Robust Adaptive Backstepping Control Research Articles

Robust Adaptive Control Law Design for Enhanced Stability of Agriculture UAV used for Pesticide Spraying

In precision agriculture, such as crop spraying, controlling UAVs presents various challenges such as variable payload, inertial coefficient variation, influence of external disturbances such as wind gusts, and uncertainties associated with the dynamics. To address these challenges, this paper proposes a hybrid control technique that combines higher-order integral sliding mode control, fast-terminal sliding mode control, and adaptive law. The objective is to mitigate the effects of variable payload, external disturbances, and uncertainties while maintaining the stability and performance of the UAV during spraying. Initially, a mathematical model is constructed for a coaxial octocopter UAV that is fitted with a spraying tank. This model takes into account the variation in mass and moment of inertia. Then, a two-loop control structure is employed to attain control of both the translational and rotational axis of the UAV. The numerical simulations are performed on a nonlinear model of the agricultural UAV system and compared with neural network based sliding mode control and robust adaptive backstepping control schemes. The robustness of the proposed scheme is tested in wind gusts and sensor measurement error conditions. Finally, hardware-in-loop simulations are performed using the Pixhawk Orange Cube flight controller to validate the real-time capability of the proposed scheme.

Event‐triggered obstacle avoidance tracking control of quadrotor unmanned aerial vehicle

SummaryThis article addresses the safe tracking control problem of quadrotor unmanned aerial vehicles (QUAV) considering uncertain aerodynamics and unknown external disturbances. First, a robust adaptive backstepping controller is designed, where the bias of the control variable, that is, the tracking error of the attitude subsystem, is considered in the design process of the position subsystem. Meanwhile, the safe obstacle avoidance objective is realized by the quadratic programming (QP) method that combines the tracking controller with the exponential control barrier function (ECBF). Furthermore, an event‐triggered mechanism is used for the QP process to conserve computing resources. Simulation validates the feasibility and superiority of the proposed control scheme in presence of multi‐obstacle.

Robust adaptive backstepping control of H‐bridge inverter based on type‐2 fuzzy optimization of parameters

AbstractA type‐2 fuzzy logic‐based adaptive backstepping control (T2FABSC) approach is designed for an H‐bridge inverter. This inverter has an LC filter to decrease the level of total harmonic distortion (THD) that can affect the efficiency of the system. Reduction of THD and stability insurance of the filter are challenging trade‐offs, tackled here by a controller design. The performance, however, is not suitable for actual applications under a wider range of disturbances, and the parameters need to be adjusted once more for more dependable operations. Backstepping control is given a Lyapunov definition‐based adaptive mechanism that can improve this scheme's stability and robustness in the face of numerous disturbances. Additionally, the system is viewed as a “Black box” without the need for a precise mathematical model, which might lead to a lighter computing burden and simpler implementation. Moreover, a fuzzy type‐2 structure is adopted that can optimize the gains of the adaptive Backstepping controller (ABSC) in challenging conditions. The antlion optimization algorithm is employed to optimize the parameters of the membership functions in the fuzzy system, hence improving the performance of the controller. In addition, compared with different optimization algorithms, it can more quickly and accurately locate the best solutions. Finally, the findings of both the simulations and the experimental outputs are examined, proving the T2FABSC's significant robustness and faster dynamics in a variety of challenging circumstances.

Decentralized robust adaptive backstepping control for a class of non-minimum phase nonlinear interconnected systems

In this paper, a class of interconnected systems is considered, where the nominal isolated subsystems are fully nonlinear and non-minimum phase. A decentralized Extended Kalman Filter-Extended High Gain Observer (EKF-EHGO) is designed to observe the system states. Then, a systematic backstepping design procedure is employed to develop a novel decentralized robust adaptive output feedback control, in which the adaptive law is designed to counter the effects of the interconnections and uncertainties. The proposed decentralized dynamic output feedback control scheme can guarantee that all the signals in the closed-loop system are uniformly ultimately bounded (UUB). Both interconnections and uncertainties are allowed to be unmatched and bounded by an unknown high-order polynomial, which is a more general form when compared with existing work. Two MATLAB simulation examples are used to demonstrate the effectiveness of the proposed method including a system comprising translational oscillator with rotating actuator (TORA) sub-systems.

