Nonlinear Observer Research Articles

Variable Kerr nonlinearity and optical bistability of a four-level lambda atomic medium

Using perturbation theory we obtain expressions for the third-order nonlinear susceptibility and the Kerr nonlinear coefficient of a four-level lambda-type atomic system in the presence of Doppler broadening. The model is applied to the Rb atomic gas medium at room temperature; the investigations demonstrate the ability to enhance and control the Kerr nonlinear coefficient according to laser parameters in single-window and double-window EIT regimes. The amplitude and the sign of the Kerr nonlinear coefficient change sensitively to the driving laser parameters as well as ambient temperature. As a representative application, this Kerr nonlinear medium is applied to optical bistability (OB) and shows that the threshold intensity and the width of OB are also easily changed according to the laser parameters. In particular, in double-window EIT regime the emergence of nonlinear coefficient at different frequency domains that leads to the appearance of OB at multiple frequency domains simultaneously. This study is a good preparation for experimental observations of Kerr nonlinearity and optical bistability.

Asymmetric full-state constrained attitude control for a flexible agile satellite with multiple disturbances and uncertainties

In this paper, an asymmetric full-state constrained attitude control method for a flexible agile satellite with multiple disturbances and uncertainties is proposed. Both the attitudes and angular velocities of the flexible agile satellite are guaranteed in the asymmetric/symmetric bounds by utilizing the time-varying integral barrier Lyapunov function (TVIBLF) and constant integral barrier Lyapunov function (IBLF) respectively. Compared with the existing error-based barrier Lyapunov functions, the asymmetric TVIBLF does not need error transformation, relaxes the conservation of the initial requirements, and has more compatibility. Furthermore, the proposed asymmetric TVIBLF can deal with the asymmetric time-varying constraints without loss of generality. In addition, the high-frequency flexible vibrations, inertial uncertainties, and unknown external disturbance torques affected on the agile satellite are considered respectively. On one hand, a modal observer is utilized to suppress the high-frequency flexible vibration effects on the attitudes. On the other hand, the inertial uncertainties and unknown external disturbance torques are estimated with a multi-variable nonlinear disturbance observer. Therefore, both the asymmetric full-state constrained performances and robustness of the attitude control system for the flexible agile satellite are achieved. The stability of the closed-loop system is proved and numerical simulations have validated the effectiveness of the proposed method.

Modeling and Active Vibration Control of Flexible Robotic Arm and Its Application in Agricultural Water Conservancy Field

In order to improve the modeling and active vibration control effectiveness of flexible manipulators, this paper combines big data technology to study the modeling and active control of flexible manipulators. In addition, this article decouples the dynamic model of the flexible joint manipulator based on voltage control method, redefines the control input of the system as the voltage of the joint motor, and uses a nonlinear state observer to control the flexible link manipulator. The control strategy proposed in this article is based on a nonlinear state observer, combined with input-output control, to achieve tracking of joint angular displacement in a flexible linkage manipulator. Through experimental research, it can be seen that the big data based modeling and active vibration control research system for flexible robotic arms proposed in this paper can effectively improve the motion control effect of flexible robotic arms.

Incremental Nonlinear Dynamics Inversion Control with Nonlinear Disturbance Observer Augmentation for Flight Dynamics

A flight controller formulation based on incremental nonlinear dynamics inversion (INDI) control with nonlinear disturbance observer (NDO) is proposed. INDI control is a nonlinear controller based on incremental dynamics. Aimed to attain robustness for nonlinear dynamics inversion (NDI)-based controller, incremental dynamics are derived using the first-order Talyor series expansion to nonlinear systems. The incremental dynamics-based controller requires information on state derivative terms to strengthen the robustness property of the nonlinear controller. The proposed controller utilizes the first-order low-pass filter to obtain the state derivative estimate to implement incremental dynamics into the system. Because the incremental form creates uncertainty term which is an aftermath of the Taylor series expansion, the proposed controller adopts the NDO to eliminate this effect. The controller is applied to the generic transport model which was developed by NASA for simulation purposes. The proposed NDO-based INDI control underwent simulations, together with an INDI controller without disturbance observer, and showed that the developed method results in better performances, providing important advantages where it compensates the uncertainties, removes the steady-state error, and shows less oscillating longitudinal body rate response than the baseline controller, desirable for aerodynamics applications with faster system response.

