Robust Finite-time Control Research Articles

Finite-time robust control of uncertain linear switched systems with comprehensive asynchronous switching

This paper focuses on designing a finite-time robust controller using the sliding mode method for uncertain linear switched systems with comprehensive asynchronous switching in the presence of disturbances, based on an observer with average dwell time. The term ‘comprehensive asynchronous switching,’ introduced for the first time in this research, refers to the possibility of the controller being activated either before or after its corresponding subsystem. This assumption is derived from real-world scenarios. The innovations of this paper are twofold: (1) the introduction of comprehensive asynchronous switching, and (2) the design of a finite-time robust controller for linear switched systems that accounts for simultaneous disturbances, comprehensive asynchronous switching, and bounded uncertainties. The effectiveness of the proposed method is evaluated through a simulation study.

Finite-time robust control of morphing aircraft based on time-varying observer

Morphable vehicles have strong nonlinear, strong coupling and strong time-varying characteristics in the process of variation, which brings great challenges to the design of their flight control systems. To address this problem, a time-varying gain extended state observer is proposed to accurately approximate the system coupling terms. Combining adaptive backstepping control technology and finite-time control theory, a finite-time bounded robust adaptive controller is designed. By designing the barrier Lyapunov function, the actual control law and the adaptive network update law are obtained step by step, ensuring that the system command tracking error can converge to a predetermined range within a finite time. Finally, the effectiveness of the designed control system is verified by attitude control simulation. The simulation results show that the morphable vehicle can track the command signal well in the process of variation and is basically not affected by the variation rate.

Robust Control Design of Under-Actuated Nonlinear Systems: Quadcopter Unmanned Aerial Vehicles with Integral Backstepping Integral Terminal Fractional-Order Sliding Mode

In this paper, a novel robust finite-time control scheme is specifically designed for a class of under-actuated nonlinear systems. The proposed scheme integrates a reaching phase-free integral backstepping method with an integral terminal fractional-order sliding mode to ensure finite-time stability at the desired equilibria. The core of the algorithm is built around proportional-integral-based nonlinear virtual control laws that are systematically designed in a backstepping manner. A fractional-order integral terminal sliding mode is introduced in the final step of the design, enhancing the robustness of the overall system. The robust nonlinear control algorithm developed in this study guarantees zero steady-state errors at each step while also providing robustness against matched uncertain disturbances. The stability of the control scheme at each step is rigorously proven using the Lyapunov candidate function to ensure theoretical soundness. To demonstrate the practicality and benefits of the proposed control strategy, simulation results are provided for two systems: a cart–pendulum system and quadcopter UAV. These simulations illustrate the effectiveness of the proposed control scheme in real-world scenarios. Additionally, the results are compared with those from the standard literature to highlight the superior performance and appealing nature of the proposed approach for underactuated nonlinear systems. This comparison underscores the advantages of the proposed method in terms of achieving robust and stable control in complex systems.

A finite-time path-tracking control algorithm for nonholonomic mobile robots with unknown dynamics and subject to wheel slippage/skid disturbances

Path planning and tracking control are two performance-critical tasks for wheeled mobile robots, particularly when nonholonomic constraints are imposed on robots in dynamically uncertain conditions. Accomplishing certain performance and safety considerations related to path-tracking, such as global stability, transient performance, and smooth finite-time convergence, becomes more difficult for nonholonomic robots. This paper is concerned with proposing a new adaptive robust finite-time tracking control approach for a large class of differential drive autonomous nonholonomic wheeled mobile robots (NWMRs) that are subject to structured uncertainties and extraneous disturbances with fully unknown dynamics. For this purpose, nonlinear kinodynamics of a type of rear-wheel drive NWMRs are developed by incorporating the skid/slippage constituents of the wheel motion. Then, a path-tracking controller is proposed using a continuous finite-time adaptive integral sliding mode control coupled with an integral backstepping approach (FTAISM-IBC). For the adaptive controller design, the entire nonlinear dynamics of the robot, including nonlinear vector functions and control gain functions, together with extraneous disturbances, are estimated by leveraging the universal approximation capabilities of radial basis neural networks (RBFNNs). The finite-time stability proof is presented by utilizing the Lyapunov stability theorem. Furthermore, the adaptive gains are derived to ensure the finite-time stability of the system subject to unknown functions, parametric variations, and unknown but bounded disturbances. Finally, the effectiveness of the proposed controller is evaluated through simulations in terms of several key performance indicators against several reported studies.

