Nonlinear Observer Research Articles

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.

An Implementation of the Particle Flow Filter in an Atmospheric Model

Abstract The particle flow filter (PFF) shows promise for fully nonlinear data assimilation (DA) in high-dimensional systems. However, its application in atmospheric models has been relatively unexplored. In this study, we develop a new algorithm, PFF-DART, in order to conduct DA for high-dimensional atmospheric models. PFF-DART combines the PFF and the two-step ensemble filtering algorithm in the Data Assimilation Research Testbed (DART), exploiting the highly parallel structure of DART. To evaluate the performance of PFF-DART, we conduct an observing system simulation experiment (OSSE) in a simplified atmospheric general circulation model and compare the performance of PFF-DART with an existing linear and Gaussian DA method. Using the PFF-DART algorithm, we demonstrate, for the first time, the capability of the PFF to yield stable results in a yearlong cycling DA OSSE. Moreover, PFF-DART retains the important ability of the PFF to improve the assimilation of nonlinear and non-Gaussian observations. Finally, we emphasize that PFF-DART is a versatile algorithm that can be integrated with numerous other non-Gaussian DA techniques. This quality makes it a promising method for further investigation within a more sophisticated numerical weather prediction model in the future. Significance Statement Data assimilation is an important tool in weather forecasting. However, fundamental issues arising from linear and Gaussian approximations still exist, which can limit our utilization of observations. The particle flow filter is a promising method that avoids these approximations, but efficient algorithms for this method have yet to be developed. In this study, we develop an algorithm for the particle flow filter that can be implemented in high-dimensional geophysical models. We have demonstrated, for the first time, that the particle flow filter runs efficiently for a yearlong experiment in an atmospheric model. The new algorithm also improves the results over a commonly used data assimilation method. The results in this work demonstrate the potential usage of the particle flow filter in the weather forecasting and other high-dimensional forecasting problems.

On IMU preintegration: A nonlinear observer viewpoint and its applications

The inertial measurement unit (IMU) preintegration approach nowadays is widely used in various robotic applications. In this article, we revisit the preintegration theory and propose a novel interpretation to understand it from a nonlinear observer perspective, specifically the parameter estimation-based observer (PEBO). We demonstrate that the preintegration approach can be viewed as a recursive implementation of PEBO in moving horizons, and that the two approaches are equivalent with perfect measurements. We then discuss how these findings can be used to tackle practical challenges in estimation problems. As byproducts, our results lead to a novel hybrid sampled-data observer design and an approach to address statistical optimality for PEBO in the presence of noise.

Performance improvement of Grid-Connected Wind Energy Conversion System through Definite Time Horizon Control and MPPT based on Adaptive Observers

This research work investigates the implementation of Definite Time Horizon Control (DTHC) through an observer in a grid-connected Wind Energy Conversion System (WECS) equipped with a Permanent Magnet Synchronous Generator (PMSG). The main objective is to achieve sensorless Maximum Power Point Tracking (MPPT). To achieve this goal, mechanical rotational speed and torque estimates are exploited from an adaptive nonlinear observer. In addition, this work explores how the DTHC improves on the MPPT technique, enabling faster and more accurate tracking of the maximum power point. The proposed controller, unlike traditional non-linear controllers, rapidly stabilizes the WECS, tracking reference trajectories in a short, pre-determined period of time. Indeed, it demonstrates robustness in the face of unpredictable WECS parameters, adapting to variations thanks to a robust control design. Mathematical demonstrations of the defined time horizon stability and the resilience of the suggested WECS controllers are detailed in this investigation. This DTHC method improves rotor speed control, enabling more efficient sensorless MPPT. It contributes to improved WECS performance for following dynamic references and enhances adaptability against unpredictable parameters. In addition, it provides sophisticated control capabilities for the grid connected converter, improving the smoothness and efficiency of electrical energy injection.