Simultaneous modeling and adaptive fuzzy sliding mode control scheme for underactuated USV formation based on real-time sailing state data

An adaptive fuzzy sliding mode control scheme based on data feedback is proposed in this paper, in order to achieve the trajectory tracking control of underactuated unmanned surface vehicles (USVs) in the present of unknown model parameters and environmental disturbances. Considering the problem of unknown model parameters, based on the feedback of sailing data, an online identification algorithm is designed to obtain real-time model parameters of USVs, which are used to establish the real-time simultaneous models of USV formation. A fuzzy control algorithm is introduced into the sliding mode controller design process to reduce convergence time and eliminate the chattering of the controller. Furthermore, a first-order low-pass filter is proposed to overcome the "differential explosion" issue, and a second-order differential tracker is designed to mitigate the jitter effects caused by higher-order derivatives of the lateral velocity. In addition, a nonlinear disturbance observer is developed to estimate and compensate the composite disturbances caused by real-time modeling inaccuracies and ocean environment disturbances. Finally, the effectiveness and robustness of the proposed control scheme are verified by several simulation experiment cases.

Observer-Based Prescribed Performance Adaptive Neural Network Tracking Control for Fractional-Order Nonlinear Multiple-Input Multiple-Output Systems Under Asymmetric Full-State Constraints

In this work, the practical prescribed performance tracking issue for a class of fractional-order nonlinear multiple-input multiple-output (MIMO) systems with asymmetric full-state constraints and unmeasurable system states is investigated. A neural network (NN) nonlinear state observer is developed to estimate the unmeasurable states. Furthermore, the barrier Lyapunov functions with the settling time regulator are employed to deal with the asymmetric full-state constraint from the fractional-order MIMO system. On this ground, the prescribed performance adaptive tracking control approach is designed, assuring that all system states do not exceed the prescribed boundaries, and the tracking errors converge to the predetermined compact sets within a predefined time. Finally, two simulation examples are presented to show the effectiveness and practicability of the proposed control scheme.

Predefined-Time Hybrid Tracking Control for Dynamic Positioning Vessels Based on Fully Actuated Approach

This study investigates the problem of tracking the trajectory of a dynamic positioning (DP) ship under sudden surges of elevated sea states. First, the tracking problem is reformulated as an error calibration problem through the introduction of fully actuated system (FAS) approaches, thereby simplifying controller design. Second, a predefined-time control term is designed to maintain the convergence time of the trajectory tracking error within a specified range; however, the upper bound of the perturbation must be estimated in advance. The high sea state during operation can result in an abrupt change in the upper bound of disturbance, thereby affecting the control accuracy and stability of the system. Therefore, a linear control matrix is developed to eliminate the system’s dependence on the estimation of the upper bound of disturbance following smooth switching, thereby achieving control decoupling and providing a conservative switching time. Additionally, a nonlinear reduced-order expansion observer (RESO) is constructed for feedforward compensation. The stability of the system is demonstrated using the Lyapunov function, indicating that the selection of appropriate poles can theoretically enhance the system’s convergence with greater control accuracy and robustness after switching. Finally, the effectiveness of the proposed method is validated through simulations and comparative experiments.

Design and implementation of a nonlinear observer for a novel Quadrotor UAV: the HELIPLANE

This study presents the design and dynamic modeling of a new type of quadrotor UAV, referred to as the Heliplane, which integrates the vertical take-off and landing (VTOL) capabilities of a multirotor with the horizontal flight efficiency of a fixed-wing aircraft. The modeling process involved creating a dynamic representation of the Heliplane, with special attention to the determination of its aerodynamic coefficients, which were calculated using SolidWorks Flow Simulation. The aerodynamic forces, including lift and drag, were analyzed based on the flow characteristics around the Heliplane's structure. To further enhance the system's performance, a nonlinear observer based on a sliding mode approach was synthesized. This observer was designed in a triangular form to ensure accurate state estimation and robust control, even in the presence of model uncertainties. The observer's key advantage lies in its finite-time convergence, which guarantees quick and precise tracking of the Heliplane's state variables. Simulation results demonstrated the effectiveness of the proposed observer in estimating the rotational and translational velocities with minimal deviation. The sliding mode observer's performance suggests its suitability for control and fault detection tasks in UAV applications, particularly in challenging operational environments.