Finite-Time Robust Path-Following Control of Perturbed Autonomous Ground Vehicles Using a Novel Self-Tuning Nonsingular Fast Terminal Sliding Manifold

This work presents a finite-time robust path-following control scheme for perturbed autonomous ground vehicles. Specifically, a novel self-tuning nonsingular fast-terminal sliding manifold that further enhances the convergence rate and tracking accuracy is proposed. Then, uncertain dynamics and external disturbances are estimated by a high-gain disturbance observer to compensate for the designed control input. Successively, a super-twisting algorithm is incorporated into the final control law, significantly mitigating the chattering phenomenon of both the input control signal and the output trajectory. Furthermore, the global finite-time convergence and stability of the whole proposed control algorithm are proven by the Lyapunov theory. Finally, the efficacy of the proposed method is validated with comparisons in a numerical example. It obtains high control performance, reduced chattering, fast convergence rate, singularity avoidance, and robustness against uncertainties.

Model-free finite-time robust control using fractional-order ultra-local model and prescribed performance sliding surface for upper-limb rehabilitation exoskeleton

To address the trajectory tracking issue of upper-limb rehabilitation exoskeleton with uncertainties and external disturbances, this paper proposes a fractional-order ultra-local model-based model-free finite-time robust controller (FO-FTRC) using predefined performance sliding surface. Different from previous model-free control strategies, a novel multi-input multi-output (MIMO) fractional-order ultra-local model which is a virtual model is proposed to approximate the complex uncertain nonlinear exoskeleton dynamics in a short sliding time window. This allows the design of controller to be independent of any exoskeleton model information and reduces the difficulty of controller design. The developed robust model-free control method incorporates a fractional-order quasi-time delay estimator (FO-QTDE), unknown disturbance estimator (UDE) as well as prescribed performance sliding mode control (PPSMC). The FO-QTDE is utilized to estimate the unknown lumped uncertainties which employs short time delayed knowledge only about the control input. However, the low-pass filter is always added for FO-QTDE when disturbances change fast, which leads to unavoidable estimation error. Then, UDE is designed to further eliminate the estimation error of FO-QTDE to enhance control performance. The PPSMC is constructed to converge sliding surface to zero in a finite time. Besides, the sliding surface is always limited in performance boundaries. After that, the overall system stability and convergence analyses are demonstrated by using the Lyapunov theorem. Finally, with the comparison to other methods of α-variable adaptive model free control (α-AMFC), time-delay estimation-based continuous nonsingular fast terminal sliding mode controller (TDE-CNFTSMC), time delay estimation (TDE)-based model-free fractional-order nonsingular fast terminal sliding mode control (MFF-TSM) and fractional-order proportion–differential (PDβ), the co-simulation results on 7-degree-of-freedom (DOF) iReHave upper-limb exoskeleton virtual prototype and experiment results on 2-DOF upper-limb exoskeleton are obtained to illustrate the effectiveness and superiority of the proposed FO-FTRC method.