Adaptive backstepping human-cooperative control of a pediatric gait exoskeleton system with high- and low-level admittance

Post-neurological disorder, passive-assist training disregards human involvement during robot-aided lower-limb rehabilitation. This work presents a novel human-cooperative framework based on the admittance and trajectory control scheme to administer the subject–exoskeleton interaction for pediatric gait rehabilitation. Initially, the mechanical design and dynamic analysis of an existing exoskeleton system are briefly attended. Thereafter, an admittance model is designed in the outer loop, which recasts the desired human trajectory into a reference trajectory. As an inner-loop control scheme, a robust adaptive backstepping controller is designed to trace the reference gait trajectory under parametric uncertainties and external disturbances. Lyapunov stability analysis is solved to guarantee the uniform boundedness of the control signals. Moreover, the well-known problem of “explosion of complexity” and “overparameterization” is avoided through the design of the robust adaptive backstepping control scheme. The performance of the proposed robust adaptive backstepping-based human-cooperative control is studied under the low- and high-level admittance model. Finally, the effectiveness of the proposed control is validated with a variable structure adaptive robust-based human-cooperative control. The co-simulation results show that the proposed control with low-level admittance allows the subject to participate in the training process more frankly. The proposed robust adaptive backstepping-based human-cooperative control tracks the reference gait more promisingly than the variable structure adaptive robust-based human-cooperative control for both admittance levels.

Robust Adaptive Backstepping Motion Control of Underwater Cable-Driven Parallel Mechanism Using Improved Linear Model Predictive Control

This paper proposes a novel motion-tracking control methodology for an underwater cable-driven parallel mechanism (CDPM) that achieves calculation of dynamic tension constraint values, tension planning, parameter linearization, and motion tracking. The control objective is divided into three sub-objectives: motion tracking, horizontal displacement suppression, and cable-tension restriction. A linear model predictive control (LMPC) method is designed to plan cable tensions for motion-tracking and displacement suppression. The robust adaptive backstepping controller converts cable tension into winch speed based on the joint-space method and command filtering. Moreover, the X−swapping method is used to linearize and identify the time−varying nonlinear parameters. An essential prerequisite for restricting cable tension is to obtain cable-tension constraint values. A novel dynamic minimum tension control (DMTC) method, based on the equivalent control concept, is proposed for this aim. The DMTC can adaptively obtain the lower cable-tension threshold through the platform posture and motion status, anchor distribution position, and cable integrity status. Compared to traditional fixed tension constraint values, DMTC can more effectively cope with sudden changes in cable tension than fixed tension constraints. Finally, several simulations are carried out to verify the effectiveness and robustness of the proposed approach.

Accurate Parking Control for Urban Rail Trains via Robust Adaptive Backstepping Approach

Nowadays, precise train parking has become a key technology of automatic train operation. Due to the high nonlinearities and various uncertainties existing in the dynamics of urban rail trains (URTs), it is challenging to develop an effective parking controller to achieve high-precision parking. To address this issue, a novel robust adaptive backstepping controller is proposed in the paper, where a robust term is employed to compensate for the system uncertainties caused by the brake shoe, and meanwhile several parametric adaption laws are equipped to estimate the uncertain system parameters as well as the external disturbances. The closed-loop stability of the controlled system is analyzed rigorously by virtue of the Lyapunov theory, and the effectiveness of the proposed control scheme in precise parking of URTs is demonstrated through numerical simulations.

Robust adaptive backstepping control for a lower-limb exoskeleton system with model uncertainties and external disturbances

ABSTRACT The main purpose of this work is to design a robust adaptive backstepping (RABS) control strategy for a pediatric exoskeleton system during passive-assist gait rehabilitation. The nonlinear dynamics of the exoskeleton system have ill-effects of uncertain parameters and external interferences. In this work, the designed robust control strategy is applied on the exoskeleton to assist children of 08–12 years, 25–40 kg weight, and 115–125 cm height. The dynamic model of the coupled human-exoskeleton system is established using the Euler–Lagrange principle. An appropriate Lyapunov function is selected to prove the uniform boundedness of the control signals. The “explosion of terms” is avoided by establishing a virtual control law without the dynamical system parameters. A Microsoft Kinect-LabVIEW experiment is carried out to estimate the desired gait trajectory. The robustness of the proposed control is validated by varying the limb segment masses and inducing the periodic external disturbances. The proposed control strategy is compared with the decentralized modified simple adaptive-PD (DMSA-PD) control strategy. From simulation results and performance improvement index, it is observed that RABS control outperforms the contrast control (DMSA-PD) to track the desired gait during passive-assist rehabilitation under the effect of model uncertainties and external disturbances.