Model reference adaptive control of electro-hydraulic servo system based on RBF neural network and nonlinear disturbance observer

Model reference adaptive control of electro-hydraulic servo system based on RBF neural network and nonlinear disturbance observer

Stability and vibration control of electrostatically excited functionally graded microresonator using nonlinear observer based sliding mode controller

The dynamic stability analysis of microsystems is an important aspect in understanding the critical operating regions under different excitations. Present study proposes an observer-based adaptive back-stepping sliding mode controller (ABSMC) model to control and stabilize an electrostatically excited functionally graded microresonator. The dynamic model of a microsystem subjected to random disturbances is derived using modified couple stress theory and Euler–Bernoulli’s beam model. The effective material properties are obtained from Mori-Tanaka scheme and the equations of motion are derived using Hamilton principle and solved by Galerkin’s method. A trained neural network estimator predicts the disturbances and the adaptive back-stepping sliding mode controller is designed for improving the system stability. The results of the proposed controller are compared with conventional sliding mode control (SMC) and proportional-derivative (PD) control solutions and it is found that ABSMC reduces settling time and input control force by 52.42% and 88.40%, respectively, with minimal chattering. The proposed control methodology effectively extends the travelling range of FG microsystems within and beyond the pull-in voltage.

Operational space robust impedance control of the redundant surgical robot for minimally invasive surgery.

The motion accuracy, compliance, and control smoothness for the surgical robot are of great importance to improve the safety of human-robot interaction. However, the end effector that interacts with soft tissue during surgery affects the dynamics of the robot. The control performance of the controller may be decreased if the changing dynamics are not identified and updated in time. This paper proposes a robust impedance controller for the redundant remote center of motion manipulator influenced by external disturbances, including external torque, uncertainties, and unmodeled terms in the dynamics. To achieve the desired impedance, a continuously switching sliding manifold is proposed. When the sliding manifold is driven to zero, the motion error will converge to a bounded region. This can overcome the adverse effects of external disturbances while guaranteeing motion accuracy and compliance. Chattering of the sliding mode control is alleviated through the formulated continuously switching sliding manifold and integrated nonlinear disturbance observer. Simulations and experiments demonstrate that the proposed controller has excellent motion accuracy, compliance, and control smoothness. This provides potential application prospects for the redundant surgical robot to guarantee safe human-robot interaction.

A Novel Estimating Algorithm of Critical Driving Parameters for Dual-Motor Electric Drive Tracked Vehicles Based on a Nonlinear Observer and an Adaptive Kalman Filter

High-speed dual-motor electric drive tracked vehicles (DDTVs) have emerged as a research hotspot in the field of tracked vehicles in recent years due to their advantages in fuel economy and the scalability of electrical equipment. The emergency braking of a DDTV at high speed can lead to slipping or even yawing (which is caused by a large deviation of forces at each track directly), posing significant challenges to the vehicle’s stability and safety. Therefore, the accurate real-time acquisition of critical driving parameters, such as the longitudinal force and vehicle speed, is crucial for the stability control of a DDTV. This paper developed a novel estimating algorithm of critical driving parameters for DDTVs equipped with conventional sensors such as rotary transformers at PMSMs and onboard accelerometers on the basis of their dynamics models. The algorithm includes a sensor signal preprocessing module, a longitudinal force estimation method based on a nonlinear observer, and a speed estimation method based on an adaptive Kalman filter. Through hardware-in-loop experiments based on a Speedgoat real-time target machine, the proposed algorithm is proven to estimate the longitudinal force of the track and vehicle speed accurately, whether the vehicle has stability control functions or not, providing a foundation for the further development of vehicle stability control algorithms.

A dead-time compensation method for motor drive inverters based on nonlinear observer

Silicon carbide (SiC) inverters and interior permanent magnet synchronous motors (IPMSMs) are widely employed in electric vehicles (EVs) due to their superior efficiency and high power density. However, the harmonics generated by the high switching frequency and the dead-time effect in SiC inverters present a significant challenge. The time-varying nature of on–off delays and conduction voltage drops in power devices makes it difficult to establish a precise nonlinear model for inverters, thus limiting the effectiveness of traditional dead-time compensation methods. This paper introduces a dead-time compensation approach for voltage source inverters (VSIs) that leverages a nonlinear observer, thereby circumventing the need for a complex inverter model while enhancing compensation accuracy. The method determines the three-phase stator current polarity of the IPMSM by deriving the relationship between the current vector angle and the rotor position angle. Along with duty cycle variations computed by the PI controller, the inverter’s nonlinearity is adaptively compensated. Simulation and experimental results indicate that the proposed method outperforms the traditional method based on the error voltage model, effectively reducing the total harmonic distortion (THD) of the phase current.

