Adaptive tracking control for a class of strict feedback systems with unknown dead-zone input

In this paper, an adaptive neural fault-tolerant control scheme is proposed and analyzed for a class of uncertain nonlinear large-scale systems with unknown dead zone and external disturbances. To tackle the unknown nonlinear interaction functions in the large-scale system, the radial basis function neural network (RBFNN) is employed to approximate them. To further handle the unknown approximation errors and the effects of the unknown dead zone and external disturbances, integrated as the compounded disturbances, the corresponding disturbance observers are developed for their estimations. Based on the outputs of the RBFNN and the disturbance observer, the adaptive neural fault-tolerant control scheme is designed for uncertain nonlinear large-scale systems by using a decentralized backstepping technique. The closed-loop stability of the adaptive control system is rigorously proved via Lyapunov analysis and the satisfactory tracking performance is achieved under the integrated effects of unknown dead zone, actuator fault, and unknown external disturbances. Simulation results of a mass-spring-damper system are given to illustrate the effectiveness of the proposed adaptive neural fault-tolerant control scheme for uncertain nonlinear large-scale systems.

In this work, an adaptive dynamic surface control scheme is studied for a class of nonlinear systems with unknown functions and unknown non-symmetric dead-zone nonlinearity. The unknown asymmetric dead-zone is described as a combination of a linear term and a disturbance-like term. Radial basis function neural networks (RBFNNs) are used in the online approximation of unknown functions and disturbance-like term of the dead-zone model and adaptive laws are designed to adjust the weights of network. Using the RBFNN-based model, the dead-zone model and the dynamic surface control (DSC) technique, the adaptive control scheme is developed for uncertain nonlinear systems with dead-zone nonlinearity. The proposed scheme eliminates the ‘explosion of complexity’ problem and presents a singular-free adaptive DSC control scheme. Also, it does not require any knowledge about unknown terms and the dead-zone nonlinearity. Simulation results are provided to demonstrate the performance and effectiveness of the proposed approach.

The problem of adaptive fuzzy tracking control is addressed for a class of nonlinear system with completely unknown symmetrical dead-zone control inputs. The dead-zone input uncertainties in the actuator are introduced by characteristic function. Takagi-Sugeno (T-S) fuzzy system is used to approximate the unknown system function. The proposed method has no need of the a priori knowledge of both the dead-zone's parameters and the bound of the approximation error. Moreover, only one parameter is necessary to be tuned online such that the complexity of the controller is reduced dramatically. The overall adaptive tracking fuzzy control scheme is shown to have asymptotical stability. Simulation results have verified the effectiveness of the adaptive controller.

In this paper, an adaptive fuzzy control problem is studied for a connected automated vehicles platoon subject to unknown dead-zone input and constraints. To better handle the unknown nonlinear dynamical functions and disturbances, the nonlinear dynamics model is transformed to a new model. Then, the fuzzy logic system (FLS) is used to identify the unknown nonlinear functions. A dead-zone inverse technique is introduced to eliminate the negative effects of the unknown dead-zone input nonlinearity. In the framework of backstepping, the tangent barrier Lyapunov function (BLF) is introduced in this paper, and a distributed adaptive fuzzy control scheme is designed so that the position, velocity and acceleration of the vehicle platoon do not violate the given constrained boundaries. Finally, based on the Lyapunov stability theory, it is noted that all signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood of the origin. The effectiveness of the proposed approach is validated by simulation results.

This paper addresses the adaptive visual tracking control problem of an uncalibrated camera robot system with unknown dead-zone inputs. The uncertainties include camera extrinsic and intrinsic parameters, robot dynamic parameters, and feature depth parameters. The control achieves a better performance by establishing a smooth inverse model of the dead-zone input, which eliminates the nonlinear effect of the actuator constraint. A novel adaptive control scheme is presented which does not require a priori knowledge of the parameter intervals of dead-zone model, to update the parameter values online. Furthermore, adaptive laws are provided to estimate the uncertainties that exist both in robot and in camera models. Meanwhile, in order to avoid the singularity of the image Jacobian matrix, a projection algorithm is also introduced. Subsequently, a novel robust adaptive controller together with dead-zone compensation is established so that the tracking error image space converges to the origin. Simulations and experimental studies are conducted to verify the effectiveness of the proposed method.