VGESO-Based Finite-Time Fault-Tolerant Tracking Control for Quadrotor Unmanned Aerial Vehicle

Based on the variable gain extended state observer, a finite-time fault-tolerant control strategy is developed for the quadrotor unmanned aerial vehicle with actuator faults and external disturbances. Firstly, a novel variable gain extended state observer is designed to estimate the unknown external disturbances, which mitigates the initial peaking phenomenon existing in traditional extended state observer-based methods. Meanwhile, the neural networks are applied to accurately approximate unknown couplings online. Moreover, with the help of the projection operator technique, the unknown actuator faults are observed in real time. Combined with the backstepping framework, the finite-time robust fault-tolerant control scheme is constructed and the stability is strictly proved via Lyapunov’s theory. Finally, the validity of the developed control scheme is demonstrated through numerical simulations.

On Resilience Guarantees by Finite-Time Robust Control Barrier Functions With Application to Power Inverter Networks

On Resilience Guarantees by Finite-Time Robust Control Barrier Functions With Application to Power Inverter Networks

Robust Finite-Time Control for Guidance Law with Uncertainties in Missile Dynamics

Robust Finite-Time Control for Guidance Law with Uncertainties in Missile Dynamics

Realizing asynchronous finite-time robust tracking control of switched flight vehicles by using nonfragile deep reinforcement learning.

In this study, a novel nonfragile deep reinforcement learning (DRL) method was proposed to realize the finite-time control of switched unmanned flight vehicles. Control accuracy, robustness, and intelligence were enhanced in the proposed control scheme by combining conventional robust control and DRL characteristics. In the proposed control strategy, the tracking controller consists of a dynamics-based controller and a learning-based controller. The conventional robust control approach for the nominal system was used for realizing a dynamics-based baseline tracking controller. The learning-based controller based on DRL was developed to compensate model uncertainties and enhance transient control accuracy. The multiple Lyapunov function approach and mode-dependent average dwell time approach were combined to analyze the finite-time stability of flight vehicles with asynchronous switching. The linear matrix inequalities technique was used to determine the solutions of dynamics-based controllers. Online optimization was formulated as a Markov decision process. The adaptive deep deterministic policy gradient algorithm was adopted to improve efficiency and convergence. In this algorithm, the actor-critic structure was used and adaptive hyperparameters were introduced. Unlike the conventional DRL algorithm, nonfragile control theory and adaptive reward function were used in the proposed algorithm to achieve excellent stability and training efficiency. We demonstrated the effectiveness of the presented algorithm through comparative simulations.

Finite-time robust formation control of multiple aerial robotic vehicles with uncertainties and time-varying complex perturbations

Formation control of aerial robotic vehicles (ARVs) has a wide range of applications in the battlefield reconnaissance, medical rescue and load transportation, etc. System parameter variations and complex disturbances are inevitable in the formation control of ARVs, and the effects of them on the formation stability control of ARVs are unnegligible. This paper addresses the robust formation control problem of finite-time leader–follower for multiple ARVs suffering from parameter uncertainties and time-varying perturbations. To ensure the states (e.g. position and velocity) of all followers to converge to leader in finite time, a novel finite-time high-order sliding mode consensus control (HOSMCC) scheme is designed. To better cope with the parameter uncertainties and time-varying disturbances, improve formation control accuracy and achieve the robust formation control of finite-time leader–follower in multiple ARV systems, a new finite time high-order sliding mode formation control (HOSMFC) scheme on the basis of finite-time HOSMCC is proposed. The finite-time stability of multi-ARV formation control system is guaranteed, and the desired formation pattern of multi-ARV systems is achieved using Lyapunov stability theorem. Performance comparisons with proportional differential formation controller (PDFC) and sliding mode formation controller (SMFC) are studied on a four-ARV formation control system. The results validate the designed formation control scheme.

A robust finite–time model reference adaptive controller for arbitrary order disturbed LTI systems

This manuscript deals with the trajectory-tracking problem for linear time-invariant systems with parameter uncertainties and time-dependent external perturbations. A robust finite-time model reference adaptive controller is proposed. In the absence of external perturbations, the proposed controller ensures finite-time convergence to zero of the tracking and parameter identification errors. In presence of time-dependent external perturbations, the tracking and parameter identification errors converge to a region around the origin in a finite time. The convergence proofs are developed based on Lyapunov and input-to-state stability theory. Finally, simulation results in an academic example and a flexible-joint robot manipulator show the feasibility of the proposed approach.

