Unknown External Disturbances Research Articles

Fault-tolerant control for Markov jump nonlinear systems based on an observer and finite-time fast integral terminal sliding mode control

This paper develops a novel fault-tolerant control based on an observer for underactuated robot manipulators with unknown external disturbances, uncertainties, and actuator faults. First, unlike the traditional approach of treating the robot system as a parameter time-varying system, the underactuated robot manipulator with different drive modes can be considered as one of the classical Markov jump nonlinear systems (MJNSs). Second, an adaptive disturbance observer is designed to estimate the state and disturbances of the system. Finally, based on the observation results, a nonsingular fast integral terminal sliding mode controller (NFITSMC) is utilized to implement fault-tolerant control of the system. Compared with traditional observer and terminal sliding mode controller, the adoption of the novel controller and observer can improve response time and reduce chattering. Especially, in order to eliminate chattering, the integral term is introduced into the nonsingular fast terminal sliding mode controller. Structuring Lyapunov–Krasovskii functional (LKF) and based on linear matrix inequalities (LMIs) techniques, the convergence of control strategy and tracking errors is proved. The simulation results show that the actuator faults can be observed successfully and the error system is finite-time stable.

Decentralized adaptive fault‐tolerant control for interconnected nonlinear time‐delay systems with uniform prescribed performance

AbstractIn this article, the prescribed performance tracking control problem is studied for interconnected nonlinear time‐delay systems with sensor and actuator faults. Based on the dynamic gain technique and the backstepping control method, a delay‐independent adaptive state feedback controller is designed. Besides, by embedding a smooth function into the controller, the unknown external disturbances, sensor and actuator faults are successfully compensated. Furthermore, we can deal with the asymmetric prescribed performance control with semi‐global or global requirements uniformly by selecting the initial value of the the scaling function. Based on Lyapunov theory, it is proved that the system output of each subsystem can closely track the desired signal and the boundedness of all signals in the closed‐loop systems can be ensured under the proposed control method. Finally, the effectiveness of the proposed control strategy is proved by two simulation examples.

Adaptive command filtered control for a class of nonlinear time delay systems with extreme learning machine

AbstractIn this paper, an extreme learning machine (ELM)‐based adaptive command filtered control method is investigated for a class of strict feedback nonlinear systems with unknown external disturbances and time delay. To begin with, the original system state equation is transformed into a new form on account of coordinate transformation. Subsequently, an ELM is adopted to approximate unknown functions which exist in the whole system states, without any prior knowledges of the ideal weight vectors and approximation errors. Secondly, a command filter is developed for the system under consideration, which can avoid the probem of “explosion of complexity” caused by repeated derivation of virtual control signals in traditional backstepping control. Meanwhile, error compensation signals are designed to conquer the shortcoming of a dynamic surface control (DSC) method. The combination of ELM and command filter technique has been used to construct corresponding controllers and adaptive laws. Effective handling of the impact of time delay terms is ensured through designing a novel Lyapunov–Krasovskii functional. The proposed strategy guarantees boundedness of all signals in the closed‐loop system and the tracking error asymptotically converges to a compact set around the origin. In the end, two continuous stirred tank reactors (CSTRs) are taken as example to further verify the efficiency of the put forward control method.

Robust Fixed-Time Fault-Tolerant Control for USV with Prescribed Tracking Performance

The unmanned surface vessel (USV) is an emerging marine tool with its advantages of automation and intelligence in recent years; the good trajectory tracking performance is an important capability. This paper proposes a novel prescribed performance fixed-time fault-tolerant control scheme for an USV with model parameter uncertainties, unknown external disturbances, and actuator faults, based on an improved fixed-time disturbances observer. Firstly, the proposed observer can not only accurately and quickly estimate and compensate the lumped nonlinearity, including actuator faults, but also reduce the chattering phenomenon by introducing the hyperbolic tangent function. Then, under the framework of prescribed performance control, a prescribed performance fault-tolerant controller is designed based on a nonsingular fixed-time sliding mode surface, which guarantees the transient and steady-state performance of an USV under actuator faults and meets the prescribed tracking performance requirements. In addition, it is proved that the closed-loop control system has fixed-time stability according to Lyapunov’s theory. Finally, upon conducting numerical simulations and comparing the proposed control scheme with the SMC and the finite-time NFTSMC scheme, it is evident that the absolute error tracking performance index of the proposed control scheme is significantly lower, thus indicating its superior accuracy.