Robust NN‐based backstepping control of non‐affine ferry ship fuel cell‐based DC MGs under stochastic disturbance inputs

Fossil fuels play a significant role in the automobile industry, as well as marine vessel systems, with a lot of benefits like high-density and low-cost power supply, which is relatively easy to reserve, apply and carry. However, fossil fuel combustion produces several emissions such as CO2, which become greenhouse gas emissions and harmful to human health. One of the most favorable emission-free modern technologies is fuel cells, which can be applied to supply power to marine vessel propulsion systems. In such a most electrified ship, the whole of the shipboard grid can be regarded as a direct current (DC) stand-alone microgrid (MG) configuration with linear resistive and nonlinear constant power loads (CPLs). The main challenge in this new configuration of the shipboard MG is stabilizing the system's currents and voltages, subjected to stochastic disturbances arising from the effect of external winds and waves. Hence, the key objective of this research is to introduce a new modified robust adaptive stochastic backstepping controller, which is equipped with an artificial neural network, for stabilizing the current and voltage of the DC MG. The developed approach is robust against uncertainties and disturbances, has a systematic design procedure, and offers a low computational burden compared to the other complicated nonlinear controllers. In the end, a simulation is run for investigating the performance of the proposed controller over the state-of-the-art methods.

Extended sliding mode observer based robust adaptive backstepping controller for electro-hydraulic servo system: Theory and experiment

This paper firstly presents an extended sliding mode observer (ESMO) for the electro-hydraulic servo systems (EHSSs) to deal with nonlinear factors like the external disturbance, parameter uncertainties as well as unmodeled characteristics in the EHSS. The model for the EHSS is established by taking these nonlinear factors into consideration and then the statespace representation is obtained. According to the state space, the ESMO for the EHSS is presented, the equivalence principle is properly utilized to simplify the ESMO and some saturation functions are employed to eliminate high frequency interferences caused by the chattering phenomenon. Based on estimated values from the ESMO, a robust adaptive backstepping controller (RABC) is presented in detail with taking some parameter uncertainties into consideration to further improve the tracking performance. The proposed controller has the following advantages: (1) utilizing the ESMO to cope with these nonlinear factors; (2) parameter online adaptive laws are employed in the RABC design to further improve the tracking performance. In order to verify the performance of the proposed controller, an experiment bench was established. Two sine waves reference signal (one amplitude 0.01 m, 1 Hz; the other 0.015 m, 2 Hz) are employed to verify the performance of the controller. Comparative experimental results show that: (1) the tracking performance of the proposed controller is better than that of a DOs based BC, a BC and a PI controller; (2) estimation values from the ESMO contains fewer noise than two conventional disturbance observers (DOs), which will decrease the control input ripples.

On Controller Design for Nonlinear Systems With Pure State Constraints

This brief is concerned with a new problem of designing a robust adaptive backstepping controller for nonlinear systems where state constraints are an explicit function of time and state variables, i.e., pure state constraints. Furthermore, a disturbance observer is designed to cope with the disturbances in the systems. Finally, a numerical example is demonstrated to show the efficacy of the proposed theoretical results.

Robust adaptive backstepping control of uncertain fractional-order nonlinear systems with input time delay

In the present work, a fractional adaptive backstepping control approach is proposed for controlling a class of uncertain fractional-order nonlinear systems subjected to unknown external disturbance and input delay. In control design, by introducing fractional command-filter, the key issue of the common backstepping method called the “explosion of complexity” is addressed. Furthermore, the Szász–Mirakyan operator is used as a simple but efficient universal approximator to approximate uncertain or unknown terms and reduce the design complexity. In addition, to enhance the capability of the proposed controller in dealing with the approximation error and the unknown disturbance, an efficient robust control term is also incorporated into it. One advantage of the suggested control approach is that the input-delay fractional-order system is effectively treated by introducing a new variable as a non-delayed fractional-order system. The other advantage is that the number of tuning variables is considerably low; specifically, for an n-order fractional nonlinear system, only n adaptive parameters are adjusted online. This makes the implementation of the proposed approach simpler. The Lyapunov stability theorem is used to prove that all of the closed-loop system’s signals are semi-globally uniformly ultimately bounded. The feasibility of the suggested control approach is shown by comparing the simulation results obtained with the fuzzy system.