This paper presents an adaptive iterative learning control (AILC) scheme for a class of nonlinear systems with unknown time-varying delays and unknown input dead-zone. A novel nonlinear form of dead-zone nonlinearity is presented. The assumption of identical initial condition for iterative learning control (ILC) is removed by introducing boundary layer function. The uncertainties with time-varying delays are compensated for by using appropriate Lyapunov-Krasovskii functional and Young's inequality. Radial basis function neural networks are used to model the time-varying uncertainties. The hyperbolic tangent function is employed to avoid the problem of singularity. According to the property of hyperbolic tangent function, 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.

This paper presents an adaptive iterative learning control (AILC) scheme for a class of nonlinear systems with unknown time-varying delays and unknown input dead-zone. A novel nonlinear form of deadzone nonlinearity is presented. The assumption of identical initial condition for ILC is removed by introducing boundary layer functions. The uncertainties with time-varying delays are compensated for with assistance of appropriate Lyapunov-Krasovskii functional and Young’s inequality. The hyperbolic tangent function is employed to avoid the possible singularity problem. According to a property of hyperbolic tangent function, 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 maintaining all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.

An adaptive robust control law is proposed for the course tracking problem of ships in this paper incorporating a Nussbaum function and an auxiliary dynamic system into the adaptive dynamic surface control (DSC) technique. The ship steering dynamics is described by the Norrbin nonlinear model with completely unknown control coefficient, parameter uncertainties, and unknown external disturbances and input saturation caused by the rudder constraint. The Nussbaum function is adopted to deal with completely unknown control coefficient and avoid the controller singularity problem. An auxiliary dynamic system is introduced to handle the effect of input saturation. The DSC technique makes the control law be simple to compute and easy to implement in engineering practice. It is proved that the proposed course tracking control law of ships makes the course tracking error be arbitrarily small by an appropriate choice of the design parameters and guarantees the uniform ultimate boundedness of all signals in the closed-loop ship course control system. Finally, simulation results on two ships and simulation comparison with an existing adaptive neural control scheme demonstrate the effectiveness and the superiority of the proposed control scheme.

In this paper, adaptive neural network control is investigated for single-master-multiple-slaves teleoperation in consideration of time delays and input dead-zone uncertainties for multiple mobile manipulators carrying a common object in a cooperative manner. Firstly, concise dynamics of teleoperation systems consisting of a single master robot, multiple coordinated slave robots, and the object are developed in the task space. To handle asymmetric time-varying delays in communication channels and unknown asymmetric input dead zones, the nonlinear dynamics of the teleoperation system are transformed into two subsystems through feedback linearization: local master or slave dynamics including the unknown input dead zones and delayed dynamics for the purpose of synchronization. Then, a model reference neural network control strategy based on linear matrix inequalities (LMI) and adaptive techniques is proposed. The developed control approach ensures that the defined tracking errors converge to zero whereas the coordination internal force errors remain bounded and can be made arbitrarily small. Throughout this paper, stability analysis is performed via explicit Lyapunov techniques under specific LMI conditions. The proposed adaptive neural network control scheme is robust against motion disturbances, parametric uncertainties, time-varying delays, and input dead zones, which is validated by simulation studies.

Most of the available results on adaptive control of uncertain nonlinear systems with input dead-zone characteristics are for canonical nonlinear systems whose relative degrees are explicit and for which a Lyapunov-based backstepping design is directly applicable. However, those results cannot be applied to noncanonical form nonlinear systems whose relative degrees are implicit and for which a Lyapunov-based backstepping design may not be applicable. This article solves the adaptive control problem of a class of noncanonical neural-network nonlinear systems with unknown input dead-zones. A complete solution framework is developed, using a new gradient-based design which is applicable to noncanonical nonlinear systems with input dead-zones. Signal boundedness of the closed-loop system and the desired tracking performance are ensured with the developed control schemes. Their effectiveness is illustrated by an application example of speed control of dc motors. This article can be readily extended to handle general parametrizable noncanonical nonlinear systems with unknown dynamics and input dead-zones, to solve such an open problem.