Practical Finite-Time Command-Filtered Adaptive Backstepping With Its Applications to Quadrotor Hovers.

In this article, a practical finite-time command-filtered adaptive backstepping (PFTCFAB) control method is presented for a class of uncertain nonlinear systems with nonparametric unknown nonlinearities and external disturbances. Unlike PFTCFAB control techniques that use neural networks (NNs) or fuzzy-logic systems (FLSs) to deal with system uncertainties, the proposed method is capable of handling such uncertainties without the need for NNs or FLSs, thus reducing complexity and increasing reliability. In the proposed approach, novel function adaptive laws are designed to directly estimate unknown nonparametric nonlinearities and external disturbances by means of command filter techniques, and a type of practical finite-time command filters is proposed to obtain such laws. Moreover, the PFTCFAB controllers and finite-time command filters are designed with practical finite-time Lyapunov stability, which ensures finite-time stability of system tracking and filter estimation errors. Experimental results with a quadrotor hover system are presented and discussed to demonstrate the advantages and effectiveness of the proposed control strategy.

Scaled Position Consensus of High-Order Uncertain Multiagent Systems Over Switching Directed Graphs.

We investigate the scaled position consensus of high-order multiagent systems with parametric uncertainties over switching directed graphs, where the agents' position states reach a consensus value with different scales. The intricacy arises from the asymmetry inherent in information interaction. Achieving scaled position consensus in high-order multiagent systems over directed graphs remains a significant challenge, particularly when confronted with the following complex features: 1) uniformly jointly connected switching directed graphs; 2) complex agent dynamics with unknown inertias, unknown control directions, parametric uncertainties, and external disturbances; 3) interacting with each other via only relative scaled position information (without high-order derivatives of relative position); and 4) fully distributed in terms of no shared gains and no global gain dependency. To address these challenges, we propose a distributed adaptive algorithm based on a acrlong MRACon scheme, where a linear high-order reference model is designed for every individual agent employing relative scaled position information as input. A new transformation is proposed which converts the scaled position consensus of high-order linear reference models to that of first-order ones. Theoretical analysis is presented where agents' positions achieve the scaled consensus over switching directed graphs. Numerical simulations are performed to validate the efficacy of our algorithm and some collective behaviors on traditional consensus, bipartite consensus, and cluster consensus are shown by precisely choosing the scales of the agents.

Fall prediction, control, and recovery of quadruped robots

When legged robots perform complex tasks in unstructured environments, falls are inevitable due to unknown external disturbances. However, current research mainly focuses on the locomotion control of legged robots without falling. This paper proposes a comprehensive decision-making and control framework to address the falling over of quadruped robots. First, a capturability-based fall prediction algorithm is derived for planar single-contact and 3D multi-contact locomotion with a predefined gait sequence. For safe fall control, a novel contact-implicit trajectory optimization method is proposed to generate both state and input trajectories and contact mode sequences. Specifically, incorporating uncertainty into the system and terrain models enables mitigating the non-smoothness of contact dynamics while improving the robustness of the resulting trajectories. Furthermore, a model-free deep reinforcement learning-based approach is presented to achieve fall recovery after the robot completes a fall. Experimental results demonstrate that the proposed fall prediction algorithm accurately predicts robot falls with up to 95% accuracy approximately 395ms in advance. Compared to classical locomotion controllers, which often struggle to maintain balance under significant pushes or terrain perturbations, the presented framework can autonomously switch to the fall controller approximately 0.06s after the perturbation, effectively preventing falls or achieving recovery with a threefold reduction in touchdown impact velocity. These findings highlight the effectiveness of the proposed framework in enhancing the stability and safety of legged robots in unstructured environments.

