Unknown Time-varying Disturbances Research Articles

Adaptive disturbance observer-based fast nonsingular terminal sliding mode control for quadrotors

In this paper, a sliding-mode disturbance observer (SMDO)-based finite-time control scheme is proposed for a quadrotor under uncertainties and external disturbances. The SMDO is used to estimate and compensate the unknown time-varying disturbance with minor chattering and rapid convergence. However, a priori bounded uncertainty may impose a priori constraint on the system state before obtaining closed-loop stability. To address this issue, an adaptive SMDO (ASMDO) with a nested adaptive structure is further introduced. As for controller design, a fast nonsingular integral terminal sliding mode controller (FNITSMC) is proposed to ensure finite-time convergence and zero tracking error for the quadrotor attitude control. Finally, effectiveness of proposed method is verified through simulations and experiments.

GBM-ILM: Grey-Box Modeling Based on Incremental Learning and Mechanism for Unmanned Surface Vehicles

Unmanned surface vehicles (USVs) have garnered significant attention across various application fields. A sufficiently accurate kinetic model is essential for achieving high-performance navigation and control of USVs. However, time-varying unobservable internal states and external disturbances pose challenges in accurately modeling the USV’s kinetics, and existing methods face difficulties in accurately estimating unknown time-varying disturbances online while ensuring precise mechanism modeling. To address this issue, a novel grey-box modeling method based on incremental learning and mechanisms (GBM-ILM) is proposed. Its union structure combines the advantages of both incremental learning networks and physical mechanisms for estimating the USV’s full kinetics. Depending on the linear parameter-varying (LPV) mechanism, it not only adheres to physical laws but also calculates the unstructured model errors. An incremental learning network is implemented to continuously refine model errors, by accounting for the USV’s time-varying characteristics and iteratively updating the network parameters and structures to adapt to different USV states and environmental disturbances. To validate this method, we developed the ‘Salmon’ USV and conducted identification experiments in a lake. Compared to tests of other state-of-the-art methods, our method has better adaptability, with 46.34%, 14.86%, and 6.87% accuracy improvements when estimating the USV’s forward, turning, and sideslip dynamic model, respectively.

Exponential Stabilization of a Rotating Body-Beam System With Boundary Output Constraint Under Unknown Time-Varying Disturbance

Exponential Stabilization of a Rotating Body-Beam System With Boundary Output Constraint Under Unknown Time-Varying Disturbance

Iterative learning control of an Euler-Bernoulli beam with time-varying boundary disturbance

This paper investigates the stabilization of Euler-Bernoulli beam systems modeled by a partial differential equation (PDE) with unknown time-varying disturbance. An iterative learning controller is designed using only boundary state feedback to realize the vibration control subject to unknown boundary disturbance. The well-posedness for the closed-loop system is given by the operator semigroup theory. Furthermore, the exponentially stable for the closed-loop system is proved by the Lyapunov method. The comparisons with existing results are made to demonstrate the effectiveness and advantages of the proposed boundary iterative learning control method.

Automatic berthing of unmanned surface vessels with predetermined performance

To solve the problem of ship automatic berthing control due to unknown time-varying disturbance and dynamic uncertainty of model parameters, an automatic berthing control law based on predefined performance time function is proposed. First, a predefined performance time function is designed and coupled with tracking error to achieve the predetermined performance of tracking error. Secondly, radial basis function neural network is used to approach the dynamic uncertainty of ship model parameters, and the complex uncertainty of model parameters and unknown time-varying disturbance is represented by linearized parameter form with single virtual parameter, which makes the calculation simple and easy to implement in engineering. On this basis, the reverse step control law is designed. Thirdly, the stability of the system is proved based on Lyapunov stability theory. Finally, the simulation results show that the control law can make the ship reach the desired position and heading angle, and realize the automatic berthing of the ship. The control law and berthing controller designed in this paper have good applicability and robustness, which provides a theoretical basis for the subsequent control research of surface intelligent ships.

An adaptive internal model control approach for unmanned surface vehicle based on bidirectional long short-term memory neural network: Implementation and field testing

This paper investigates a practical adaptive internal model control (IMC) for an unmanned surface vehicle (USV) with unknown time-varying nonlinear model parameters and environmental disturbances. Firstly, an internal model of the USV is presented using the Bidirectional Long Short-Term Memory (BiLSTM) neural network. Then, an adaptive neural IMC controller is designed for the trajectory tracking of USV by using the IMC method. The internal model and the controller are updated by an error threshold algorithm. The proposed control scheme comprises of a trajectory guidance module via the Line-of-Sight (LOS) guidance method and a tracking control module designed by IMC theory. Under the proposed control scheme, the development processes of the vehicle platform and the control algorithms are described, and accurate tracking control can be achieved. Finally, the results of simulation and field experiments are presented and discussed to validate the effectiveness of the proposed control scheme.

