Adaptive Backstepping Control for a Class of Nonlinear Uncertain Systems using Fuzzy Neural Networks

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.

In oil and gas drilling engineering, the anti-phase synchronization of two co-rotating rotors in a tri-motor vibration system is easy to implement owing to its inherent coupling characteristics, which can lead to the exciting force generated by the vibrating system being very small. Thus, an adaptive back-stepping control strategy is proposed to apply in a tri-motor vibrating system and improve the processing capacity of drilling fluid shaker screens. The algorithm developed in this paper is that a complex higher-order nonlinear system is simplified into lower-order subsystems by the adaptive back-stepping control theory, and then the adaptive law for varying load torque is derived by combining with the adaptive theory to regulate the velocity of motors in a closed loop. Firstly, a dynamical model to describe the tri-motor vibration system is established, and the dynamical equations of the vibrating system are derived based on the Lagrange equation. Then, the speed error controller and the phase difference error controller are designed by combining the adaptive back-stepping control algorithm with the master–slave control (MSC) structure. According to Barbalat’s lemma, the stability of the control system is analyzed to verify the feasibility of the control method. Finally, the dynamical equations of the vibrating system are used to establish an electromechanical coupling control model of a tri-motor driven planar system through the Runge–Kutta method, and it verified the reliability of the control strategy, the robustness, and the stability of the control system, respectively, and intuitively revealed the synchronization characteristics of tri-motor vibration control system. The results demonstrate the phase difference among the three motors can be accurately stabilized at zero by a phase synchronization control strategy based on the adaptive back-stepping control method, and the method is simple and fast-speed and the control system has better robustness.

To improve position tracking performance of servo systems, a position tracking control using adaptive back-stepping control(ABSC) scheme and recurrent fuzzy neural networks(RFNN) is proposed. An adaptive rule of the ABSC based on system dynamics and dynamic friction model is also suggested to compensate nonlinear dynamic friction characteristics. However, it is difficult to reduce the position tracking error of servo systems by using only the ABSC scheme because of the system uncertainties which cannot be exactly identified during the modeling of servo systems. Therefore, in order to overcome system uncertainties and then to improve position tracking performance of servo systems, the RFNN technique is additionally applied to the servo system. The feasibility of the proposed control scheme for a servo system is validated through experiments. Experimental results show that the servo system with ABS controller based on the dual friction observer and RFNN including the reconstruction error estimator can achieve desired tracking performance and robustness.

This study aims to address the inherent uncertainty in plug loads and load extraction, distributed generation, and the inevitable circulating current in a parallel structure. Therefore, in this paper, an adaptive backstepping control scheme with an online parameter estimator (OPE) for a plug-and-play parallel converter system in a four-port power switcher is proposed. The adaptive backstepping control method was designed in the dq0 coordinate system to suppress the circulating current in the zero-component; the circulating current can be suppressed by using an embedded algorithm and omitting the extra controller. An adaptive update law was designed to weaken the influence of the arbitrary plug and extraction operations in the DC and AC buses to realize the plug-and-play function. The transient tracking performance is governed by the limitation of maximum total errors in the voltage and current. As a result, the settling times of the voltage, current, and power decreased. Additionally, to further improve the system robustness, an online inductance and resistance estimator was established using an optimal algorithm that solves the weighted least squares problem. In the estimator, there are no additional voltage and current sensors needed, and the mean squared error (MSE) of the estimation can be minimized. Simulation studies on a two-converter parallel system with a plug-and-play function were conducted using MATLAB/SIMULINK (R2018b, MathWorks, Natick, MA, USA) to verify the effectiveness of the proposed adaptive backstepping control strategy. The results show that this strategy improves system performance over that of a system with unbalanced parameters among a parallel structure with AC and DC system disturbances caused by arbitrary plug and extraction operations.

In this paper, an adaptive backstepping control scheme is proposed for a class of nonlinear systems with unknown time delay. The unknown time delay in the system depends on all system states, which will inevitably destroy the triangular structure of the control system. Therefore, traditional backstepping can not be used to design the controller. In order to overcome the problem caused by “non-triangular structure”, we construct a linear projection between the state vector and its transform in controller design. Using inequality and adaptive backstepping control, we compensate the uncertainties caused by unknown time delays. Finally, the simulation results show that the proposed algorithm is effective.

A neural network (NN)-based backstepping adaptive control is proposed for the stabilized platform system of shipborne weapons (SPOSW) with uncertain nonlinear friction torque and load disturbance. First, with the using of NN approximator, an equivalent model is developed. Where the NN is used to estimate the uncertain nonlinear friction torque. Then, based on the equivalent model, address the problem of reconstruction error and disturbance load, an adaptive backstepping control scheme is proposed for the stabilized platform system. Moreover, the analysis of stability can be completed by Lyapunov stability theory, and the convergence rate of the tracking error can be governed by the choice of the control parameter values. Finally, to demonstrate the effectiveness of the proposed control scheme, simulation results are illustrated.

This article presents a new command-filtered composite adaptive neural control scheme for uncertain nonlinear systems. Compared with existing works, this approach focuses on achieving finite-time convergent composite adaptive control for the higher-order nonlinear system with unknown nonlinearities, parameter uncertainties, and external disturbances. First, radial basis function neural networks (NNs) are utilized to approximate the unknown functions of the considered uncertain nonlinear system. By constructing the prediction errors from the serial-parallel nonsmooth estimation models, the prediction errors and the tracking errors are fused to update the weights of the NNs. Afterward, the composite adaptive neural backstepping control scheme is proposed via nonsmooth command filter and adaptive disturbance estimation techniques. The proposed control scheme ensures that high-precision tracking performances and NN approximation performances can be achieved simultaneously. Meanwhile, it can avoid the singularity problem in the finite-time backstepping framework. Moreover, it is proved that all signals in the closed-loop control system can be convergent in finite time. Finally, simulation results are given to illustrate the effectiveness of the proposed control scheme.

