Unknown Time-varying Disturbances Research Articles

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.

Receding Galerkin Optimal Control with High-Order Sliding Mode Disturbance Observer for a Boiler-Turbine Unit

The control of the boiler-turbine unit is important for its sustainable and robust operation in power plants, which faces great challenges due to the control unit’s serious nonlinearity, unmeasurable states, variable constraints, and unknown time-varying lumped disturbances. To address the above issues, this paper proposes a receding Galerkin optimal controller with a high-order sliding mode disturbance observer in a composite scheme, in which a high-order sliding mode disturbance observer is first employed to estimate the lumped disturbances based on a deviation form of the mathematical model of the boiler-turbine unit. Subsequently, under the hypothesis of state constraint, a receding Galerkin optimal controller is designed to compensate the lumped disturbances by embedding their estimates into the mathematically based predictive model at each sampling time instant. With the help of an interpolation polynomial, Gauss integration, and nonlinear solvers, an optimal control law is then obtained based on a Galerkin optimization algorithm. Consequently, disturbance rejection, target tracking, and constraint handling performance of a controlled closed-loop system are improved. Some simulation cases are conducted on a mathematical boiler-turbine unit model to demonstrate the effectiveness of the proposed method, which is supported by the quantitative result analysis, such as tracking and disturbance rejection performance indexes.

Event-triggered adaptive finite time trajectory tracking control for Underactuated Vessel considering unknown time-varying disturbances

Abstract This paper aims to solve the finite-time trajectory tracking problem of underactuated surface ships under the influence of dynamic uncertainty, unknown external time-varying interference and limited communication resources, an event-triggered robust adaptive finite-time trajectory tracking control method for underactuated ships is designed by combing the existing trajectory tracking control methods and engineering needs in actual navigation. It can obviously improve the tracking accuracy of the ship, and complete the tracking task safely and efficiently. This scheme transforms the composite uncertain vector synthesized by uncertain parameters and external disturbances into a linear parameterized form. Next, considering the limitation of communication resources, a relative threshold event triggering mechanism is introduced to further extend the triggering time interval on the basis of the fixed threshold triggering scheme. Then, an event-triggered robust adaptive finite-time trajectory tracking control scheme is designed for underactuated ships, and a rigorous stability proof is provided for the finite-time trajectory tracking control scheme designed above through Lyapunov stability theory. Simulation experiment is carried out in MATLAB and the results show that the finite-time trajectory tracking control scheme proposed in this paper can effectively solve the problems of dynamic uncertainty, unknown time-varying interference from the outside world, and limitation of communication resources. This paper can provide theoretical support for the autonomous navigation of intelligent ships.

Precision motion control for electro-hydraulic axis systems under unknown time-variant parameters and disturbances

This article focuses on asymptotic precision motion control for electro-hydraulic axis systems under unknown time-variant parameters, mismatched and matched disturbances. Different from the traditional adaptive results that are applied to dispose of unknown constant parameters only, the unique feature is that an adaptive-gain nonlinear term is introduced into the control design to handle unknown time-variant parameters. Concurrently both mismatched and matched disturbances existing in electro-hydraulic axis systems can also be addressed in this way. With skillful integration of the backstepping technique and the adaptive control, a synthesized controller framework is successfully developed for electro-hydraulic axis systems, in which the coupled interaction between parameter estimation and disturbance estimation is avoided. Accordingly, this designed controller has the capacity of low-computation costs and simpler parameter tuning when compared to the other ones that integrate the adaptive control and observer/estimator-based technique to dividually handle parameter uncertainties and disturbances. Also, a nonlinear filter is designed to eliminate the “explosion of complexity” issue existing in the classical back-stepping technique. The stability analysis uncovers that all the closed-loop signals are bounded and the asymptotic tracking performance is also assured. Finally, contrastive experiment results validate the superiority of the developed method as well.