Fixed-time coordination control for 6-DOF attitude-orbit coupled spacecraft formation flying

This paper presents a distributed fixed-time control protocol for 6-DOF(degree-of-freedom) attitude-orbit coupled spacecraft formation flying with external disturbances. Firstly, the 6-DOF attitude-orbit coupled dynamics is established. The communication topology between the spacecraft in the formation is described by a directed graph. Secondly, a fixed-time disturbance observer (FxTDO) is designed to ensure that the estimation errors of the unknown external disturbances can converge to zero in fixed time. Thirdly, based on non-singular fixed-time terminal sliding mode (NFFTSM) surface, the fixed-time coordination control protocol is proposed combined with the fixed-time disturbance observer, which can guarantee that each spacecraft can track their desirable positions and attitudes in fixed time. The stability of the closed-loop system is proved through Lyapunuov method. Finally, simulation results for a formation with one virtual leader and five followers demonstrate the effectiveness of the proposed control scheme.

Disturbance Observer-Based Adaptive Intelligent Control of Marine Vessel With Position and Heading Constraint Condition Related to Desired Output.

This article studies the adaptive control about the geodetic fixed positions and heading of three-degree-of-freedom dual-propeller vessel. During the navigation of a vessel at sea, due to the unpredictable sea, on the one hand, it is important to ensure that the vessel can smoothly follow the desired geodesic fixed position and heading; on the other hand, when the sailing environment is harsh, it is even more important that the vessel can adapt to the desired geodesic fixed position and heading that change at any time for safe driving. Therefore, this article selects the time-varying function related to the desired geodesic fixed position and heading as the constraint condition, and the constraint condition will change in real time as the expected position and heading change. The design of the control strategy is difficult, and the designed control strategy will be more suitable for complex maritime navigation conditions. First, the article constructs a log-type barrier Lyapunov function. Second, by introducing an unknown external disturbance observer, the external disturbances caused by the environment that may be encountered during the vessel's voyage can be observed. Then, combined with the backstepping algorithm, a neural network (NN) control strategy and adaptive law are designed. Among them, for the uncertain function in the process of designing the control strategy, the NN is used to approximate it. Furthermore, through the Lyapunov stability analysis, it is shown that applying the designed control strategy to the vessel system in this article can ensure that the system is closed-loop stable. The final simulation experiment shows the effectiveness of the designed control strategy.

Fixed-time trajectory tracking for autonomous surface vehicles via output feedback under various constraints

This paper proposes a novel fixed-time output feedback trajectory tracking control method suitable for autonomous surface vehicles (ASVs). Firstly, various complex uncertainty terms, such as unknown external disturbances, unmodeled errors, and actuator faults are considered in this paper. And these terms are uniformly converted into the total uncertainty terms through model transformation for convenience. Then, a fixed-time extended state observer (FTESO) with the newly expanded state is designed to observe and estimate the total uncertainty terms. Next, the saturation dynamic filter (SDF) is adopted to address the input saturation, and the saturation factors of SDF are incorporated into the trajectory error calculation to reduce the torque mutation caused by an excessive error in the control input. Finally, a fixed-time control law is proposed by taking into account the ASV system error and FTESO estimation state. Simulation experiments show that this method has excellent control performance, and this conclusion is validated through stability proof and case comparison.

Neural Network-Based Distributed Consensus Tracking Control for Nonlinear Multi-Agent Systems with Mismatched and Matched Disturbances

In practice, disturbances, including model uncertainties and unknown external disturbances, are always widely present and have a significant impact on the cooperative control performance of a networked multi-agent system. In this work, the distributed consensus tracking control problem for a class of multi-agent systems subject to matched and mismatched uncertainties is addressed. In particular, the dynamics of the leader agent are modeled with uncertain terms, i.e., the leader’s higher-order information, such as velocity and acceleration, is unknown to all followers. To solve this problem, a robust consensus tracking control scheme that combines a neural network-based distributed observer, a barrier function-based disturbance observer, and a tracking controller based on the back-stepping method was developed in this study. Firstly, a neural network-based distributed observer is designed, which is able to achieve effective estimation of leader information by all followers. Secondly, a tracking controller was designed utilizing the back-stepping technique, and the boundedness of the closed-loop error system was proved using the Lyapunov-like theorem, which enables the followers to effectively track the leader’s trajectory. Meanwhile, a barrier function-based disturbance observer is proposed, which achieves the effective estimation of matched and mismatched uncertainties of followers. Finally, the effectiveness of the robust consensus tracking control method designed in this study was verified through numerical simulations.