Adaptive Integral Sliding Mode Control with Chattering Elimination Considering the Actuator Faults and External Disturbances for Trajectory Tracking of 4Y Octocopter Aircraft

This paper presents a control strategy for a 4Y octocopter aircraft that is influenced by multiple actuator faults and external disturbances. The approach relies on a disturbance observer, adaptive type-2 fuzzy sliding mode control scheme, and type-1 fuzzy inference system. The proposed control approach is distinct from other tactics for controlling unmanned aerial vehicles because it can simultaneously compensate for actuator faults and external disturbances. The suggested control technique incorporates adaptive control parameters in both continuous and discontinuous control components. This enables the production of appropriate control signals to manage actuator faults and parametric uncertainties without relying only on the robust discontinuous control approach of sliding mode control. Additionally, a type-1 fuzzy logic system is used to build a fuzzy hitting control law to eliminate the occurrence of chattering phenomena on the integral sliding mode control. In addition, in order to keep the discontinuous control gain in sliding mode control at a small value, a nonlinear disturbance observer is constructed and integrated to mitigate the influence of external disturbances. Moreover, stability analysis of the proposed control method using Lyapunov theory showcases its potential to uphold system tracking performance and minimize tracking errors under specified conditions. The simulation results demonstrate that the proposed control strategy can significantly reduce the chattering effect and provide accurate trajectory tracking in the presence of actuator faults. Furthermore, the efficacy of the recommended control strategy is shown by comparative simulation results of 4Y octocopter under different failing and uncertain settings.

Nonlinear Extended State Observer and Prescribed Performance Fault-Tolerant Control of Quadrotor Unmanned Aerial Vehicles Against Compound Faults

Addressing trajectory and attitude control challenges in quadrotor UAVs amid compound faults and unknown external disturbances, this paper introduces a fault-tolerant control method predicated on nonlinear extended state observers. Initially, the UAV’s dynamic model is optimized and decoupled, forming a rapid non-singular terminal sliding mode surface that circumvents the singular phenomena typical in conventional terminal sliding mode controls. A nonlinear extended state observer is then deployed to estimate the unknown states triggered by compound faults and disturbances within the control system. Theoretical analysis shows that beyond accurately estimating faults and disturbances, the proposed controllers adaptively adjust the system’s dynamic and steady-state performances, ensuring rapid stabilization of all error responses. Numerical simulations indicate significant enhancements in control precision and robustness against compound faults and disturbances, with response times and energy consumption remaining within acceptable limits for practical applications.

A non-singular predefined-time sliding mode tracking control for space manipulators

This research presents a predefined-time control strategy for the trajectory tracking of a space manipulator subjected to parametric uncertainty and time-varying disturbance. Firstly, a nonlinear disturbance observer with predefined time convergence is constructed to achieve accurate estimation of the lumped disturbance without requiring any prior information. Subsequently, a unique predefined-time terminal sliding surface containing arctan function is proposed, which avoids the singularity problem that exists in traditional terminal sliding surfaces. Afterwards, a novel robust terminal sliding mode control law is designed based on the estimated knowledge. The developed controller ensures the predefined time stability of the closed-loop system, and the convergence time’s upper bound can be explicitly defined in advance through two specific parameters for any initial conditions. Finally, numerical simulations and comparative tests verify the effectiveness and superiority of the suggested controller.

Event-triggered prescribed-time control for vehicular platoon systems with unknown disturbances

An event-triggered prescribed-time control scheme is proposed for vehicular platoon systems (VPSs) subject to parameter uncertainties, unknown external disturbances and actuator saturation. By utilizing the time-scaling method and the finite-time stable theory, we transform the prescribed-time stability problem of the VPSs in finite time domain into the asymptotic stability problem in infinite time domain. On the basis of this, this work proposes a nonlinear prescribed-time disturbance observer for each follower vehicle, which can accurately estimate unknown lumped disturbance within a prescribed settling time. Then, a novel event-triggered prescribed-time control scheme is designed for the VPSs, which combines back-stepping technology and time-scaling method. This scheme simultaneously addresses the issues of ensuring the convergence of tracking errors within the prescribed settling time and reducing wastage of communication resources. What’s more, the proposed scheme ensures the stability of the closed-loop system within the prescribed settling time, while guaranteeing the tracking performance of the VPSs. The settling time is not affected by the initial states of the systems and the parameters of the controllers. Finally, the effectiveness of the proposed control method is confirmed through numerical simulations.