Adaptive backstepping fast terminal sliding mode control of dynamic positioning ships with uncertainty and unknown disturbances

Considering the complexity of the operating environment of marine ships, higher demands are placed on the positioning accuracy and positioning performance of Dynamic Positioning (DP) systems. This paper designs an Adaptive Backstepping Fast Terminal Sliding Mode Control (ABFTSMC) to solve the problems of low positioning accuracy, slow convergence, and poor anti-interference performance in ship positioning due to uncertainty of dynamic model parameters and unknown time-varying environmental disturbances. A Fast Terminal Sliding Mode Control (FTSMC) is combined with backstepping techniques to ensure the robustness of the system to uncertainties and disturbances. Meanwhile, an adaptive law is used to estimate the unknown uncertainty terms. Moreover, the Lyapunov stability criterion is used to prove the convergence and stability of the designed controller. Multiple simulation results show that ABFTSMC has better control performance compared with Adaptive Backstepping Control (ABC) and Adaptive Backstepping Sliding Mode Control (ABSMC). All the comparisons could fully verify the effectiveness and superiority of the proposed control method.

Event-triggered tracking control for nonlinear time-varying delay systems with full state constraints and unknown control coefficients

This paper addresses the problem of event-triggered control for a class of nonlinear systems with unknown control coefficients, time-varying delays, full state constraints and external disturbances, simultaneously. Firstly, based on integral Barrier-Lyapunov Functionals, an adaptive event-triggered controller is designed to account for the impacts of complete state constraints, unknown time-varying delays and external disturbances. Using fuzzy logic systems, the unknown functions of systems are then roughly estimated. The system redundancy can be significantly reduced by implementing the event-triggered control technique in the meanwhile. By introducing the separation technique and Lyapunov–Krasovskii functionals, it is shown that the strategy can ensure tracking performance greatly and all the closed-loop signals of the system are bounded. Compared with the existing results, the proposed design scheme is less conservative and has a wilder application range. Finally, the simulation results show the effectiveness of the proposed approach.

Quadrotor Neural Network Adaptive Control: Design and Experimental Validation

This letter presents the design and experimental study of an adaptive nonlinear controller for Unmanned Aerial Vehicles (UAVs) in the presence of unknown time-varying disturbances, and model parametric uncertainty. We employ an adaptive Neural Network (NN), used to approximate the partially unknown system, in tandem with a simple controller designed for trajectory tracking, not of the center of mass, but of a point located along the UAV's vertical body axis. This strategy allows: (i) to avoid the two-subsystems control paradigm generally adopted by conventional UAV controllers; (ii) all control inputs to be defined at once; and (iii) to lump all unknown dynamics from both translational and rotational levels into a single vector term. The weights of the NN are determined online by an adaptive law based on the Lyapunov synthesis method. The tracking and adaptation errors are shown to be uniformly ultimately bounded. Simulation and experimental results, including comparison data, are provided to validate and assess the proposed control solution.

Fixed-time tracking control for high-order nonlinear systems with unknown time-varying input delay

Fixed time tracking control for nonstrict feedback high-order nonlinear systems with unknown time-varying external disturbance and unknown time-varying input delay has been studied in this research. Firstly, the obstacle caused by unknown time-varying input delay has been tackled by introducing a compensation signal. The unknown nonlinear functions are identified by neural networks and the algebraic loop problem for nonstrict feedback systems has been overcome by using the properties of neural networks. Further, a bound estimation mechanism is employed to estimate the identify error and unknown time-varying external disturbance without using the priori knowledge of the boundary. Regarding the obstacle caused by high-order terms and the singularity problem have been tackled by using adding a power integrator mechanism and the inequality transformation technique, respectively. The boundedness of all the signals in the closed-loop systems has been proved by using the Lyapunov stability theorem, and the convergence time is independent of the initial value of the system state. Finally, the simulation results show the effectiveness of the proposed method.

Adaptive Leader-Follower Consensus Control of Multiple Flexible Manipulators With Actuator Failures and Parameter Uncertainties

In this paper, the leader-follower consensus problem for a multiple flexible manipulator network with actuator failures, parameter uncertainties, and unknown time-varying boundary disturbances is addressed. The purpose of this study is to develop distributed controllers utilizing local interactive protocols that not only suppress the vibration of each flexible manipulator but also achieve consensus on joint angle position between actual followers and the virtual leader. Following the accomplishment of the reconstruction of the fault terms and parameter uncertainties, the adaptive neural network method and parameter estimation technique are employed to compensate for unknown items and bounded disturbances. Furthermore, the Lyapunov stability theory is used to demonstrate that followers' angle consensus errors and vibration deflections in closed-loop systems are uniformly ultimately bounded. Finally, the numerical simulation results confirm the efficacy of the proposed controllers.