Observer-based finite-time robust control of nonlinear time-delay uncertain systems with different power Hamiltonian function

Using the Hamiltonian function method with different powers, this paper studies the observer-based finite-time robust control problem of general nonlinear uncertain systems with time delay and presents some new results on this issue. First, by applying Hamiltonian realization method, the paper develops an equivalent Hamiltonian form of original system and designs its observer system. Then, based on the observer system, we study finite-time control problem and present several finite-time stabilization and finite-time robust stabilization results by using the augmented technology and the Lyapunov method. Finally, a real unmanned vehicle is used to verify the performance of the observer-based finite-time robust stabilization controller. Different from the existing literature on Hamiltonian method, the Hamiltonian function in the paper has different powers, which implies that the results developed in the paper have a wider range of application.

Robust Finite-Time Control for a Class of Networked Switched Systems Using an Event-Triggered Observer

Robust Finite-Time Control for a Class of Networked Switched Systems Using an Event-Triggered Observer

Observer-based finite-time robust control for nonlinear systems with different power Hamiltonian functions

This work uses the Hamiltonian function approach to investigate the observer-based finite-time robust control problem of a broad nonlinear system and presents various new results. To begin, the Hamiltonian technique is used to convert the original system to its equivalent form, and then the observer system is designed. Afterward, utilizing the technology and the Lyapunov method, we investigate the finite-time control issue and give several finite-time stabilization results based on the observer method. Finally, a real unmanned vehicle is used to verify the performance of the observer-based finite-time robust stabilization controller. Different from the existing literature on the Hamiltonian method, the Hamiltonian function in this article has different powers, which implies that the results developed in this article have a wider range of application.

Finite-time robust speed control of synchronous reluctance motor using disturbance rejection sliding mode control with advanced reaching law.

In recent years, there has been a significant focus on synchronous reluctance motors (SynRM) owing to their impressive efficiency and absence of magnetic material. Although the SynRM shows great potential for use in electric vehicles, its widespread adoption is limited by unmodeled dynamics and external disturbances. Moreover, the uncertainty factor significantly restricts SynRM's peak efficiency and superior control performance, leading to an unjustifiable current loop reference command. To address these issues, this work presents various new research contributions which focus on the robust control of SynRM to optimize performance through the novel reaching law-based sliding mode control. Initially, a novel advanced sliding mode control reaching law (ASMCRL) with adaptive gain is proposed, to enhance the acceleration of the system state reaching the sliding surface. After that, an extended state observer (ESO) is designed to estimate and compensate for the overall disturbances of the system. Finally, the ASMCRL and ESO are integrated to design two nonlinear controllers namely, the disturbance-rejection sliding mode controller (DRSMC) and the disturbance-rejection sliding mode speed regulator (DRSMSR) for SynRM. The proposed DRSMSR eliminates the steady-state error and eradicates inherent chattering in DRSMC. Moreover, this yields a system trajectory that converges to a predetermined proximity of the sliding surface, irrespective of any lumped disturbances. The steady-state error of DRSMSR is less as compared to DRSMC. Furthermore, the speed response of this technique is 22.62% faster as compared to the state-of-the-art finite-time adaptive terminal sliding mode control. Additionally, the asymptotic stability of the proposed system is validated using Lyapunov's theorem. Thus the experimental results demonstrate the effectiveness and robustness of the proposed approach.

