynamic surface control of nonaffine nonlinear systems with time delay and input hysteresis nonlinearities

In this paper, neural networks (NNs)-based adaptive dynamic surface control is investigated for a class of pure-feedback nonlinear systems with unknown time delay and input hysteresis nonlinearities. The design difficulty appeared in this paper due to time delay is handled by combining neural networks with finite covering lemma instead of using Krasovskii functionals, and the assumptions on the time-delay functions are removed based the finite covering lemma and NNs. Meanwhile, completely unknown backlash-like hysteresis control input that frequently exists in practice is also considered. By combining the adaptive backstepping recursive design technique with the universal approximation ability of neural networks, an adaptive neural control algorithm is systemically designed for the system under consideration, and the explosion of complexity exists in traditional backstepping design is avoided by using dynamic surface technique. It is shown that the designed adaptive controller can guarantee that all the signals are ultimately uniformly bounded and the desired signal can be tracked with a small domain of the origin. A numerical example and an example of a real plant for adjustable metal cutting system are provided to show the feasibility of the proposed method.

A Prescribed Performance Adaptive Control for Hysteresis Hammerstein System

A prescribed performance adaptive control (PPAC) is proposed for Hammerstein system where nonlinearity is described by backlash-like hysteresis. In order to simplify the controller design as well as guarantee the precision of the controlled system, the tracking error is transformed into performance error by two steps. The first step is to transform the tracking error into scalar error, but it magnifies the tracking error decreasing the accuracy of the controlled system. Therefore, a new S(z) is proposed for prescribed performance function (PPF) and the second step is transforming the scalar error into performance error by the proposed PPF, which guarantees the scalar error converges to a prescribed bound to improve the control accuracy. Finally, Lambert W function is introduced for the Lyapunov function candidate to guarantee the closed-loop system bounded and the tracking error converged. Simulations demonstrate the effectiveness of the proposed approaches.

Multiscale Chebyshev Neural Network Identification and Adaptive Control for Backlash-Like Hysteresis System

An adaptive control based on a new Multiscale Chebyshev Neural Network (MSCNN) identification is proposed for the backlash-like hysteresis nonlinearity system in this paper. Firstly, a MSCNN is introduced to approximate the backlash-like nonlinearity of the system, and then, the Lyapunov theorem assures the identification approach is effective. Afterward, to simplify the control design, tracking error is transformed into a scalar error with Laplace transformation. Therefore, an adaptive control strategy based on the transformed scalar error is proposed, and all the signals of the closed-loop system are uniformly ultimately bounded (UUB). Finally, simulation results have demonstrated the performance of the proposed control scheme.

Adaptive neural output feedback control for a class of switched non-linear systems with unknown backlash-like hysteresis of the actuator

This paper investigates the problem of adaptive neural output feedback control for a class of switched non-linear systems, and the unknown backlash-like hysteresis of the actuator is also taken into consideration. First, neural networks are used to approximate the uncertain functions in the studied system. Second, a state-observer is proposed to estimate the system states. Finally, an adaptive neural output feedback control algorithm based on a backstepping technique is constructed; in addition, dynamic surface control is applied to eliminate the explosion in complexity caused by the backstepping technique. By using Lyapunov stability theory, it is proved that all the signals of the switched system are bounded under the proposed control scheme. The effectiveness of the proposed approach is further confirmed by simulation experiments.

Adaptive Fuzzy Synchronization of Fractional-Order Chaotic Neural Networks with Backlash-Like Hysteresis

An adaptive fuzzy synchronization controller is designed for a class of fractional-order neural networks (FONNs) subject to backlash-like hysteresis input. Fuzzy logic systems are used to approximate the system uncertainties as well as the unknown terms of the backlash-like hysteresis. An adaptive fuzzy controller, which can guarantee the synchronization errors tend to an arbitrary small region, is given. The stability of the closed-loop system is rigorously analyzed based on fractional Lyapunov stability criterion. Fractional adaptation laws are established to update the fuzzy parameters. Finally, some simulation examples are provided to indicate the effectiveness and the robust of the proposed control method.

Disturbance observer based adaptive neural prescribed performance control for a class of uncertain nonlinear systems with unknown backlash-like hysteresis

Abstract In this paper, an adaptive neural tracking control is studied for a class of strict-feedback nonlinear systems with guaranteed predefined performance subject to unknown backlash-like hysteresis input, uncertain parameters and external unknown disturbance. An adaptive neural control method combined with backstepping technique, and the radial basis function neural networks (RBFNNs) is proposed for the systems under consideration. In recursive backstepping designs, the tracking control performance can be guaranteed by exploiting a new performance function. A disturbance observer is employed to approximate the unknown disturbance. It is shown that by using Lyapunov methods, the designed controller can guarantee the prespecified transient and ensure semi-globally uniformly ultimately bounded (SGUUB) of all signals within the closed-loop systems. Simulation results are presented to illustrate the validity of the approach.