Cooperative Target Tracking of Multiple Autonomous Surface Vehicles Under Switching Interaction Topologies

This paper is concerned with the cooperative target tracking of multiple autonomous surface vehicles (ASVs) under switching interaction topologies. For the target to be tracked, only its position can be measured/received by some of the ASVs, and its velocity is unavailable to all the ASVs. A distributed extended state observer taking into consideration switching topologies is designed to integrally estimate unknown target dynamics and neighboring ASVs' dynamics. Accordingly, a novel kinematic controller is designed, which takes full advantage of known information and avoids the approximation of some virtual control vectors. Moreover, a disturbance observer is presented to estimate unknown time-varying environmental disturbance. Furthermore, a distributed dynamic controller is designed to regulate the involved ASVs to cooperatively track the target. It enables each ASV to adjust its forces and moments according to the received information from its neighbors. The effectiveness of the derived results is demonstrated through cooperative target tracking performance analysis for a tracking system composed of five interacting ASVs.

Increasing the region of attraction in DC microgrids

Based on the port-Hamiltonian framework, this paper proposes a novel control scheme for stabilising the voltage in DC networks affected by (i) unknown ZIP-loads, i.e., nonlinear loads consisting of the parallel combination of constant impedance (Z), current (I) and power (P) load types, and (ii) unknown (but bounded) time-varying disturbances. Differently from the results existing in the literature, where restrictive (sufficient) conditions on the load parameters, voltage trajectory and voltage reference are assumed to be satisfied, this is the first paper (to the best of our knowledge) proposing a controller that relaxes such conditions and guarantees the exponential stability of the desired equilibrium point, whose region of attraction can be increased by simply tuning the control gains. In the case the network is affected by unknown time-varying disturbances, local input-to-state stability (l-ISS) is ensured. Furthermore, if non-ideal P-loads are considered, excluding the unrealistic possibility that the load absorbs infinite current when the voltage approaches zero, the aforementioned stability results hold globally.

Adaptive generalized predictive control for dynamic positioning system of ships with model unknown parameters

This paper proposes an adaptive generalized predictive control for dynamic positioning of ships with unknown model parameters and unknown time-varying environmental disturbances. The controlled auto-regressive integrated moving average (CARIMA) model is employed to describe the movements of ships with model parameter and disturbance uncertainties. The recursive least square method with forgetting factor is utilized to design adaptive laws to estimate the CARIMA model parameters online. Considering both the positioning accuracy and the change intensity of control increments, a cost function is constructed. The optimal control increments that minimize the cost function are obtained by using Lagrange multiplier method. Then, the adaptive control law is designed to maintain ship’s position and heading at desired values. Finally, simulation studies in different cases are carried out and simulation results demonstrate the effectiveness of the proposed control scheme.

Ship Dynamic Positioning Output Feedback Control with Position Constraint Considering Thruster System Dynamics

In order to simultaneously address the issues of ship operating area limitation, unknown time-varying disturbances, immeasurable ship speed, unknown dynamics, and input saturation, this paper investigates the position-constrained ship dynamic positioning output feedback control, taking thruster system dynamics into account. Firstly, a barrier Lyapunov function (BLF) is utilized to limit the ship position inside the dynamic positioning system’s acceptable working range and to limit the ship position error. Second, the set total disturbance, which is made up of unknown time-varying disturbances and unknown dynamics and is further handled by the control strategy, is estimated using a fixed-time extended state observer (FDESO). Additionally, the thruster system dynamics equations are incorporated into the controller design process so that the generated thrust signal varies gradually without abrupt fluctuations, in keeping with engineering realities. Furthermore, the thruster input saturation issue is dealt with using a finite-time auxiliary dynamic system. Finally, a robust control term is introduced to handle the errors generated in the controller design. The stability proof section demonstrates that the designed control strategy can cause the ship to arrive and maintain at the desired location and heading, as well as stay continuously inside the designated operating area with all signals of the closed-loop control system being consistently and eventually bounded. The simulation results demonstrate that the proposed system is valid.