Robust neural network‐based backstepping landing control of quadrotor on moving platform with stochastic noise

AbstractThis article introduces a novel nonlinear control approach for quadrotor landing on a moving ship. The dynamics of the relative position and attitude dynamics with uncertainties, unmodeled dynamics, external disturbances, and control input saturation is derived. Then, a novel robust adaptive constrained backstepping control law for the propeller and torques of the quadrotor is designed. To deal with uncertainties and un‐modeled dynamics, radial basis function is employed. The bounded‐in‐probability stability is used to alleviate the destructive influence of the stochastic Wiener process on the system positions and attitudes. Whereas the quadrotor is under‐actuated, a redundant control input technique, which affects the attitude commands, is presented. The actual control input saturation limits are turned into unknown saturation limits of the redundant control inputs. Also, since two phases for the landing problem are considered, a smooth switching mechanism between the control inputs is developed. Simulation results show the merits and applicability of the developed robust adaptive nonlinear controller.

Dynamic positioning of ship using backstepping controller with nonlinear disturbance observer

This paper studies the adaptive dynamic positioning control problem of the full-actuated ship with uncertain time-varying environmental disturbances. Considering the disturbances with unknown boundaries, the inversion control technique is combined with the disturbance observation compensation method to design the robust adaptive backstepping control law of the ship dynamic positioning system. The Lyapunov function is adopted to prove the errors of the ship’s position and heading angle are uniformly ultimately bounded using the designed control law. The nonlinear disturbance observer can adaptively estimate and compensate for uncertain external disturbances caused by winds, waves and currents. Afterward, the verification of the proposed controller through a typical CyberShip Ⅱ model subject to environmental disturbances is carried out using a hardware-in-the-loop simulation where a thrust distribution model is established. The simulation results show the effectiveness of the proposed control law.

Optimal robust adaptive fuzzy backstepping control of electro-hydraulic servo position system

In this paper, an optimal robust adaptive fuzzy backstepping control is presented to the position control of the electro-hydraulic servo (EHS) system in the presence of structured and unstructured uncertainties. Initially, the robust control using the backstepping technique is presented to overcome the existing uncertainties in the dynamic equations. Mathematical proof demonstrates that the closed-loop system in the presence of uncertainties has a global asymptotic stability. Then, to overcome the chattering problem, a very simple fuzzy approximator is presented where it approximates the bounds of the uncertainties. Although the proposed robust fuzzy backstepping control has a desirable performance, it has no mathematical analysis to prove the stability of the closed-loop system. Therefore, to solve this problem, the proposed fuzzy approximator has been transformed into a one-law adaptive fuzzy approximator with a single-input single-output fuzzy rule. Mathematical analysis illustrates that the closed-loop system in the presence of uncertainties has a global asymptotic stability under the proposed robust adaptive fuzzy backstepping control. Furthermore, a novel modified harmony search algorithm (MHSA) has been developed, by using the original harmony search algorithm (OHSA) as an optimization technique, to achieve the optimal values of the membership functions and the control coefficients. Finally, a comparative study has been conducted between the proposed control scheme under the MHSA and the OHSA, and other existing advanced control approaches to verify the effectiveness of the proposed control. Results show that the proposed control scheme under the MHSA can suppress the chattering problem and reduce the disturbances effectively while ensuring that the performance is tracked.

