Robust Tracking Control Research Articles

Decoupled robust backstepping tracking control for variable stiffness actuated robot with input saturation

Due to the energy storage and release capability introduced by stiffness adjustment, a variable stiffness actuator is essential to achieve human-like energy efficiency for robots. However, it is not trivial to control the strongly coupled and nonlinear system, especially with highly dynamic stiffness variation. In this work, decoupled and robust command filtered backstepping tracking controllers for position and stiffness are proposed. Furthermore, a disturbance observer is introduced to estimate the lumped disturbances caused by directly decoupled dynamics and unmodeling errors. Since the input control torques can be easily saturated due to limited deformation of elastic elements, anti-windup compensation is introduced into the tracking control laws to reduce its negative influence. Thus, by combining the command filtered backstepping controller, disturbance observers, and anti-windup compensation, the stability proof of the proposed composite controller is provided. The tracking control performance is validated through simulations of multi-DoF variable stiffness actuated robots.

Robust Data-Driven Compensation Iterative Learning Consensus Tracking Control for MIMO Multiagent Systems With Random Packet Dropouts

Robust Data-Driven Compensation Iterative Learning Consensus Tracking Control for MIMO Multiagent Systems With Random Packet Dropouts

Modified Smith predictor-based robust tracking control design for fractional-order singular semi-Markovian jump systems

This paper focuses on addressing the robust tracking control problem as well as the compensation of delay and external disturbances for fractional-order singular semi-Markovian jump systems. Moreover, a multi-periodic modified repetitive control scheme is developed to guarantee the exact tracking performance of the considered system. Subsequently, by implementing the Majhi-Atherton modified Smith predictor approach, input delays and disturbances occurring in the addressed system are compensated. Precisely, the incorporation of disturbance estimator with the conventional Smith predictor frame can accurately estimate and attenuate the external disturbances. Further, the linear matrix inequality-based conditions for ascertaining the required results are procured with the aid of Lyapunov stability theory. Following this, by solving the acquired criteria, the precise framework of the gain matrices can be reckoned. Finally, the effectiveness and supremacy of the suggested control approach are assessed by using the outcomes of simulations obtained from two numerical examples.

Robust bilinear tracking control of a parabolic trough solar collector via saturation

This paper investigates the problem of robust tracking control of heat transport in a Parabolic Trough Solar Collector (PTSC), where the output has to track a desired reference trajectory. In this work, the PTSC is modeled by state-space bilinear dynamics. The manipulated variable is the pump volumetric flow rate, and the source term, i.e., solar irradiance, is assumed to be unmeasured. In addition, the actuator’s physical constraints induce saturation bounds on the manipulated variable and need to be considered explicitly in the controller design. To deal with these challenges, we first propose a saturated state-feedback law that meets the control objectives. Then, we reconstruct the unknown time-varying source term using an adaptive estimator. Later, through Lyapunov stability analysis, we prove that the closed-loop system and the output tracking error are uniformly ultimately stable. Numerical simulations attest to the performance of the proposed control strategy.

Approximation-Free Robust Tracking Control of Unknown Redundant Manipulators With Prescribed Performance and Input Constraints

Approximation-Free Robust Tracking Control of Unknown Redundant Manipulators With Prescribed Performance and Input Constraints

Adaptive Robust Tracking Control With Active Learning for Linear Systems With Ellipsoidal Bounded Uncertainties

Adaptive Robust Tracking Control With Active Learning for Linear Systems With Ellipsoidal Bounded Uncertainties

Distributed robust tracking control for multiple unmanned aerial vehicles: theory and experimental verification

The distributed trajectory tracking problem for multiple UAVs under unknown external disturbance is investigated. A new nonlinear robust trajectory tracking strategy for multiple UAVs is proposed. The dynamic model for the UAVs' formation is illustrated in the Tangent frame. For the trajectory tracking problem, a Robust formation tracking control strategy based on robust integral of the signum of error (RISE) is designed to compensate for the effects of unknown external disturbances, which improves the robustness of the UAVs' formation system. Based on the Lyapunov stability analysis, it is proved that the global asymptotic convergence of the coordination errors and the semi-global asymptotic convergence of the UAVs' position tracking errors are achieved. The proposed formation control strategy is validated via real-time experiments that are performed on the self-build UAVs' formation flight control testbed. Flights without wind disturbance and flights with disturbance are all performed. The performance comparison experiment with the conventional sliding mode control algorithm is performed. The experimental results show that the designed control strategy can achieve good coordinated trajectory tracking of multiple UAVs, and has better control performance compared with normal sliding mode control law.