State estimation of networked nonlinear systems with aperiodic sampled delayed measurement

This paper aims to study the remote state estimation of networked nonlinear systems subject to aperiodic sampled delayed measurement. A novel sampled-data non-affine nonlinear observer (SNNO) is designed to address this issue. The designed observer is composed of two parts: the first part is a continuous-time observer, and the second part is an auxiliary variable design that provides continuous compensation of output estimation errors for the first part’s state observer. The design of this auxiliary variable provides a new compensation scheme for sampled delayed measurement. The input-to-state stability of the SNNO with respect to the system and output disturbance is proved by means of trajectory-based stability theory. The new theoretical tool reveals the relationship between the convergence rate of the proposed SNNO and the sampling and delay periods. Simulations and comparative analyses with other sampled-data observers are given.

Application of derivative and integral terminal sliding modes in leader-follower type systems"

Subject matter: The study focuses on the control methods for dr20 type robot swarms, specifically on the derivative and integral terminal sliding mode control combined with a nonlinear disturbance observer. The problem of effective swarm control is highly relevant in the current conditions of automation and robotics, especially in the context of performing complex tasks in limited space and in the presence of disturbances. Goal: The development and analysis of a simulation model for the movement of a robot swarm using advanced control methods to ensure system accuracy and stability. The research aims to improve the control methods for robot swarms, enhancing their efficiency and reliability in various operational conditions. Tasks: 1) Develop a simulation model of a robot swarm in the CoppeliaSimEDU environment, considering all necessary parameters for modeling real operating conditions. 2) Implement control algorithms for the leader and followers to maintain the swarm structure and avoid collisions. 3) Conduct a series of experiments to test the effectiveness of the proposed methods, analyzing the results in terms of stability and control accuracy. Methods: Modeling in CoppeliaSimEDU, implementing control algorithms based on derivative and integral terminal sliding mode control, applying a nonlinear disturbance observer to improve system stability. The applied methods allow for the consideration of various disturbances and ensure high control accuracy. Results: he proposed control model allows achieving high following accuracy and collision avoidance even in complex conditions. Experiments have shown that the control methods ensure the stability and accuracy of the robot swarm's movement, reducing the response time to external disturbances. The research results demonstrate that the use of derivative and integral terminal sliding mode control combined with a nonlinear disturbance observer significantly enhances the efficiency of multi-robot systems. Conclusions: The use of advanced control methods significantly improves the efficiency of multi-robot systems, ensuring their reliability and accuracy in real operating conditions. The proposed methods can be applied in various fields where the coordination of a large number of robots is required, including logistics, rescue operations, and environmental monitoring.

Adaptive Event-Triggered Consensus Control of Nonlinear Multi-Agent Systems via Output Feedback Methodology: An Application to Energy Efficient Consensus of AUVs

For dealing with the energy consumption in multi-agent systems (MASs), an event-triggered (ET) methodology is promising, which relies on the activation of communication devices only when communication of data is needed. This paper explores the leaderless consensus for nonlinear MASs using an adaptive ET approach via an output feedback methodology. This adaptive ET scheme is preferred as it can adapt to the environment through setting a communication threshold. The proposed approach renders the observed states of agents by use of nonlinear observers in an output feedback control dilemma, making it more practical. Simple Luenberger observers are developed to avoid the problem of always measuring agents’ states. The strategy of adaptive ET-based control is employed to minimize resource use and information transmission. Design conditions for the observer-based adaptive ET consensus control of nonlinear MASs have been derived via a Lyapunov function, containing state estimation error, consensus error, adaptation term, and nonlinearity bounds. In contrast to the existing methods, the present approach applies a more practical output feedback schema, uses adaptive ET proficiency, and deals with nonlinear agents. An example of a formation of autonomous underwater vehicles achieving the basic consensus realization between displacement and velocity is included to illustrate the viability of the resultant approach.

Disturbance observer based adaptive predefined‐time sliding mode control for robot manipulators with uncertainties and disturbances

AbstractThis article develops a predefined‐time sliding mode control approach for systems with external disturbances and uncertainties through a nonlinear disturbance observer (DO). For addressing predefined‐time stabilization problem of robotic manipulator system, a predefined‐time sliding mode surface is proposed, ensuring system states converge to origin within a predefined‐time once sliding mode surface is attained. Compared to conventional fixed‐time and finite‐time control strategies, a distinctive advantage of this scheme is that system settling time can be explicitly chosen in advance and independent of system states. To achieve predefined‐time performance, a disturbance observer is introduced to generate the disturbance estimate, which can be incorporated into controller to counteract disturbance. To address the systems uncertainty, an adaptive law is employed to estimate the unknown upper boundary of system uncertainties. Finally, the effectiveness and performance of the proposed scheme are illustrated by simulation and experiment.

