Unknown Backlash-like Hysteresis Research Articles

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 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.

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.

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.

Adaptive dynamic surface error constrained control for MIMO systems with backlash-like hysteresis via prediction error technique

In this paper, we are concerned with the problem of adaptive dynamic surface error constrained control for a class of nonlinear multiple-input-multiple-output systems with unknown backlash-like hysteresis nonlinearities. By transforming the tracking errors into new virtual error variables which are incorporated into the proposed prescribed performance control strategy, the prescribed steady-state and transient performance can be ensured. Compared with the existing methods, we introduce the prediction error which is generated between the system state and the serial–parallel estimation model to construct the adaptive laws for neural network weights. The proposed prediction error technique can be used to compensate the tracking error, which implies that a higher accuracy of the identified neural network model is achieved. 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 the desired trajectory, while the tracking error are confined all times within the prescribed bounds. Finally, a simulation example is provided to confirm the effectiveness of the proposed approach.

Minimal-Approximation-Based Decentralized Backstepping Control of Interconnected Time-Delay Systems.

A decentralized adaptive backstepping control design using minimal function approximators is proposed for nonlinear large-scale systems with unknown unmatched time-varying delayed interactions and unknown backlash-like hysteresis nonlinearities. Compared with existing decentralized backstepping methods, the contribution of this paper is to design a simple local control law for each subsystem, consisting of an actual control with one adaptive function approximator, without requiring the use of multiple function approximators and regardless of the order of each subsystem. The virtual controllers for each subsystem are used as intermediate signals for designing a local actual control at the last step. For each subsystem, a lumped unknown function including the unknown nonlinear terms and the hysteresis nonlinearities is derived at the last step and is estimated by one function approximator. Thus, the proposed approach only uses one function approximator to implement each local controller, while existing decentralized backstepping control methods require the number of function approximators equal to the order of each subsystem and a calculation of virtual controllers to implement each local actual controller. The stability of the total controlled closed-loop system is analyzed using the Lyapunov stability theorem.

Adaptive consensus of nonlinear multi-agent systems with unknown backlash-like hysteresis

In this brief, we consider the consensus problem of high-order nonlinear multi-agent systems with unknown backlash-like hysteresis and unknown control direction. By using backstepping technique, a distributed adaptive control scheme, with the adoption of Nussbaum-type function, is developed to solve this consensus problem. Radial basis function neural network is employed to neutralize the uncertain nonlinear dynamics. The approximation error of the neural networks, together with external disturbance and a bounded term from the hysteresis model, is adaptively estimated and counteracted by a robust term. Under undirected connected communication topology, it is proved that the consensus can be achieved asymptotically with the proposed control protocol. Finally, a numerical example is presented to illustrate the performance of the proposed protocol.

Adaptive Dynamic Surface Output-Feedback Control for a Class of Hysteric Nonlinear Systems with Prespeeified Tracking Performance

In this paper, a high-gain observer based adaptive dynamic surface output-feedback control is proposed for a class of nonlinear systems preceded by unknown backlash-like hysteresis. The main features are 1) the RBF neural networks are employed to approximate the unknown smooth functions; 2) by using the proposed control scheme and the tracking error transformation functions, the tracking performance could be prespecified; 3) the derivative-explosion problem when the hysteresis is fused with backstepping design can be eliminated, which greatly simplifies the control law; 4) by combining with the estimation of vector norm of the unknown parameters, the computational burden is greatly reduced. Simulation results show the effectiveness of the proposed scheme.

Adaptive control of a class of non-linear systems preceded by backlash-like hysteresis

We consider a class of uncertain non-linear systems preceded by unknown backlash-like hysteresis, which is modelled by a differential equation. We propose a new state feedback robust adaptive control scheme using a backstepping technique and properties of the differential equation. In this control scheme, we construct a new continuous function to design an estimator to estimate the unknown constant parameters and the unknown bound of a ‘disturbance-like’ term. The transient performance of the output tracking error can be guaranteed by the introduction of pre-estimates of the unknown parameters in our controller together with update laws. We do not require bounds on the ‘disturbance-like’ term or unknown system parameters in this scheme. The global stability of the closed-loop system can be proved.

Global adaptive output feedback tracking for a class of non‐linear systems with unknown backlash‐like hysteresis

The authors consider a class of non-linear systems preceded by unknown backlash-like hysteresis. Unlike other schemes dealing with hysteresis, the non-linear systems of this study not only involve unknown parameters but also take non-linear terms linear in the unmeasured states into account. An adaptive output feedback controller by utilising a modified high-gain observer and backstepping approach is proposed, which is able to mitigate the effects of the hysteresis, and guarantee the global stability of the closed-loop system and the arbitrarily small steady-state tracking error. Moreover, it is proved that by introducing an initialisation technique, the ℒ∞ tracking performance can be achieved.

