Backlash-like Hysteresis Research Articles

Adaptive Critic Design for Pure-Feedback Discrete-Time MIMO Systems Preceded by Unknown Backlashlike Hysteresis

This paper concentrates on the adaptive critic design (ACD) issue for a class of uncertain multi-input multioutput (MIMO) nonlinear discrete-time systems preceded by unknown backlashlike hysteresis. The considered systems are in a block-triangular pure-feedback form, in which there exist nonaffine functions and couplings between states and inputs. This makes that the ACD-based optimal control becomes very difficult and complicated. To this end, the mean value theorem is employed to transform the original systems into input-output models. Based on the reinforcement learning algorithm, the optimal control strategy is established with an actor-critic structure. Not only the stability of the systems is ensured but also the performance index is minimized. In contrast to the previous results, the main contributions are: 1) it is the first time to build an ACD framework for such MIMO systems with unknown hysteresis and 2) an adaptive auxiliary signal is developed to compensate the influence of hysteresis. In the end, a numerical study is provided to demonstrate the effectiveness of the present method.

Partial State Constraints-Based Control for Nonlinear Systems With Backlash-Like Hysteresis

This paper focuses on the adaptive control problem for a class of nonlinear single-input single-output lower triangular systems with partial state constraints and unknown backlash-like hysteresis. To prevent the partial states from transgressing the predefined constrained region, a barrier Lyapunov function is presented, whose values will increase to infinity when any of its parameters grows to a given boundary value. To counteract the effect caused by the backlash-like hysteresis, an auxiliary variable with its adaptive mechanism is introduced in the backstepping technique. At the same time, the output of the considered systems can track the reference signal, and all the variables in the design procedure are uniformly ultimate boundedness. In the end, a numerical example is employed to validate the efficiency of the developed theoretical method.

Distributed Adaptive FBC of Uncertain Nonaffine Multiagent Systems Preceded by Unknown Input Nonlinearities With Unknown Gain Sign

An adaptive filtered backstepping control (FBC) is proposed for cooperative tracking control of uncertain nonaffine nonlinear multiagent systems preceded by input nonlinearities with unknown gain sign. The input nonlinearities can be backlash-like hysteresis and dead-zone. The gains of input nonlinearities are unknown nonlinear functions with unknown sign. To cope with unknown nonlinearities neural networks based on universal approximation theorem are utilized. The weights of neural networks are derived based on appropriate adaptive rules. Using the proposed adaptive FBC desirable steady-state and transient response can be achieved. Based on Lyapunov synthesis approach all the adaptive laws are extracted. It is proved that all the signals in the closed-loop network are semi-globally uniformly ultimately bounded and the outputs of the agents track the leader’s output asymptotically. Simulation results demonstrate the applicability and effectiveness of the proposed method.

ADAPTIVE FUZZY OUTPUT FEEDBACK TRACKING CONTROL FOR A CLASS OF NONLINEAR TIME-VARYING DELAY SYSTEMS WITH UNKNOWN BACKLASH-LIKE HYSTERESIS

This paper considers the problem of adaptive output feedback tracking control for a class of nonstrict-feedback nonlinear systems with unknown time-varying delays and unknown backlash-like hysteresis. Fuzzy logic systems are used to estimate the unknown nonlinear functions. Based on the Lyapunov–Krasovskii method, the control scheme is constructed by using the backstepping and adaptive technique. The proposed adaptive controller guarantees that all the closed-loop signals are semiglobally uniformly ultimately bounded and the tracking error can converge to a small neighborhood of the origin. Finally, Simulation results further show the effectiveness of the proposed approach.

Adaptive fuzzy dynamic surface tracking control for a class of nonlinear systems with unknown distributed time delays and backlash-like hysteresis

In this article, an adaptive fuzzy backstepping dynamic surface control approach is developed for a class of nonlinear systems with unknown backlash-like hysteresis and unknown state discrete and distributed time-varying delays. Fuzzy logic systems are used to approximate the unknown nonlinear functions and a fuzzy state observer is designed for estimating the immeasurable states. Then, by combining the backstepping technique and the appropriate Lyapunov–Krasovskii functionals with the dynamic surface control approach, the output-feedback adaptive fuzzy tracking controller is designed. The main advantages of this article are (i) the existence of the state discrete and distributed time-varying delays such that the investigated systems are more general than that of the existing results, (ii) the proposed control scheme can eliminate the problem of “explosion of complexity” inherent in the backstepping design method, and (iii) for the nth nonlinear system, only one fuzzy logic system is used to approximate the unknown continuous time-varying delay functions since all of them are lumped into one unknown nonlinear function, which makes our design scheme easier to be implemented in practical applications. It is proven that the proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error can converge to a small neighborhood of origin with an appropriate choice of design parameters. Finally, the simulation results demonstrate the effectiveness of the proposed approach.