Nonlinear Model Predictive Control for a Dynamic Positioning Ship Based on the Laguerre Function

In this paper, we present a novel nonlinear model predictive control (NMPC) algorithm based on the Laguerre function for dynamic positioning ships to solve the problems of input saturation, unknown time-varying disturbances, and heavy computation. The nonlinear model of a dynamic positioning ship is presented as a linear model, transformed from a standard affine nonlinear state-space model by precise feedback linearization. The environmental disturbance is overcome using an integrator. The time cost of the proposed nonlinear control algorithm is decreased by inducing the Laguerre function to describe the feedback-linearization system input increments. The Laguerre function reduces the matrix dimensions of the nonlinear optimization problem. The simulation results for a DP supply vessel showed that the novel algorithm maintained the effective control performance of the original nonlinear model predictive control algorithm and had a reduced computation load to satisfy the requirements of real-time operation.

Composite RISE control for vehicle-mounted servo system with unknown modeling uncertainties and unknown time-varying disturbances

In light of the problem of trajectory tracking control in vehicle servo systems with system model uncertainty and external time-varying disturbance, an effective trajectory tracking control method that can handle system model uncertainty and external time-varying disturbances is proposed. To achieve this goal, a novel composite robust integral of the sign of the error (RISE) control method is introduced that combines a multi-layer neural network and an extended state observer. Specifically, multi-layer neural networks are utilized to approximate the uncertainty of the system model, while an extended state observer is employed to estimate the fitting near-error and the external time-varying interference, which are used as feedforward compensation. Finally, the RISE controller is implemented as a robust feedback controller. By applying Lyapunov theory for stability analysis and conducting experiments, the results demonstrate that the proposed approach exhibits excellent performance and robustness in addressing the uncertainties and disturbances involved in trajectory tracking control for vehicle servo systems.

PSO-Based Predictive PID-Backstepping Controller Design for the Course-Keeping of Ships

Ship course-keeping control is of great significance to both navigation efficiency and safety. Nevertheless, the complex navigational conditions, unknown time-varying environmental disturbances, and complex dynamic characteristics of ships pose great difficulties for ship course-keeping. Thus, a PSO-based predictive PID-backstepping (P-PB) controller is proposed in this paper to realize the efficient and rapid course-keeping of ships. The proposed controller takes the ship’s target course, current course, yawing speed, as well as predictive motion parameters into consideration. In the design of the proposed controller, the PID controller is improved by introducing predictive control. Then, the improved controller is combined with a backstepping controller to balance the efficiency and stability of the control. Subsequently, the parameters in the proposed course-keeping controller are optimized by utilizing Particle Swarm Optimization (PSO), which can adaptively adjust the value of parameters in various scenarios, and thus further increase its efficiency. Finally, the improved controller is validated by carrying out simulation tests in various scenarios. The results show that it improves the course-keeping error and time-response specification by 4.19% and 9.71% on average, respectively, which can efficiently achieve the course-keeping of ships under various scenarios.

Fault-tolerant control of underactuated MSVs based on neural finite-time disturbance observer: An Event-triggered Mechanism

This paper deals with the problem of fault-tolerant control synthesis for underactuated marine surface vessels (MSVs) with dynamic uncertainties, external time-varying disturbances, and input saturation. In control design, with the help of neural networks (NNs) to reconstruct the dynamic uncertainty of the system, a novel nonlinear finite-time disturbance observer (FTDO) is established to reconstruct the compound uncertainty online, including unknown time-varying disturbances, approximation errors, bias faults and parts of loss-of-effectiveness (LOE) faults. Combining finite-time control (FTC) theory, event-triggered control (ETC) technology and backstepping design method, a new fault-tolerant control scheme for underactuated MSVs is designed. Based on the Lyapunov stability theory, it is proved that all signals in the closed-loop tracking system are bounded, and the tracking error of the underactuated MSVs converges to a small set near the origin in finite-time. The effectiveness of the proposed novel fault-tolerant control scheme is verified by computer simulation.

Robust adaptive tracking control for dynamic positioning ships subject to dynamic safety constraints and actuator saturation

This paper proposed a novel robust adaptive trajectory tracking control scheme for dynamic positioning (DP) ships subjected to unknown time-varying disturbances, unknown model parameters, dynamic safety constraints, and actuator saturation. The dynamic safety constraints were guaranteed based on the tan-type barrier Lyapunov function (BLF) technique, which ensured the position and velocity of the DP vessel within the given constraints. Moreover, the radial basis function neural network (RBFNN) was adopted to approximate the unknown parameters of the dynamics model, and an adaptive neural disturbance observer (ANDO) was designed to compensate for lumped disturbances. An anti-windup system was developed to handle the actuator saturation effect. By combining the above techniques and back-stepping method, the final control law was presented, and the semi-global asymptotic convergence was achieved via rigorous theoretical analysis and Lyapunov proof. The results of simulations demonstrated the superiority and robustness of this approach in resolving the trajectory tracking challenges of DP ships. Moreover, the proposed control scheme is highly effective in optimizing the trajectory tracking of DP ships, as it takes into account the multiple constraints that may arise during the process, which is a valuable contribution to the field of DP ship trajectory tracking, providing a more comprehensive and effective solution to this complex problem.