Variations in Finite-Time Multi-Surface Sliding Mode Control for Multirotor Unmanned Aerial Vehicle Payload Delivery with Pendulum Swinging Effects

Multi-surface sliding mode control addresses the limitations of traditional sliding mode control by employing multiple sliding surfaces to handle uncertainties, disturbances, and nonlinearities. The design process involves developing sliding surfaces, designing switching logic, and deriving control laws for each surface. In this paper, first, a robust finite-time multi-surface sliding mode controller will be presented and its performance analyzed by applying it to a multirotor subjected to a suspended payload, modeled in the form of a single pendulum, itself defined as a spatial (3D) dynamic model. Next, an adaptive finite-time multi-surface sliding mode controller will be derived—adding a variable adaptive parameter to the existing sliding surfaces of the robust finite-time control—and applied to the same system. It will be shown that the adaptive controller, with an adaptive parameter that adjusts itself based on the present value of the multi-surface sliding mode parameter, creates an improved fast finite-time convergence by obtaining an optimal settling time and minimizing undershoot of the multirotor state vector. Empirical verification of the effectiveness of the adaptive control will be carried out by presenting the control performances against a step response. It is also shown that the control may be utilized to approximate external disturbances—represented by the pendulum—and that with the application of control, the vehicle’s motion may be stabilized and the payload swing suppressed. Lyapunov stability theory-based stability proofs for the controllers’ designs are developed, showing the asymptotic stability of the output and uniform boundedness of the errors in the system dynamics. It is verified that the multi-surface sliding mode control can account for system uncertainties—both matched and mismatched—in addition to changes in internal dynamics and disturbances to the system, where the single pendulum payload is representative of the changes in dynamics that may occur to the system. Numerical simulations and characteristics are presented to validate the performance of the controllers.

Finite-time adaptive event-triggered control for USV with COLREGS-compliant collision avoidance mechanism

This paper focuses on the real time intelligent navigation scheme for unmanned surface vehicle (USV) subject to collision avoidance regulations. The proposed approach is formulated as two segments: the real time guidance principle with COLREGS-compliant collision avoidance mechanism and the finite-time adaptive event-triggered control algorithm. The pointed improvement for the artificial potential field (APF) can guarantee USV possess the excellent avoidance function in accordance with COLREGS regulations. Especially, when the obstacle makes dangerous actions, the emergency obstacle avoidance operation (EOAO) is implemented according to the real time position of obstacles. Based on the proposed guidance principle, a finite-time robust neural control algorithm is developed by fusion of the finite-time stability theory and event-triggered mechanism. The intermittent computing and communication can effectively reduce the energy and resource consumption of the control system. Moreover, the finite-time adaptive controller design contributes to smaller computation load and facilitates the implementation of the algorithm in ocean engineering. The semi global finite-time uniformly boundedness (SGFTUB) of the closed-loop system is guaranteed through the Lyapunov theory. Finally, the numerical simulation and comparison experiment are illustrated to verify the guidance and control performance of the proposed algorithm.

Robust Finite-Time Control of a Multi-AUV Formation Based on Prescribed Performance

This paper focuses on the finite-time formation-control problem of a multi-AUV formation under unknown perturbations with prescribed performance. First, the nonlinear AUV model is transformed into a second-order integral model using feedback linearization. Suitable prescribed performance functions are selected to constrain the control errors of AUVs within a preset range and convert AUV tracking errors into unconstrained tracking errors using an error-conversion function to facilitate controller design. Finite-time sliding-mode disturbance observers are designed for unknown disturbances in the ocean so that they can accurately estimate the unknown disturbances in finite time. Based on the unconstrained tracking error and the unknown disturbance observer, the fast terminal sliding-mode formation controller is designed so that the multi-AUV formation can converge in finite time. Finally, the simulation experimental results show that the finite-time formation-control method with prescribed performance proposed in this paper can better cancel the unknown disturbance in the ocean in finite time and improve the robustness of the multi-AUV formation control.

Robust finite-time fault-tolerant control for vehicle height and posture regulation with air suspension system subject to actuator faults, uncertainties and external disturbance

Robust finite-time fault-tolerant control for vehicle height and posture regulation with air suspension system subject to actuator faults, uncertainties and external disturbance