Distributed finite-time velocity-free robust formation control of multiple underactuated AUVs under switching directed topologies

This paper proposes a distributed finite-time velocity-free robust formation control scheme for multiple underactuated autonomous underwater vehicles (AUVs) under switching directed topologies in the presence of uncertain dynamics and unknown time-varying external disturbances. Here, a novel finite-time velocity observer is created for each AUV to estimate its neighbors’ velocities within a finite time so that only its neighbors’ positions need to be transmitted, which reduces the communication burden between AUVs. Then, a super-twisting extended state observer is constructed for each AUV to estimate its total disturbances lumped by the uncertain dynamics and the unknown time-varying external disturbances, whose estimation errors can converge to zero within a finite time. Further, a distributed finite-time velocity-free robust formation control law is proposed incorporating the above into the nonsingular terminal sliding mode technique. Theoretical analysis and simulation results indicate that the proposed formation control law can make the multiple AUVs achieve the desired formation pattern while guaranteeing the formation errors converge to zero within a finite time.

State-unknown single parameter learning adaptive output feedback control for ship dynamic positioning

This paper focuses on the ship adaptive dynamic positioning output feedback control considering the thruster system dynamics, solving the problems of the ship output end affected by measurement noise, unmeasurable ship speed, unknown time-varying disturbance, model parameter ingestion, and input saturation simultaneously. First, a high-gain state observer is used for online estimation of the unknown ship speed, and an update gain technique is introduced to ensure the speed of state construction and reduce the effect of measurement noise. In addition, a single-parameter learning neural network is used to solve the unknown time-varying disturbance and ship model parameter ingestion problem. Furthermore, the thruster system dynamic equation is considered to solve the thruster system dynamic characteristics. Finally, the finite-time auxiliary dynamic system is used to deal with the input saturation problem. The analysis process shows that the control method can make the ship finally reach and stay in the desired position and desired heading, and all control variables in the designed dynamic positioning system are consistent and eventually bounded. The simulation results show that the proposed dynamic positioning control method is effective.

Fast fixed-time vertical plane motion control of autonomous underwater gliders in shallow water

In this paper, a fast fixed-time vertical plane motion controller is proposed for autonomous underwater gliders (AUGs) gliding in shallow water. The influence of speed-sensorless conditions, model uncertainties, unknown time-varying external disturbances, input saturations, and state delay are taken into account. To improve control performance, a fast fixed-time stable system is first presented. Based on the system, an adaptive extended state observer (ESO) is developed for estimating speed, model uncertainties, and external disturbances. A fast fixed-time controller is designed for improving the gliding efficiency and reducing the risk of hitting the ocean floor. Moreover, an input saturation auxiliary system and an advance compensation method are presented to cope with input saturations and state delay. According to Lyapunov theory, it is proved that the AUG states can converge into a small neighborhood within a fixed time. Finally, simulation results demonstrate the rapidity and effectiveness of the designed control method.

An enhanced trajectory tracking control of the dynamic positioning ship based on nonlinear model predictive control and disturbance observer

This paper proposes a robust control approach based on nonlinear model predictive control (NMPC) for dynamic positioning (DP) ships subject to unknown time-varying disturbances with the physical limitation of thrusters. An improved nonlinear disturbance observer (INDO) based on super-twisting control is constructed for disturbances estimation and attenuation. Furthermore, the NMPC optimization problem is formulated to reject the disturbances by combining the disturbance estimates into the prediction model. To mitigate the difference between commanded forces and actual forces, the low-level thrust allocation algorithm is integrated into the high-level motion controller. In light of this, a detailed time-iteration NMPC algorithm for DP ships is presented. Numerical simulations based on the INDO-based NMPC (INDO-NMPC) strategy under the scenario of trajectory tracking are performed to explore the robustness of DP system. Theoretical analysis and simulation results well prove the effectiveness and superiority of the proposed control law.

Robust Distributed Nash Equilibrium Seeking for Games Under Attacks and Communication Delays

In this article, a noncooperative game in which the engaged players are of double integrator-type dynamics, is investigated. The dynamics of the players are considered to be subject to unknown time-varying disturbances and unmodeled terms. Besides, the communication topology among the players suffers from attacks and time-varying communication delays. To find a Nash equilibrium for such games, a distributed robust Nash equilibrium seeking algorithm is proposed. By utilizing average dwell-time and time-ratio constraints to tackle the attacks, the closed-loop system is modeled as a hybrid system with memory. To analyze the stability of the distributed switched algorithm, a Lyapunov functional is constructed, by which we show the uniform global asymptotic stability of the equilibrium. Finally, an example is given to illustrate our results.