Robust adaptive output feedback for the formation control of heterogeneous ships based on a nonlinear extended state observer

This study considers the formation control problem of heterogeneous ships with unknown time-varying disturbances, dynamic uncertainties, and unmeasurable speeds, a robust adaptive output feedback formation control scheme for the heterogeneous ships based on nonlinear extended state observer is developed. In order to solve the heterogeneous ships formation control problem with leader-following structure, transforming the formation control problem into a class of ship trajectory tracking problem by improving the design of the virtual ship. Firstly, a nonlinear extended state observer is designed for estimating ship speeds due to technical limitations and external disturbances. Then, combining the adaptive neural networks with disturbances adaptive law to deal with the unknown time-varying disturbances and dynamic uncertainties. Meanwhile, the second-order tracking differentiator is designed to calculate the derivative of the virtual control law, which has higher precision comparing to the first-order filter. Stability theory is proved that all the signal of closed-loop control system are uniformly ultimately bounded, and the tracking errors can converge into arbitrary small neighborhoods around zero. Finally, comparative simulations were performed to demonstrate the effectiveness of the proposed controller.

A Distributed Robust Two-Time-Scale Switched Algorithm for Constrained Aggregative Games

Robust Nash equilibrium (NE) seeking for a constrained aggregative game is explored. Our setting has the following three features: 1. Local feasibility sets are considered. 2. Each player has first-order dynamics that are influenced by unknown time-varying disturbances and unmodeled terms. 3. The communication topology among players may be influenced by attacks. The existence of unknown disturbances results in the trajectories of the players going out of the feasible sets even though the initial values start from inside. To make the ideas clear, we first use an example that exhibits the three features to introduce the problem formulation to be studied. Subsequently, a two-time-scale distributed, projected algorithm is proposed. The simulation results are also shown. To further illustrate the effectiveness of the proposed algorithm through theoretical analysis, such an algorithm is generalized into a two-time-scale hybrid system by using an average dwell-time automaton and a time-ratio monitor to impose restrictions on the frequency and relative activation time of the attacks. To analyze stability of such a hybrid system, the reduced system and the boundary layer system are presented and corresponding Lyapunov functions are constructed. Correspondingly, uniform (uniform global) asymptotic stability is obtained under some mild assumptions. Also, some results are given for systems without attacks. Finally, two aggregative games are used to show the effectiveness of the proposed algorithm and theoretical analysis.

Finite-time output feedback trans-media tracking control of a slender body trans-media vehicle via neural network extended state observer

The emerging trans-media vehicle is significant due to its amphibious ability. A finite-time output feedback trans-media tracking control scheme is proposed for a slender body trans-media vehicle with unknown time-varying hydrodynamics and external disturbances. First, a novel neural network extended state observer is developed to observe the vehicle’s velocities and handle the time-varying hydrodynamics and total disturbances simultaneously. Then, combined with the proposed observer, the finite-time command filtered backstepping technique is carefully constructed to yield the finite-time output feedback tracking control. The strength of the proposed approach to the existing methods is that it ensures the trans-media tracking errors converge to the small region of origin within a finite time, even in the absence of velocity measurements. The simulations are given to illustrate the superiority of the proposed scheme.

Improved Finite-Time Disturbance Observer-Based Control of Networked Nonholonomic High-Order Chained-Form Systems

This article investigates the finite-time leader–follower tracking problem for consensus control of nonholonomic MASs with chained-form dynamics under unknown time-varying disturbances. First, a finite-time distributed observer, consisting of the tangent hyperbolic function with an induced high gain effect, is constructed to estimate the leader’s information both quickly and accurately for each follower leading to communication loop avoidance. Besides, to cope with the adverse impact resulting from external disturbances, a finite-time disturbance observer is developed to provide accurate estimations of unknown terms within a finite time. A finite-time backstepping control scheme with a fast convergence rate is then proposed for each follower based on estimated disturbances to track the estimated states of the leader. Regardless of how close or how far away from the equilibrium point the follower states are, this method accelerates the convergence rate. An approximation technique using piecewise functions is also employed to bring the upper estimate of the convergence time closer to its real value. Finally, the efficiency of the presented control protocol is verified by some simulations on a number of connected wheeled mobile robots under external disturbances.