Position Control of Asymmetric Nonlinearities for a Cable-Conduit Mechanism

Cable-conduit mechanism (CCM) is widely used in robotic hands, rescue robots, rehabilitation robots, and surgical robots because it offers efficient transmission of forces/torques from the external actuator to the end effector with lightweight and high flexibility. However, the accurate position control is challenging in such mechanism due to friction and backlash-like hysteresis between the cable and the conduit. In this paper, a new control approach is proposed to enhance the trajectory tracking performances of the CCM. Unlike current approaches for the CCM in the literature, the proposed scheme considers the position transmission of the CCM as an approximation of backlash-like hysteresis nonlinearities without requiring the exact values of model parameters and their bounds. Online approximation-based robust control laws, which have the capabilities of estimating unknown system parameters, are also established. In addition, the deigned controller can adapt to any changes of the cable-conduit configuration and it is stable. The results of the proposed control techniques have been experimentally validated on a flexible robotic system using a flexible endoscope. Experimental validations show substantial improvements on the performances of position tracking for the use of CCM regardless of the arbitrary changes of the cable-conduit configurations.

Adaptive Predefined Performance Control for MIMO Systems With Unknown Direction via Generalized Fuzzy Hyperbolic Model

An adaptive predefined performance control problem is investigated for a class of multiple-input multiple-output systems with unknown control direction and unknown backlash-like hysteresis nonlinearities by using generalized fuzzy hyperbolic model (GFHM). Compared with the existing methods, the main features are as follows: the prediction error is introduced to construct the adaptive laws, which means that the approximate accuracy of the GFHM is solved; the Nussbaum-type gain is utilized to deal with the unknown control direction, which avoids the requirement of direction a priori ; and by transforming the tracking errors into new error variables, the prescribed steady-state and transient performance can be ensured. It is shown that the proposed control approach can guarantee that all the signals of the resulting closed-loop systems are bounded, and the output tracks a desired trajectory, while the tracking errors are confined all times within the prescribed bounds. Finally, two simulation results and some comparisons are provided to verify the effectiveness of the proposed approach. Since the proposed control strategy is only implemented in a healthy case, how to extend the strategy to a faulty case will be a further topic.

Adaptive iterative learning control of a class of nonlinear time-delay systems with unknown backlash-like hysteresis input and control direction

This paper presents an adaptive iterative learning control scheme for a class of nonlinear systems with unknown time-varying delays and control direction preceded by unknown nonlinear backlash-like hysteresis. Boundary layer function is introduced to construct an auxiliary error variable, which relaxes the identical initial condition assumption of iterative learning control. For the controller design, integral Lyapunov function candidate is used, which avoids the possible singularity problem by introducing hyperbolic tangent funciton. After compensating for uncertainties with time-varying delays by combining appropriate Lyapunov-Krasovskii function with Young's inequality, an adaptive iterative learning control scheme is designed through neural approximation technique and Nussbaum function method. On the basis of the hyperbolic tangent function's characteristics, the system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapunov-like composite energy function (CEF) in two cases, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.

Adaptive fuzzy controller for a class of nonlinear systems with unknown backlash-like hysteresis

ABSTRACTThis paper proposes an adaptive fuzzy logic control scheme for a class of strict-feedback nonlinear systems with unknown backlash-like hysteresis. The proposed controller exploits the properties of the newly developed adaptive control in conjunction with the approximation capability of fuzzy systems. The developed controller is fast, the adaptation can be as fast as the CPU permits, and robust by virtue of the adaptive control structure and the direct estimation of the system nonlinear functions via fuzzy logic systems. As a result, the proposed adaptive fuzzy controller has a simpler form and requires fewer adaptation parameters. The inverted pendulum and Duffing forced oscillation systems are used in simulation studies to verify the effectiveness of the proposed adaptive fuzzy control scheme.

Adaptive neural prescribed performance control for a class of strict-feedback stochastic nonlinear systems with hysteresis input

This paper studies an adaptive neural tracking control problem for a class of strict-feedback stochastic nonlinear systems with guaranteed predefined performance subject to unknown backlash-like hysteresis input. First, utilizing the prescribed performance control, the predefined tracking control performance can be guaranteed via exploiting a new performance function without considering the accurate initial error. Second, by integrating neural network approximation capability into the backstepping technique, a robust adaptive neural control scheme is developed to deal with unknown nonlinear functions, stochastic disturbances and unknown hysteresis input. The designed controller overcomes the problem of the over-parameterization. Under the proposed controller, all the signals in the closed-loop system are 4-Moment (or 2 Moment) semi-globally uniformly ultimately bounded (SGUUB), and the prespecified transient and steady tracking control performance are guaranteed. Simulation studies are performed to demonstrate and verify the effectiveness of the proposed method.