Model-free anti-disturbance tracking control for high-order discrete-time nonlinear system based on concurrent learning extended state observer

The research objective of this paper is to address the tracking control problem of high-order discrete-time nonlinear systems in the presence of completely unknown internal uncertainties, unknown external disturbances, and unknown control input gain. To address this challenge, the paper proposes a high-order discrete-time model-free anti-disturbance tracking control method without relying on prior knowledge of system parameters. The core of the approach is the development of a data-driven concurrent learning extended state observer. The uniqueness of this observer lies in its ability to estimate unknown control input gains without the persistent excitation and ensure the convergence of the estimates. Based on the concurrent learning extended state observer, a high-order discrete-time tracking control law is designed to precisely track the reference signal, ensuring the stability of the nonlinear closed-loop system. The effectiveness of this method was verified by applying simulation verification to the heading tracking control of surface automatic vehicles.

Adaptive disturbance rejection neural output feedback control of hydraulic manipulator systems

This paper proposes an adaptive disturbance rejection neural output feedback control (ADRNC) scheme for multi-degree-of-freedom (n-DOF) hydraulic manipulator systems, subjected to unknown nonlinearities, external disturbances and unmeasured system states. The controller design is formulated by integrating Radial Basis Function Neural Networks (RBFNNs) with state and disturbance observers using the backstepping method. The RBFNNs are synthesized to handle unknown nonlinear functions and the residual estimate error, coupled with external disturbances, is estimated through the combination of state observer and disturbance observer. The unique features of the proposed controller lies in its capability to estimate both matched and unmatched lumped disturbances. The auxiliary disturbance estimation law is guided by the neural learning weights and estimated system states provided by state observers. By effectively utilizing neural networks to approximate and mitigate most nonlinear uncertainties, the workload of the disturbance observer is substantially reduced. High-gain feedback is therefore avoided and improved tracking performance can be expected. Moreover, to avoid the tedious analysis and the problem of “explosion of complexity” in the conventional backstepping method, we employ a first-order sliding-mode differentiator. Rigorous analysis via Lyapunov methods establishes the stability of the entire closed-loop system, ensuring guaranteed and satisfactory tracking performance under the integrated influence of unknown nonlinearities, unmeasured states, and external disturbances. Extensive simulations are conducted to verify the effectiveness of the nested control strategy.

Distributed formation control for leader‐follower quadrotor unmanned aerial vehicles system based on practical sliding mode and event‐triggered mechanisms

AbstractThis article investigates the distributed formation trajectory tracking problem of a homogeneous quadrotor unmanned aerial vehicles (UAVs) system using a leader‐follower consensus protocol in three‐dimensional space. To enable the follower UAVs in the swarm to track a single leader UAV and form a desired formation under undirected topology, a six‐degree‐of‐freedom dynamic model with bounded time‐varying disturbances is established, which is divided into a tracking subsystem and a stabilizing subsystem. A practical sliding mode control (PSMC) based event‐triggered algorithm is proposed to achieve distributed formation control for a leader‐follower quadrotor UAVs system and reduce the network transmission resources. To address the potential issue of inter‐UAVs collisions during formation, an artificial potential field (APF) method is introduced in the tracking subsystem, and an disturbance observer is introduced in the stabilizing subsystem to estimate the unknown external disturbances. The boundedness of signals in the closed‐loop system is demonstrated using Lyapunov stability theory, and the exclusion of Zeno behavior can be ensured by having a positive lower bound on the inter‐event time between two consecutive triggering events. Finally, the effectiveness of the proposed event‐triggered algorithm is validated through simulation examples.