Distributed Event-Triggered Fixed-Time Leader–Follower Formation Tracking Control of Multiple Underwater Vehicles Based on an Adaptive Fixed-Time Observer

This paper focuses on the fixed-time leader–follower formation control of multiple underwater vehicles (MUVs) in the presence of external disturbances. First, an adaptive fixed-time disturbance observer (AFxDO) is developed to deal with unknown time-varying environmental disturbances. The developed AFxDO guarantees the fixed-time convergence property of the disturbance observation error and no prior information on the external disturbances or their derivatives is required. Then, with the aid of the developed AFxDO, a distributed event-triggered fixed-time backstepping controller was developed to achieve the leader–follower formation tracking control of MUVs. To solve the “explosion of complexity” problem inherent in the conventional backstepping, a nonlinear filter is introduced to obtain the derivative of the virtual control law. Furthermore, to reduce the communication burden, the event-triggered mechanism is integrated into the formation tracking controller. The stability analysis shows that the closed-loop MUV system is practical fixed-time stable. Finally, simulation results demonstrate the effectiveness of the proposed scheme.

Robust adaptive finite-time course tracking control of vessel under actuator attacks

This paper studies the course tracking control problem of unmanned surface vessels under the influence of uncertain dynamics, external unknown disturbances, constraints, and actuator attacks. In the design of the control scheme, adaptive technology is applied to approach the uncertain dynamics of the system, and a nonlinear finite-time disturbance observer is established to reconstruct the actuator attack signal and the unknown time-varying disturbances online. Combining disturbance compensation and adaptive technology, a finite-time course tracking control scheme is designed. The control scheme does not need to obtain the prior knowledge of the model in advance, and it has good robustness in the face of uncertain dynamics within the system, external disturbances, and actuator attacks. A rigorous stability analysis is provided for the control scheme based on the Lyapunov stability theory. Finally, the simulation shows that the proposed control scheme can effectively resist the influence of actuator attacks and external uncertain disturbances.

Robust coverage control of multiple USVs with time-varying disturbances

This paper investigates the problem of optimal coverage control for multiple unmanned surface vehicles (USVs) in the presence of time-varying disturbances. To solve this problem, the disturbance vector observer is designed to approximate the unknown time-varying disturbances. It is demonstrated that the estimated disturbance vector converges to the actual disturbance vector within a finite time. To achieve the optimal coverage effect of the task region, the control idea of layer-by-layer design is borrowed, and the desired velocities of the USV are designed. By following the desired velocities, the USV network can achieve the optimal coverage effect of the task region. Based on the estimated disturbances, a robust coverage controller is designed to achieve the tracking of desired velocities by the USV within a finite time, ultimately achieving optimal coverage effect of the task region by the USV network. Finally, corresponding simulation results are provided to validate the effectiveness of the proposed approach.

PTESO based robust stabilization control and its application to 3-DOF ship-borne parallel platform

In this paper, a prescribed-time extended state observer (PTESO) is constructed for a three degree-of-freedom (3-DOF) parallel ship-borne platform to estimate the platform’s total disturbances, including dynamic uncertainties, unknown time-varying external disturbances and coupling between the platform motion state variables. The constructed PTESO offers the advantages of converging within a prescribed time, suppressing initial peaking phenomenon and easy implementation. Furthermore, a PTESO based PD-like robust stabilization control law is designed, which maintains the support surface of the platform at a given horizontal position and orientation in the inertial space. Theoretical analyses show that the resulting closed-loop stabilization control system is stable. Simulation results with comparisons are presented to verify the effectiveness of our proposed robust stabilization control strategy.

Robust fixed-time trajectory tracking control of the dynamic positioning ship with actuator saturation

This paper addresses the fixed-time trajectory tracking control and setpoint regulation problems for dynamic positioning (DP) ships subject to unknown time-varying disturbances, system uncertainties, and actuator saturation. To meet the resistance of the low-frequency disturbances and system uncertainties, a continuous fixed-time disturbance observer (FTDO) based on integral sliding mode and fixed-time control is constructed. A nonlinear auxiliary dynamic system is introduced to mitigate the inconsistency between command forces and actual control forces, in which the feedback of the bias Δτ guarantees the input constraints for the design of the proposed controller. The explosion-of-complexity problem inherent in traditional backstepping is addressed based on a nonlinear first-order filter. Furthermore, a robust fixed-time control law with constraints is developed to track the predefined trajectory and the desired setpoint. Theoretical analyses demonstrate the fixed-time stability of the closed-loop system via Lyapunov analysis. Numerical simulation results illustrate the effectiveness and robustness of the proposed control approach.