In this article, a fuzzy-approximation-based adaptive backstepping control method for dual-arm of a humanoid robot was proposed. The purpose of this control system is to provide coordinated movement assistance to enable the humanoid robot’s human-like forearm to grab objects coordinately (or track any continuous desired trajectory), even in the presence of environmental disturbances and parametric uncertainties. We analyze the proposed adaptive backstepping by mathematical modeling and actually measure the robot dual-arm motion information of a number of case when they simulate the trajectory to verify the model. We design the adaptive fuzzy-approximation control strategy and combining the synthesis of the robust design, backstepping control, and Lyapunov function method, the proposed adaptive fuzzy backstepping control does not need to know the humanoid robot’s arms model precisely. In the control system proposed here, once the desired trajectories of the robot’s dual-arm positions are given, the adaptive fuzzy system was closed to any unknown functions and to the derivative of the virtual control law of the humanoid robot system. In this case, a robust design scheme was utilized to compensate for any approximation errors. With the proposed trajectory tracking, not only able to generate the coordinate motions for a humanoid robot’s two arms, but it can also control the arms to move to the desired positions. The proposed closed-loop system under the adaptive fuzzy backstepping control design was effective and that asymptotic stability was successfully achieved. The adaptive fuzzy-approximation backstepping control strategy should be more complete and intelligent and more actual test should be conducted to further evaluate the effect of the proposed trajectory tracking. The instability of dual-arm of humanoid robot system is systematically analyzed and a backstepping control strategy based on the adaptive fuzzy-approximation to improve the continuity of trajectory tracking of the robot’s arms is proposed.

Robust adaptive integral backstepping control for opto-electronic tracking system based on modified LuGre friction model

ABSTRACTQuick and timely fault detection is of great importance in control systems reliability. Undetected faulty sensors could result in irreparable damages. Although fault detection and isolation (FDI) methods in control systems have received much attention in the last decade, these techniques have not been applied for some classes of nonlinear systems yet. This paper deals with the issues of sensor fault detection and isolation for a class of Lipschitz uncertain nonlinear system. By introducing a coordinate transformation matrix for states and output, the original system is first divided into two subsystems. The first subsystem is affected by uncertainty and disturbance. The second subsystem just has sensor faults. The nonlinear term is separated to linear and pure nonlinear parts. For fault detection, two sliding mode observers (SMO) are designed for the two subsystems. The stability condition is obtained based on the Lyapunov approach. The necessary matrices and parameters are obtained by solving the linear matrix inequality (LMI) problem. Furthermore, two sliding mode observers are designed for fault isolation. Finally, the effectiveness of the proposed approach is illustrated by simulation examples.

Based on backstepping technique, an adaptive inverse control scheme is proposed for a class of uncertain nonlinear systems preceded by unknown hysteretic nonlinearities which are described by Krasnosel'skii-Pokrovkii (KP) model. The pseudo-inversion is introduced to compensate the hysteresis nonlinearities and the error caused by the hysteresis model and pseudo-inversion is estimated online by the adaptive controller. To avoid the possible chattering caused by the sign function, a smooth adaptive controller is designed. The proposed controller ensures the uniformly ultimate boundedness of the closed-loop system. Simulation results show the effectiveness of the proposed scheme.

In this article, we consider the adaptive fractional-order backstepping control problem for a class of high-order integer-order systems with uncertainties and unknown external disturbance. To obtain enhanced control performance, fractional-order calculus is integrated within the conventional backstepping controller design procedure. Theoretical proof is provided based on the Lyapunov stability theorem to ensure the global stability of the closed-loop system in the sense that all the closed-loop signals are uniformly ultimately bounded and the output tracking error to a reference signal converges to an adjustable arbitrarily small range by tuning certain design parameters. Both numerical simulation and experimental results verify the efficacy of the proposed adaptive fractional-order backstepping control scheme.

This article aims at proposing an adaptive neural control strategy for a class of nonlinear time-delay systems with input delays and unknown control directions. Different from previous researches that investigated delays and constraints separately, the novelty of this article lies in that it simultaneously considers delays (state and input delays) and input constraints (magnitude and rate constraints) for a class of uncertain nonlinear systems. In this article, the uncertain states and input delays are handled by integrating a constructed auxiliary system that functions as an observer with neural networks (NNs), with which the adverse effects caused by the uncertain states and input delays can be approximated and compensated. By involving smooth hyperbolic tangent functions in the designed auxiliary system, the problem of magnitude and rate constraints of the control input is fully addressed. Then, the backstepping technique runs through the entire control designing process, which allows the designed adaptive neural control strategy to handle the input constraints and delays at the same time. Furthermore, Nussbaum functions are employed to resolve the problem of unknown control directions. Due to the introduction of an input-driven filter, only the output of the system is required to be measured as the control feedback, which promotes the applicability of the designed controller. Under the proposed control scheme, semiglobal, uniform, and ultimate boundedness of all signals of the closed-loop system is realized with uncertain control directions, input and state delays, and guaranteed magnitude and rate constraints of control inputs. Finally, simulation results are illustrated to verify the effectiveness of the presented control method.

Cascade control for a class of uncertain nonlinear systems: a backstepping approach

Command-filter-based adaptive tracking control for nonlinear systems with unknown input quantization and mismatching disturbances