Multi-group formation tracking fault-tolerant control for matched nonlinear multi-agent systems with switching topologies and unknown control inputs

The multi-group formation fault-tolerant control problem for high-order nonlinear multi-agent systems with parameter uncertainties, unknown external disturbances, switching topologies, and non-cooperative targets are investigated in this paper. A fully distributed formation tracking control protocol is proposed based on the total interaction information between subgroups being zero and the neighboring relative information of multi-agent in the subgroups. In addition, an algorithm is proposed to design the parameters of time-varying formation tracking control protocol. At the same time, it does not require knowing the bounds of actuator faults, parameter uncertainties, control inputs of the leaders, and unknown disturbances. Then, it is proved that the designed control protocols can make the high-order nonlinear multi-agent systems accomplish the desired time-varying multi-group formation, and the errors are uniformly asymptotically bounded stable. Finally, the effectiveness of the designed control protocol is demonstrated by simulation examples of three subgroups.

Robust output regulation of a class of uncertain nonlinear minimum phase systems perturbed by unknown external disturbances

This paper addresses the problem of robust output regulation for uncertain nonlinear minimum phase systems affected by an unknown external disturbance. We present a novel unknown input observer (UIO)-embedded high-gain stabilizer to completely reconstruct the disturbance in a finite time. A new saturation function is introduced to prevent finite time escape of the closed-loop trajectories. This allows us to achieve a semi-globally exponential regulation of the regulated output. The proposed method features the exact cancellation rather than approximate cancellation, for both structured and/or unstructured external disturbance. The presented controller is finite-dimensional and does not require the nominal model of the plant. Finally, a numerical experiment is conducted to demonstrate the effectiveness of the proposed method.

Disturbance Observer-Based Fixed-Time Tracking Control for a Tilt Trirotor Unmanned Aerial Vehicle

This paper proposed a new fixed-time trajectory tracking control strategy based on the disturbance observer (DOB) for a tilt trirotor unmanned aerial vehicle (TTUAV) which is subject to unknown external disturbances. To facilitate the TTUAV's trajectory tracking controller design, the dynamic model of the TTUAV is divided into two subsystems, the position subsystem (outer-loop) and the attitude subsystem (inner-loop). For the dynamics of the TTUAV's outer-loop, the unknown external disturbances consist of the unknown wind disturbances, the unknown aerodynamic frictions forces, the lateral force generated by the rear servo and the states coupling between the outer-loop and the inner-loop. Then, a nonlinear DOB is designed to estimate the unknown external disturbances, and a nonsingular terminal sliding-mode controller (NTSMC) is further developed to drive the TTUAV's position tracking errors to zero in a fixed time. For the dynamics of the TTUAV's inner-loop, the unknown external disturbances are mainly introduced by the aerodynamic frictions torques. Then, a modified sliding mode controller is designed to reject the unknown external disturbances, and to ensure that the attitude tracking errors converge to zero exponentially. In addition, a composite stability analysis based on Lyapunov stability theory is provided to guarantee the fixed-time convergence of the closed-loop dynamics of the TTUAV. Finally, the results of the real-time experiments are presented to verify the effectiveness of the proposed control strategy.

Robust Policy Iteration of Uncertain Interconnected Systems With Imperfect Data

This paper investigates the robust optimal control problem of a class of continuous-time, partially linear, interconnected systems. In addition to the dynamic uncertainties resulted from the interconnected dynamic system, unknown bounded disturbances are taken into account throughout the learning process, wherein the system’s dynamics and the disturbances are assumed unknown. These challenges lead the collected online data to be imperfect. In this scenario, traditional data-driven control techniques, such as adaptive dynamic programming (ADP) and robust ADP, encounter a challenge in approximating the optimal control policy precisely due to imperfect data and computational errors. In this paper, a novel data-driven robust policy iteration method is proposed to simultaneously solve the robust optimal control problems. Without relying on the knowledge of the system’s dynamics, the external disturbances or the complete state, the implementation of the proposed method only needs to access the input and partial state information. Based on the small-gain theorem, the notions of strong unboundedness observability and input-to-output stability, it is guaranteed that the learned robust optimal control gain is stabilizing and that the solution of the closed-loop system is uniformly ultimately bounded despite the existence of dynamic uncertainties and unknown external disturbances. The simulation results reveal the efficiency and practicality of the proposed data-driven control method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work is motivated by the use of reinforcement learning to improve the quality of designing adaptive optimal controllers for engineering applications. Adaptive dynamic programming methods, in particular policy iteration (PI), are widely used in solving optimal control problems. However, due to the iterative nature of PI, the approximated optimal control policy may be inaccurate and imprecise. Especially, when using imperfect system’s measurements instead of the modelling information. This can result in causing the learned control policy to deviate from the actual optimal policy. This becomes more challenging in the existence of dynamic uncertainties and unknown external disturbances which corrupt the measurements and result in imperfect data. This work investigates the conditions on the uncertainties such that the proposed novel data-driven PI algorithm is robust to system’s uncertainties, unknown external disturbances and imperfect measurements. The approximated robust optimal control policy performs robustly in the existences of imperfect data and uncertainties, and at the same time is close enough to the optimal control policy.