Adaptive Neural Output Feedback Control for Nonstrict-Feedback Stochastic Nonlinear Systems With Unknown Backlash-Like Hysteresis and Unknown Control Directions.

This paper investigates the problem of output feedback adaptive stabilization for a class of nonstrict-feedback stochastic nonlinear systems with both unknown backlashlike hysteresis and unknown control directions. A new linear state transformation is applied to the original system, and then, control design for the new system becomes feasible. By combining the neural network's (NN's) parameterization, variable separation technique, and Nussbaum gain function method, an input-driven observer-based adaptive NN control scheme, which involves only one parameter to be updated, is developed for such systems. All closed-loop signals are bounded in probability and the error signals remain semiglobally bounded in the fourth moment (or mean square). Finally, the effectiveness and the applicability of the proposed control design are verified by two simulation examples.

Adaptive Neural Synchronization Control for Bilateral Teleoperation Systems With Time Delay and Backlash-Like Hysteresis.

This paper considers the master and slave synchronization control for bilateral teleoperation systems with time delay and backlash-like hysteresis. Based on radial basis functions neural networks' approximation capabilities, two improved adaptive neural control approaches are developed. By Lyapunov stability analysis, the position and velocity tracking errors are guaranteed to converge to a small neighborhood of the origin. The contributions of this paper can be summarized as follows: 1) by using the matrix norm established using the weight vector of neural networks as the estimated parameters, two novel control schemes are developed and 2) the hysteresis inverse is not required in the proposed controllers. The simulations are performed, and the results show the effectiveness of the proposed method.

Adaptive neural network control of a robotic manipulator with unknown backlash‐like hysteresis

This study proposes an adaptive neural network controller for a 3-DOF robotic manipulator that is subject to backlash-like hysteresis and friction. Two neural networks are used to approximate the dynamics and the hysteresis non-linearity. A neural network, which utilises a radial basis function approximates the robot's dynamics. The other neural network, which employs a hyperbolic tangent activation function, is used to approximate the unknown backlash-like hysteresis. The authors also consider two cases: full state and output feedback control. For output feedback, where system states are unknown, a high gain observer is employed to estimate the states. The proposed controllers ensure the boundedness of the control signals. Simulations are also performed to show the effectiveness of the controllers.

Adaptive tracking control for uncertain switched stochastic nonlinear pure-feedback systems with unknown backlash-like hysteresis

In this paper, an adaptive tracking control problem is studied for a class of switched stochastic nonlinear pure-feedback systems with unknown backlash-like hysteresis under arbitrary switching. The mean-value theorem is used to overcome the difficulty arising from the pure-feedback structure. Based on neural networks’ approximation capability, an adaptive tracking control approach is developed via the adaptive backstepping technique and common Lyapunov function method. It is proved that the proposed control scheme can guarantee that all signals in the closed-loop system are semi-globally uniformly ultimately bounded in probability and the tracking error converges to an adjustable neighborhood of the origin. Finally, a simulation example further shows the effectiveness of the presented control scheme.

Neural adaptive quantized output-feedback control-based synchronization of uncertain time-delay incommensurate fractional-order chaotic systems with input nonlinearities

This research is concerned with the problem of generalized function projective synchronization of nonlinear uncertain time-delay incommensurate fractional-order chaotic systems with input nonlinearities. The considered problem is challenging owing to the presence of unmeasured master-slave system states, external dynamical disturbances, unknown nonlinear system functions, unknown time-varying delays, quantized outputs, unknown control directions unknown actuator nonlinearities (backlash-like hysteresis, dead-zone and asymmetric saturation actuators) and distinct fractional-orders. Under some mild assumptions and using Caputo's definitions for fractional-order integrals and derivatives, the design procedure of the proposed neural adaptive controller consists of a number of steps to solve the generalized function projective synchronization problem. First, smooth functions and the mean value theorem are utilized to overcome the difficulties from actuator nonlinearities and distributed time-varying delays, respectively. Then, a simple linear observer is established to estimate the unknown synchronization error variables. In addition, a Nussbaum function is incorporated to cope with the unknown control direction and a neural network is adopted to tackle the unknown nonlinear functions. The combination of the frequency distributed model, the Razumikhin Lemma, the neural network parameterization, the Lyapunov method and the Barbalat's lemma is employed to perform the stability proof of the closed-loop system and to derive the adaption laws. The major advantages of this research are that: (1) the Strictly Positive Real (SPR) condition on the estimation error dynamics is not required, (2) the considered class of master-slave systems is relatively large, (3) all signals in the resulting closed-loop systems are semi-globally uniformly ultimately bounded and the synchronization errors semi-globally converge to zero. Finally, numerical examples are presented to illustrate the performance of the proposed synchronization scheme.