Disturbance-Rejection-Based Optimized Robust Adaptive Controllers for UAVs

Most applications for small unmanned aerial vehicles (sUAVs) have a critical need for appropriate position and attitude control in environments with extreme external dynamic disturbances such as wind gusts. Moreover, to maximize flight time, UAVs have to operate within strict constraints on payload and under computational efficiency. This article presents an optimized robust adaptive controller for a UAV in the presence of realistic wind gusts that are flying in an urban environment at an altitude lower than 400 ft. The position controller is based on two degree-of-freedom proportional-integral-derivative controller tuned with particle swarm optimization, while the attitude controll is based on a robust adaptive integral backstepping controller. By assuming the knowledge of the predetermined limits of the external and unstructured disruptions (for example, wind gusts) at low altitude, a guaranteed quality of transient and steady-state tracking performance were attained. The aerodynamics, wind gust model, and control modules are integrated into a six-degree-of-freedom UAV with a fully nonlinear robust adaptive controller. Optimal power is obtained for UAVs using the radial inflow model in the presence of wind gusts that are compared with the simplified model. Two case studies were performed systematically for two representative flight paths, namely, up-cruise-down and circular paths. The simulation results demonstrate the robustness and adaptive property of controllers against wind gusts. These results are useful for a variety of UAV applications, e.g. accurate trajectory tracking and autonomous waypoint navigation without loss of performance in the presence of wind disturbances under computational efficacy.

Robust adaptive control of hypersonic flight vehicle with asymmetric AOA constraint

This paper investigates the state-constrained controller design of a hypersonic flight vehicle (HFV) based on an asymmetric barrier Lyapunov function (ABLF). The robust adaptive back-stepping controller with integral terms is applied for the HFV longitudinal dynamics. Considering the asymmetric angle of attack (AOA) constraint caused by the unique structure and scramjet, the controller is modified by constructing an ABLF, where the asymmetric constraint on AOA tracking error is introduced. Combined with the constraint on virtual control, the AOA is restricted to a predefined asymmetric interval. The system stability and the AOA constraint are guaranteed via Lyapunov analysis. Simulation results verify that the AOA can be kept in the given asymmetric interval while the altitude reference signal is tracked.

DESIGNING A ROBUST ADAPTIVE TRACKING BACKTEPPING CONTROLLER CONSIDERING ACTUATOR SATURATION FOR A WHEELED MOBILE ROBOT TO COMPENSATE UNKNOWN SLIPPAGE

This article highlights a robust adaptive tracking backstepping control approach for a nonholonomic wheeled mobile robot (WMR) by which the bad problems of both unknown slippage and uncertainties are dealt with. The radial basis function neural network (RBFNN) in this proposed controller assists unknown smooth nonlinear dynamic functions to be approximated. Furthermore, a technical solution is also carried out to avoid actuator saturation. The validity and efficiency of this novel controller, finally, are illustrated via comparative simulation results.

Adaptive Robust Neural-Network-Based Backstepping Control of Tethered Satellites With Additive Stochastic Noise

This article introduces a new method for mitigating the fluctuations of a two-body tethered satellite system (TSS). Initially, a state-space representation of the TSS is derived from the extended Lagrange method; and, due to the uncertainties, unmodeled dynamics, and external disturbances exist in the TSS modeling, a novel robust adaptive backstepping controller is proposed. The presented approach utilizes the radial basis function (RBF) to estimate online the unmodeled dynamics and the uncertainties of the system and the concept of the bounded in probability to minimize the effect of the stochastic Weiner process on the system angles. Due to the special structure of the TSS, the angles dynamics of the TSS are stabilized separately, which simplifies the design procedure. Through the Lyapunov stability and the Ito concept, the tracking error is assured to be bounded in probability and the error dynamics of the RBF neural network estimated weights are bounded in the Lyapunov sense. The proposed controller is applied to the nonlinear TSS for two cases of nominal and uncertain perturbed systems. Simulation results verify the applicability and effectiveness of the proposed controller in eliminating the tether libration for the nondisturbed system and decreasing the tether libration for the disturbed system.

Robust adaptive dynamic surface back-stepping tracking control of high-order strict-feedback nonlinear systems via disturbance observer approach

In this study, we propose an adaptive tracking dynamic surface back-stepping control based on Nussbaum disturbance observer for uncertain high-order strict-feedback MIMO nonlinear systems with external disturbances, unknown parameters and modelling uncertainties. It is assumed that the control action is affected by input saturation; so to compensate the resulted undesirable effects, the tanh(.) function is used as an approximation to the saturation function. To tackle the unknown external disturbances and uncertainties, a Nussbaum disturbance observer is proposed. Moreover, an appropriate adaptive law is presented to deal with the unknown parameters. Then, the dynamic surface control method is used to overcome the inherent problem ‘explosion of complexity’ that appeared in the conventional back-stepping method. The Lyapunov stability analysis proves that the closed-loop system is semi-globally uniformly bounded. At last, reasonable effectiveness and applicability of the adaptive tracking dynamic surface control are illustrated by simulation results.