Adaptive Set-Membership Filter Based Discrete Sliding Mode Control for Pneumatic Artificial Muscle Systems With Hardware Experiments

Pneumatic artificial muscle (PAM), featuring good flexibility and safety, has been widely used in rehabilitation and bionic robots. However, the complex hysteretic nonlinearities and uncertainties of the PAM cause great difficulties and challenges to the accurate modeling and controller design, especially when confronted with unknown external disturbances in applications. This paper proposes a robust control strategy with disturbance compensation for the hysteresis compensation and trajectory tracking of PAMs. Considering the high hysteretic nonlinearity of the PAM, a modified Prandtl-Ishlinskii model is used as a feedforward hysteresis compensator. For the linearized system, adaptive set-membership filtering (ASMF) is used to estimate the nonlinear terms and external disturbances of the overall system. A sliding mode controller (SMC) with disturbance compensation is designed and cascaded to the feedforward hysteresis compensator in series. The stability of the closed-loop system is theoretically proved. The proposed method guarantees that the tracking error of the PAM system is bounded. Finally, the effectiveness and robustness of the proposed controller are verified via a series of experiments on an in-house built testbench for PAMs. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —With the increasing demand on human-robot interaction, the safety and compliance of robots have become one key requirement. PAM is a compliant actuator, exhibiting good flexibility, safety, and clean energy. PAM is widely used in rehabilitation robots, whereas its strong hysteresis nonlinearity and sensitivity to external disturbances affect its motion accuracy. This paper proposes an ASMF-based discrete SMC, which uses an inverse hysteresis model to compensate for the strong hysteresis of the PAM and uses ASMF to estimate the lumped disturbance of the system. Compared with the other filters, ASMF is unique in that its estimation error is bounded, which is very useful in the stability proof of the overall system. The effectiveness of the proposed controller is experimentally verified. Experimental results show that PAM’s hysteresis can be efficiently compensated, and the influence of external disturbances can be attenuated by the proposed controller, resulting in improved motion accuracy and robustness. In future work, efforts will be directed towards the modeling and control of PAMs in multi-DOF robots.

Nonlinear Disturbance Observer-Based Fault-Tolerant Sliding-Mode Control for 2-D Plane Vehicular Platoon With UTVFD and ANAS.

This article investigates a nonlinear disturbance observer (NDO)-based fault-tolerant sliding-mode control (SMC) for 2-D plane vehicular platoon systems subjected to actuator faults with unknown time-varying fault direction (UTVFD), asymmetric nonlinear actuator saturation (ANAS), nonlinear unmodeled dynamics, and unknown external disturbance. The Nussbaum-type function approach is adopted to solve the problem of actuator faults with UTVFD. The designed NDO not only can estimate the lumped disturbance accurately but also can reduce the control peaking and chattering phenomena caused by the Nussbaum-type function. Then, an adaptive saturation compensator is designed to compensate for the influence of actuator saturation on the system. In addition, by combining SMC technology with the prescribed tracking performance (PTP) approach, a distributed fault-tolerant control scheme is developed to not only ensure collision avoidance and communication connectivity but also realize a variety of driving scenarios, such as multilane vehicle merging and vehicular platoon lane changing. Finally, simulation results are presented to show the proposed scheme's effectiveness and advantages.