Design of Neural Network-Based Multi-Fault Tolerant Control System for Unmanned Aerial Vehicles

Actuator failure seriously threatens the flight safety of unmanned helicopters. Considering the problem of multiple faults such as actuator bias and failure in unmanned helicopters, a composite fault-tolerant flight control algorithm is proposed. For actuator bias fault, a nonlinear fault observer is designed to estimate it in real time; for actuator failure fault, a same-dimensional auxiliary system is constructed and processed by neural network technology. The composite fault-tolerant flight controller of the unmanned helicopter is designed by backstepping method, and the Lyapunov stability theory is used to prove that the error signals of the closed-loop system are bounded and convergent. Simulation results show that the proposed control algorithm can improve the fault tolerance of the unmanned helicopter when multiple actuator faults occur, ensuring its safe flight.

An Adaptive Controller with Disturbance Observer for Underwater Vehicle Manipulator Systems

Dynamic control of underwater vehicle manipulator systems (UVMSs) is the key part of underwater intervention tasks. In this paper, we propose an adaptive controller with a disturbance observer that mainly consists of two parts: the first part is the adaptive control law that estimates the changes in the center of mass (COM) and the center of buoyancy (COB) of the vehicle, and the second part is the nonlinear disturbance observer that estimates the external disturbance and model uncertainties. To attenuate the overestimation problem, a damping term is introduced to the adaptive law. The stability of the proposed method is proven on the basis of Lyapunov theory. We develop three scenarios on the Simurv platform and illustrate the effectiveness of the proposed method with a short response time and high tracking performance.

Robust adaptive prescribed performance control for nonlinear systems with arbitrary initial states

The initial state of nonlinear MIMO strict feedback systems is often unpredictable and random, and existing prescribed performance control (PPC) techniques can only guarantee system output constraints within a fixed initial value performance boundary. In this paper, an adaptive PPC method tailored for nonlinear systems was introduced, enabling the system stable tracking regardless of the arbitrary initial states. To guarantee that the tracking error consistently meets the prescribed performance boundary(PPB) envelope, we introduce a nonlinear mapping between the initial value of the prescribed performance functions(PPFs) and the system tracking errors, resulting in an asymmetric time-varying performance boundary. Building upon this foundation, an adaptive PPC scheme is proposed under the backstepping framework, integrated with a nonlinear disturbance observer (NDO). This method ensures that the tracking error remains within the desired PPB, regardless of external disturbances or system initial states. To prevent ‘complexity explosion’, a dynamic surface control (DSC) technology is employed to filter the virtual control signals of each subsystem. Furthermore, the ultimate uniform boundedness of the closed-loop signal has been demonstrated, and a practical flight vehicles roll control case was introduced to validate the efficacy of the proposed method.

Adaptive robust fault-tolerant control of spinning tether system for space debris removal

The Spinning Tether System (STS) is currently recognized as one of the most effective and ideal platforms for removing space debris. It offers several advantages, including a non-contact mechanism, rapid deorbit capabilities, stable spinning, and a short preparation time for subsequent missions. The system primarily depends on the thrusters of the main spacecraft and the capture device for its spin-up process. Although modern technology and quality management methods strive to minimize thruster failures, the capture of debris significantly affects the STS. This impact can induce tether oscillations and cause actuator failures, thereby destabilizing the spin-up process. Given these challenges, this paper explores the design of fault-tolerant control strategies to enhance system reliability during the post-capture spin-up phase. Initially, a dynamic model using quaternions as generalized coordinates was established based on the constrained Lagrange equation. This model facilitated a detailed analysis of potential thruster failure modes. Subsequently, the optimal trajectory for the spin-up process was planned using the pseudo-spectral method, ensuring efficiency and safety in control execution. To address the identified vulnerabilities, the study introduces an adaptive robust fault-tolerant controller. This controller, based on a BLF and integrated with a nonlinear neural network disturbance observer, is designed to operate effectively under fault conditions. Numerical simulations were conducted to validate the performance of the controller, demonstrating its capability to maintain stable control of the system, both after detecting a fault signal and following an actuator failure.