Adaptive neural tracking control for a class of uncertain switched nonlinear systems with unknown backlash-like hysteresis control input

This paper is concerned with the problem of adaptive tracking control for a class of uncertain switched nonlinear systems. Completely unknown backlash-like hysteresis control input that frequently exists in practice is also considered. By combining adaptive backstepping technique with neural networks approximation ability, an adaptive neural control algorithm is presented for the systems under consideration. A common virtual control function is deigned to construct a common Lyapunov function for the system. The explosion of complexity in traditional backstepping design is avoided by using dynamic surface control. It is demonstrated that the practical output tracking performance is achieved by using the proposed state-feedback controllers, and all the signals remain bounded. Finally, simulation results are given to show the effectiveness of the theoretical approaches.

Adaptive neural network backstepping control for a class of uncertain fractional-order chaotic systems with unknown backlash-like hysteresis

In this paper, we consider the control problem of a class of uncertain fractional-order chaotic systems preceded by unknown backlash-like hysteresis nonlinearities based on backstepping control algorithm. We model the hysteresis by using a differential equation. Based on the fractional Lyapunov stability criterion and the backstepping algorithm procedures, an adaptive neural network controller is driven. No knowledge of the upper bound of the disturbance and system uncertainty is required in our controller, and the asymptotical convergence of the tracking error can be guaranteed. Finally, we give two simulation examples to confirm our theoretical results.

Non-smooth predictive control for mechanical transmission systems with backlash-like hysteresis

This paper proposes a non-smooth predictive control approach for mechanical transmission systems described by dynamic models with preceded backlash-like hysteresis. In this type of system, the work platform is driven by a DC motor through a gearbox. The work platform is represented by a linear dynamic sub-model connected in series with a backlash-like hysteresis inherent in gearbox. Here, backlash-like hysteresis is modeled as a non-smooth function with multi-valued mapping. In this case, the conventional model predictive control for such system cannot be implemented directly since the gradients of the control objective function with respect to control variables do not exist at non-smooth points. In order to solve this problem, a non-smooth receding horizon strategy is proposed. Moreover, the stability of predictive control of such non-smooth dynamic systems is analyzed. Finally, a numerical example and a simulation study on a mechanical transmission system are presented for validating the proposed method.

Operator-based robust control for nonlinear uncertain systems with unknown backlash-like hysteresis

In this paper, operator based robust control for nonlinear uncertain system with unknown backlash-like hysteresis is considered. In detail, a continuous backlash-like hysteresis operator is proved to be corresponding to a one-to-one operator, that is, it is suitable to be used in operator theoretic based control theory. Moreover, an internal model control (IMC) structure with one parallel compensating operator is proposed for nonlinear uncertain system with unknown backlash-like hysteresis. Based on the proposed control scheme, the designed system is robustly stable and the desired output tracking performance can be realized simultaneously. Finally, a simulation example about nonlinear plant preceded by backlash is given to show the design procedure of the proposed method.

Adaptive neural networks output feedback dynamic surface control design for MIMO pure-feedback nonlinear systems with hysteresis

An adaptive neural networks (NNs) output feedback tracking control approach is proposed for a class of multi-input and multi-output (MIMO) pure-feedback nonlinear systems with unknown backlash-like hysteresis and immeasurable states. Radial basis function neural networks (RBF NNs) are utilized to approximate the unknown nonlinear functions of the controlled systems, and a state observer is designed to estimate the unmeasured states. The filtered signals are introduced to circumvent algebraic loop problem encountered in the implementation of the controller, and an adaptive compensation technique are used to solve the problem of unknown backlash-like hysteresis. Based on the designed state observers, and combining the backstepping and dynamic surface control (DSC) techniques, an adaptive NN output feedback tracking control approach is developed. The proposed method not only overcomes the problem of “explosion of complexity” inherent in the backstepping control design but also guarantees that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking errors converge to a small neighborhood of the origin. Two simulation examples are provided to show the effectiveness of the proposed approach.