Iterative learning robust security predictive tracking control for small delay batch processes: Deception attacks on unreliable network channel

During the batch process, the need for security control is becoming increasingly urgent with the gradual penetration of network control technology. For small time delay batch processes subject to deception attacks, an iterative learning robust security predictive tracking control approach is developed. Reviewing previous studies for iterative learning control, the issue that the repetitive character of the batch process would mask the characteristics of deception attacks was not considered. Moreover, the gains of iterative learning control law are utilized offline, which makes large deviations for the system state as the operating time increases. This will lead to “excessive-input” conditions for control inputs, which means more consumption of energy and production resources. To address these challenges, we introduce robust security invariant sets to improve the robustness of the system by constraining the system state to be in a safe range. Also, the design of the iterative learning controller incorporates deception attack data for historical batches, which is continuously improved and optimized to withstand deception attacks. Meanwhile, by calculating stability conditions online, the real-time control law gain is obtained, which could make the control inputs adjusted online based on the real-time system’s dynamic characteristics, avoiding excessive inputs and improving the efficiency of energy and resource utilization. Additionally, the stability analysis proves that the system is input to state stability. Ultimately, simulation verifies the effectiveness and feasibility of the developed method.

Robust Formation Tracking Control for Noncooperative Heterogeneous Multiagent Systems.

The robust formation tracking problems (FTPs) are investigated for noncooperative heterogeneous multiagent systems (MASs). The parameters and state dimensions of each agent in the MASs can be heterogeneous. The leader is noncooperative and has an unknown external input. The followers are affected by uncertainties and disturbances. A distributed extended state observer is designed to estimate the leader's state and the unknown external input. Then a robust formation tracking control method is proposed. It turns out that the output formation tracking error can reduce to any size neighborhood near the origin by selecting appropriate parameters. Finally, the effectiveness of the proposed observer and controller is demonstrated by a numerical simulation example and a hardware-in-the-loop (HITL) simulation example.

Fully distributed prescribed time robust synchronous tracking control of multi-unmanned systems under communication link faults

Fully distributed prescribed time robust synchronous tracking control of multi-unmanned systems under communication link faults

Development of autonomous navigation system based on neural network and visual servoing for row-crop tracking in vegetable greenhouses

Accurate navigation line localization strategy and robust path tracking control scheme are two key techniques for advancing precision agriculture and enhancing the sustainability of smart farms. In this paper, a superior and cost-effective autonomous navigation system for a visual servoing-based agricultural vehicle in the greenhouse scenario with a distinct layout of two crop rows in each ridge is presented. First, based on image segmentation techniques, a neural network model named DGLNet integrating recognition of crop rows and prediction of the effective area of the navigation line is designed. The linear equation of the navigation line we required is obtained through post-processing operations of linear fitting completed in the effective area. According to experimental results, directly teaching the neural network to learn navigation line localization features utilizes the semantic and spatial information in the feature map to establish a stronger relationship between crop rows and the navigation line, which greatly improves the generalization of the navigation line localization in the case of large-angle yaw scenarios without additional training datasets. In addition, the performance of the network is significantly enhanced by adding an attention mechanism in the backbone based on U-Net. Subsequently, a dataset of cabbage vegetable images covering a wide range of complexities in the greenhouse scenario is created, and is available to support future academic research now. Further, a path tracking control scheme based on point-feature and line-feature is proposed, which can control the agricultural vehicle using the information from camera images without the need to perform explicit localization or maintain a global map. Finally, extensive field experiments have been carried out to show that this autonomous navigation system can preserve the stability of the vehicle and ensure timely convergence of deviations in different complex scenarios, which indicates that this control scheme is reliable and robust. Meanwhile, benefit from the efficiency of this recognition algorithm and the unnecessity of the complete representation of the path in the control scheme, the system has high real-time performance in every scenario.

Automatic Overtaking Path Planning and Trajectory Tracking Control Based on Critical Safety Distance

The overtaking process for autonomous vehicles must prioritize both efficiency and safety, with safe distance being a crucial parameter. To address this, we propose an automatic overtaking path planning method based on minimal safe distance, ensuring both maneuvering efficiency and safety. This method combines the steady movement and comfort of the constant velocity offset model with the smoothness of the sine function model, creating a mixed-function model that is effective for planning lateral motion. For precise longitudinal motion planning, the overtaking process is divided into five stages, with each stage’s velocity and travel time calculated. To enhance the control system, the model predictive control (MPC) algorithm is applied, establishing a robust trajectory tracking control system for overtaking. Numerical simulation results demonstrate that the proposed overtaking path planning method can generate smooth and continuous paths. Under the MPC framework, the autonomous vehicle efficiently and safely performs automatic overtaking maneuvers, showcasing the method’s potential to improve the performance and reliability of autonomous driving systems.

Robust Adaptive Fuzzy Control for Second-Order Euler-Lagrange Systems With Uncertainties and Disturbances via Nonlinear Negative-Imaginary Systems Theory.