Adaptive neural tracking control for a class of nonstrict-feedback stochastic nonlinear systems with unknown backlash-like hysteresis.

This paper considers the problem of adaptive neural control of stochastic nonlinear systems in nonstrict-feedback form with unknown backlash-like hysteresis nonlinearities. To overcome the design difficulty of nonstrict-feedback structure, variable separation technique is used to decompose the unknown functions of all state variables into a sum of smooth functions of each error dynamic. By combining radial basis function neural networks' universal approximation capability with an adaptive backstepping technique, an adaptive neural control algorithm is proposed. It is shown that the proposed controller guarantees that all the signals in the closed-loop system are four-moment semiglobally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood of the origin in the sense of mean quartic value. Simulation results further show the effectiveness of the presented control scheme.

Adaptive fuzzy output feedback control of nonlinear uncertain systems with unknown backlash-like hysteresis based on modular design

In this paper, an adaptive fuzzy output feedback control approach is presented for a class of single-input single-output uncertain nonlinear systems with unknown backlash-like hysteresis and unmeasured states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a state filter observer is designed to estimate unmeasured states. Combining the backstepping recursive design with modular design techniques, a new adaptive fuzzy output control scheme is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. A simulation is included to illustrate the effectiveness of the proposed approach. The important feature of the proposed control approach is that it can solve the states immeasurable problem of nonlinear systems with unknown backlash-like hysteresis and the problem of unknown virtual control coefficients.

Adaptive fuzzy output feedback control of MIMO nonlinear uncertain systems with time-varying delays and unknown backlash-like hysteresis

In this paper, an adaptive fuzzy backstepping output feedback control approach is developed for a class of multi-input and multi-output (MIMO) nonlinear systems with time-varying delays and unknown backlash-like hysteresis. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and an adaptive fuzzy state observer is designed to estimate the unmeasured states. By utilizing the adaptive fuzzy observer, and combining the fuzzy adaptive control theory with backstepping approach, an adaptive fuzzy output feedback control approach is developed. The proposed control approach can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded (SUUB), and the observer error and tracking error are proved to converge to a small neighborhood of the origin. Two simulation examples are included to illustrate the effectiveness of the proposed approach.

Adaptive fuzzy output feedback control of uncertain nonlinear systems with unknown backlash-like hysteresis

In this paper, the problem of adaptive fuzzy output-feedback control is investigated for a class of uncertain nonlinear systems with unknown backlash-like hysteresis and unmeasured states. The fuzzy logic systems are used to approximate the nonlinear system functions, and a fuzzy state observer is designed to estimate the unmeasured states. By utilizing the fuzzy state observer, and combining the adaptive backstepping technique with adaptive fuzzy control design, an observer-based adaptive fuzzy output-feedback control approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SUUB), and both observer error and tracking error can converge to a small neighborhood of the origin. Two simulations are included to illustrate the effectiveness of the proposed approach.

An adaptive output feedback dynamic surface control for a class of nonlinear systems with unknown backlash-like hysteresis

This paper is devoted to the output feedback control for a class of nonlinear systems with unknown backlash-like hysteresis at the input. Based on a high-gain observer, an adaptive dynamic surface control scheme is proposed which is able to mitigate the effect of the hysteresis, to eliminate the explosion of terms inherent in backstepping control, and in particular, by introducing an initialization technique, to guarantee the ∞ performance of the system's tracking error. Another advantage of the proposed scheme is that the adaptive law is needed only at the first design step, which greatly simplifies the design procedure and makes our control easy to implement. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Adaptive Control of Nonlinear Systems with Unknown Backlash-like Hysteresis

Adaptive Control of Nonlinear Systems with Unknown Backlash-like Hysteresis

A Robust Adaptive Dynamic Surface Control for Nonlinear Systems with Hysteresis Input

Abstract In this paper, a robust adaptive dynamic surface control (DSC) for a class of uncertain perturbed strict-feedback nonlinear systems preceded by unknown backlash-like hysteresis is proposed. The main advantages of our scheme are that it can eliminate the explosion of complexity problem when the hysteresis is fused with backstepping design, and by introducing an initializing technique, and the ▪∞ performance of system tracking error can be guaranteed. It is proved that the new scheme can guarantee semiglobal stability of the closed-loop system and make the convergence of the tracking error into an arbitrarily small residual set. Simulation results are presented to demonstrate the efficiency of the proposed scheme.