Learning‐based robust control methodologies under information constraints

This article investigates the path-following control problem of an autonomous ground vehicle (AGV) with unknown external disturbances and input deadzones. Neural networks are used to estimate unknown external disturbances, dead zones, and nonlinear functions. The minimum learning parameter scheme is employed to adjust the neural network to reduce the computational load. A backstepping control is proposed to facilitate the tracking of the target path. The steady-state path-following error is decreased by adding an integral error term to the backstepping controller. Command filtering is employed to address the explosion of the complexity issue of the conventional backstepping approach, and the filtering error is compensated via an auxiliary signal. Lyapunov stability study indicates that the AGV closed-loop system is bounded by the proposed control with reasonable accuracy. At last, simulations are given to demonstrate the potential of the proposed scheme in path-following control.

In this paper, an adaptive bearing rigid formation control strategy for a class of nonlinear system with unknown dead-zone inputs and external disturbance is proposed. Firstly, the I-Type fuzzy system is used to approximate the unknown nonlinear dynamics of the formation model, and the approximation errors and unknown external disturbance are eliminated by the parameter adaptive estimation. Furthermore, the adaptive dynamic estimation algorithm is utilized to estimate and compensate the unknown dead-zone parameters, effectively suppressing the impact of dead-zone on formation system performance. Finally, the stability of the formation system is proved based on LaSalle’s invariance principle, and the effectiveness of the algorithm is verified by simulation results.

In this paper we focus on the adaptive control of structural acoustics using intelligent structures with embedded piezoelectric (PZT) patches and low cost digital signal processor systems. After a discussion on the adaptive feedforward control scheme, a hybrid adaptive control scheme is proposed, which takes advantage of both feedback control and adaptive feedforward control. The two schemes are realized on a low-cost, small volume, convenient and universal digital signal processing (DSP) board. A carbon fiber reinforced polymer plate with two embedded PZT patches is developed and used in two experiments. The first experiment is adaptive interior noise control using the intelligent plate, in which the adaptive feedforward control scheme is employed. Obvious noise reduction is obtained for constant frequency, swept frequency and varying amplitude harmonic disturbances. The second experiment is adaptive control of sound-induced vibration of the plate, where two embedded PZT patches are used as an actuator and a sensor, respectively, and the hybrid adaptive controller is applied. The full vibration reduction for various harmonic excitations is obtained, verifying the advantage of the hybrid adaptive control. It is demonstrated that active control of structural acoustics can be efficiently achieved by employing intelligent structures, advanced adaptive control schemes and the low-cost DSP board.

In this paper, an adaptive neural output feedback control scheme is proposed for uncertain nonlinear systems that are subject to unknown hysteresis, external disturbances, and unmeasured states. To deal with the unknown nonlinear function term in the uncertain nonlinear system, the approximation capability of the radial basis function neural network (RBFNN) is employed. Using the approximation output of the RBFNN, the state observer and the nonlinear disturbance observer (NDO) are developed to estimate unmeasured states and unknown compounded disturbances, respectively. Based on the RBFNN, the developed NDO, and the state observer, the adaptive neural output feedback control is proposed for uncertain nonlinear systems using the backstepping technique. The first-order sliding-mode differentiator is employed to avoid the tedious analytic computation and the problem of “explosion of complexity” in the conventional backstepping method. The stability of the whole closed-loop system is rigorously proved via the Lyapunov analysis method, and the satisfactory tracking performance is guaranteed under the integrated effect of unknown hysteresis, unmeasured states, and unknown external disturbances. Simulation results of an example are presented to illustrate the effectiveness of the proposed adaptive neural output feedback control scheme for uncertain nonlinear systems.