Ensuring robust and precise tracking control in the presence of uncertain multi-input-multi-output (MIMO) system dynamics and environmental variations is a significant challenge in the field of robust and adaptive control theory. While fuzzy control strategies have demonstrated good tracking performance in normal conditions, designing and tuning fuzzy controllers can be a challenging task in highly uncertain environments. In this study, we investigate a novel approach that combines robust nonlinear negative-imaginary (NI) systems theory with a self-adaptive fuzzy control scheme and the Lyapunov synthesis to develop a robust adaptive negative-imaginary-fuzzy (RANIF) control scheme. We optimize the critical parameters of the proposed fuzzy system using a self-tuning technique with a proportional-derivative sliding manifold. Furthermore, unlike the existing adaptive fuzzy control methods, we propose a small number of membership functions and systematically derive the fuzzy rules by employing Lyapunov, nonlinear NI, and dissipativity theories, which simplify the tuning process, work out the matter of "explosion of complexity," and reduce computational complexity. We demonstrate the global stability of the closed-loop system using nonlinear NI theory. To evaluate the effectiveness of our proposed approach, we present simulation results for two examples involving uncertain MIMO second-order Euler-Lagrange systems. These systems, known for their capacity to represent a diverse range of practical physical systems, serve as suitable testbeds for our methodology. Our results show that RANIF outperforms other control methods, such as nonlinear strictly NI-Fuzzy, fuzzy-logic control, model predictive control, and conventional PID control, in terms of robustness to disturbances and inestimable faults, trajectory tracking performance, and computational complexity.

Lyapunov-based robust model predictive tracking controller design for discrete-time linear systems with ellipsoidal terminal constraint

In this article, a robust model predictive control (MPC) method is introduced based on Lyapunov-theory to control the discrete-time uncertain linear systems due to external disturbances. The structure of the proposed controller consists of two parts designed based on the offline/online schemes. In the offline-scheme, an H ∞ -based robust tracking controller is provided to satisfy the robust and tracking performance. Based on the H ∞ performance, a new linear matrix inequality problem is developed to calculate the offline-controller gains. By considering the Lyapunov-function of the offline-controller as the terminal cost of the MPC and the designed offline-controller, the online optimisation problem (OOP) is structured. This means, the MPC is designed based on the stabilised system to satisfy the physical limitations of the overall controller and the system states. Moreover, to improve the feasibility problem of the OOP, an ellipsoidal terminal constraint is added to the proposed MPC problem. Therefore, compared with the existing min–max MPC and tube MPC, the advantages of the overall controller are feasibility improvement and reducing the computational complexity with less conservatism while the robustness against parametric uncertainties and disturbances is achieved. Two simulation examples are employed to show the superiorities of the proposed robust MPC.

Fault-tolerant control of underactuated unmanned surface vessels in presence of deception and injection attacks

This paper studies the trajectory tracking control problem of underactuated unmanned surface vessels (USVs) under the influence of internal and external uncertainties, actuator faults, and injection and deception attacks. In the control design, we separately designed virtual adaptive laws to compensate for the time-varying gains suffered by the kinematics channel and combined the event-triggered control (ETC) mechanism to establish an online approximator to compensate for the time-varying gains of the kinematics channels and the loss-of-effectiveness (LOE) and bias faults suffered by the system. Combining robust neural damping technology and finite-time disturbance observer (FTDO), the dynamic uncertainties and external disturbances are suppressed. Finally, a novel robust adaptive trajectory tracking control scheme is proposed. The scheme achieves active compensation for heterogeneous uncertainties including internal and external uncertainties, actuator faults, and attack signals. The Lyapunov stability theory analysis shows that all signals of the tracking system are bounded. The simulation results prove the effectiveness of this control scheme.

Learning-based robust output tracking control for unknown discrete-time nonlinear systems with dynamic uncertainty

Although numerous approximate dynamic programming (ADP) methods have been proposed and applied to robust control problems, research on the use of ADP methods for robust tracking control in nonlinear systems remains limited, especially for discrete time (DT) nonlinear systems. In this paper, we propose an efficient robust learning-based output tracking control method, referred to as r-LTC, for a class of unknown DT nonlinear systems with dynamic uncertainty. The objectives are achieved by: 1) using a system identification technique based on network-type coefficients Auto-Regressive with eXogenous variables (ARX) model to identify completely unknown systems; 2) reformulating the identified model into a state space model in terms of deviations from the reference trajectory, such that the robust tracking problem can be converted into a robust regulation problem; 3) transforming the robust regulation problem into an equivalent optimal regulation problem for a nominal system with a modified utility function; 4) alternately implementing the performance evaluation and control policy update through two neural networks (NNs) to numerically solve DT Hamilton-Jacobi-Bellman (HJB) equation, such that the approximated optimal feedback control inputs for nominal system can be obtained, allowing for realization of all unknown bounded uncertainties. The proposed method does not require a state observer and any steady state knowledge, only the measurable system input and output data are utilized. The convergence of NNs’ approximate weights and stability of the closed-loop uncertain systems are rigorously proven using the Lyapunov method. Lastly, a case study is performed using real data collected from the Shenzhen Metro Line 12 tunneling project to examine the performance of the proposed r-LTC algorithm in terms of the set value tracking accuracy, control system stability, and robustness against different types of disturbances.

Hybrid offline–online neural identification-based robust adaptive tracking control for quadrotors

This paper proposes a novel hybrid offline–online neural identification-based robust adaptive control strategy for quadrotors subject to parameter uncertainties and external disturbances. A new method of using hybrid offline–online neural identification is developed to compensate for the residual force and moment caused by parameter uncertainties. Unlike previous methods that ignore the relevance of uncertainties in the time dimension, the proposed neural identification method mines temporal features of states from historical data by introducing long short-term memory (LSTM) networks, resulting in high identification accuracy. Furthermore, an online adaptation update law is designed to optimize the weights of the network estimates for strong robustness. Consequently, based on the identification of the network, a robust tracking controller on SE(3) is constructed, which is capable of attenuating the bounded disturbances by introducing anti-disturbance components. Finally, numerical simulations and experiments in the real physical world are carried out to verify the performance. The experimental results demonstrate that the proposed strategy not only achieves more accurate uncertainty identification in comparison to the existing methods, but also realizes a 44.28% reduction in the root-mean-square error (RMSE) of the position under the lump uncertainties, which illustrates enhanced robustness and generalizability. Video: https://youtu.be/3kIG5fcQaVE.

Attitude tracking control of a foldable wave energy powered AUV based on linear time-varying MPC under position constraints

In this paper, we investigate the tracking control of attitude and specific spatial position for a foldable wave energy powered autonomous underwater vehicle (FWEPAUV) under space constraints. In order to reduce energy consumption and maximizing the efficiency of the charging, a cascaded dual closed-loop control strategy is proposed. Firstly, we utilize model predictive control (MPC) with multi-variable constraint capabilities to design the kinematics controller. The output constraints are set as space constraints for MPC, and an objective function is used to strike a balance between control accuracy and energy consumption. The improved chaotic firefly algorithm (ICFA) is chosen due to its rapid convergence and strong robustness. It is employed in the rolling optimization process of MPC to secure a viable solution. Secondly, the kinematics controller is combined with the dynamics controller based on adaptive sliding mode control (ASMC) to achieve robust tracking control. In order to eliminate the interference from time-varying ocean currents and complex external forces meanwhile utilizing these interferes to reduce energy consumption, An ocean current observer based on ICFA-PI control and a prescribed time disturbance observer (PTDO) are devised to estimate them. Finally, an event-triggered (ET) mechanism is applied to integrate with the trajectory tracking controller to decrease the computational load. The stability of the ICFA-MPC controller and the ASMC controller is proven using the Lyapunov stability theory. Simulation results demonstrate that in complex external interference environments, the controller can achieve stable tracking control of the attitude and a specific spatial position, thereby meeting predefined goals such as space constraints, energy savings, and maximizing the efficiency of the charging.

Optimal robust online tracking control for space manipulator in task space using off-policy reinforcement learning

This study addresses the demands for adaptability, uncertainty management, and high performance in the control of space manipulators, and the inadequacies in achieving optimal control and handling external uncertainty in task space in previous research. Based on off-policy reinforcement learning, a model-free and time-efficient method for online robust tracking control in task space is devised. To address the complexity of dynamic equations in task space, a mixed-variable approach is adopted to transform the multivariable coupled time-varying problem into a single-variable problem. Subsequently, the optimal control policy is derived with the disturbance convergence, stability, and optimality of the control method being demonstrated. This marks the first instance of achieving robust optimal tracking control in task space for space manipulators. The efficacy and superiority of the presented algorithm are validated through simulation.

Fractional finite-time control for robust tracking of nonlinear systems subject to Hölder disturbances with application to UAVs

The aim of the present article is to design a robust fractional-order (FO) finite-time (FnT) control able to tackle Hölder disturbances of second-order nonlinear systems. First, a novel sliding manifold with Arc-Tangent function is suggested for second nonlinear systems. It has been proven that the system states globally converge to the origin in FnT using the proposed sliding mode variable. To ensure a FnT stability of the sliding variable, a robust control is developed. By using fractional operators, a uniformly continuous control law is designed to tackle Hölder disturbances. Furthermore, the suggested approach is shown to be resistant to matched Hölder disturbances and uncertainties that are continuous but not necessarily differentiable. Moreover, the FnT stability of quadrotors using the proposed control, that is our second result. The quadrotor simulations analysis demonstrates the practicality of the proposed FnT controller in the presence of Hölder disturbances.