Nonlinear observation of battery microscopic states utilizing adaptive super-twisting sliding-mode observers based on a compact electrochemical-thermal-aging model

Accurate microscopic-state estimation of lithium-ion batteries (LIBs) is a potential candidate for advanced battery management systems. This paper proposes an adaptive super-twisting sliding-mode observer (SMO) for LIB microscopic state perception using a compact and observable electrochemical-thermal-aging model. Considering the physical structure and mathematical model, a simplified single-particle mode with electrolyte is standardized as a compact state-space form after observability analysis. Results show that the compact model is capable of capturing the LIB terminal voltage and temperature with maximum errors of 39.8 mV and 0.2 °C, respectively. After that, the super-twisting SMO is integrated with a neural network-based adaptive law for addressing external disturbances and chattering. Estimation results show that during the majority of cycles, the errors of state of charge, volume-averaged concentration, temperature, and capacity are <3 %, 0.87 kmol/m3, 0.2 °C, and 0.1 Ah, respectively. The side-reaction overpotential of lithium plating prevention can be predicted. Comparable experiments with different observers and hardware-in-the-loop experiments are conducted to explore the estimation accuracy and real-time feasibility of the adaptive observer.

Robust observer-based-α-variable model-free supertwisting fractional order sliding mode control for nonlinear PEMFC system with uncertainties and disturbance

The service life and efficiency of proton exchange membrane fuel cells (PEMFCs) are significantly related to the control performance of the air supply system. Therefore, this research develops a novel robust observer-based- [Formula: see text]-variable model-free supertwisting fractional-order sliding mode control ([Formula: see text]-MF-STFOSMC) for complex nonlinear PEMFC air supply system with unmeasurable state variables, model uncertainties, and external disturbance. First, the fifth-order nonlinear PEMFC air supply system model is presented, and the unmeasured state variables are estimated using a nonlinear disturbance observer (NDOB1). Second, the ultra-local model (ULM) algorithm is employed to reconstruct the complex nonlinear PEMFC air supply system, avoiding the need for precise modeling and reducing the controller design difficulty. To estimate and compensate for the uncertain dynamics in the ULM algorithm, another NDOB2 is proposed to realize zero estimation error and finite-time observation. Besides, to achieve optimal control performance with less input chattering, finite-time convergence, and fast response speed, the [Formula: see text]-MF-STFOSMC is designed using super-twisting fractional-order sliding mode control (STFOSMC) algorithm. Furthermore, the stability of [Formula: see text]-MF-STFOSMC via a closed-loop system is verified using the Lyapunov theorem. Finally, the nonlinear PEMFC air supply system model with the proposed controller is realized in MATLAB/Simulink environment, and the simulation results are given to show the superiority and effectiveness of the proposed technique.

Another look at residual dynamic mode decomposition in the regime of fewer snapshots than dictionary size

Residual Dynamic Mode Decomposition (ResDMD) offers a method for accurately computing the spectral properties of Koopman operators. It achieves this by calculating an infinite-dimensional residual from snapshot data, thus overcoming issues associated with finite truncations of Koopman operators (e.g., Extended Dynamic Mode Decomposition), such as spurious eigenvalues. Spectral properties computed by ResDMD include spectra, pseudospectra, spectral measures, Koopman mode decompositions, and dictionary verification. In scenarios where the number of snapshots is fewer than the dictionary size, particularly for exact DMD and kernelized Extended DMD, ResDMD has traditionally been applied by dividing snapshot data into a training set and a quadrature set. We demonstrate how to eliminate the need for two datasets through a novel computational approach of solving a dual least-squares problem. We analyze these new residuals for exact DMD and kernelized Extended DMD, demonstrating ResDMD’s versatility and broad applicability across various dynamical systems, including those modeled by high-dimensional and nonlinear observables. The utility of these new residuals is showcased through three diverse examples: the analysis of a cylinder wake, the study of airfoil cascades, and the compression of transient shockwave experimental data. This approach not only simplifies the application of ResDMD but also extends its potential for deeper insights into the dynamics of complex systems.

Adaptive complementary sliding mode control of ship course under environmental disturbance

In this paper, an adaptive complementary sliding mode control strategy based on nonlinear extended state observer (NESO) is proposed for the ship course tracking control subject to environmental disturbances. By introducing the adaptive law, the system uncertainty is estimated and adjusted, so that the boundary layer of the complementary sliding mode control can realize dynamic changes and ensure the system robustness. At the same time, the auxiliary control system is introduced to compensate the complementary sliding mode control law to guarantee the system stability under finite actuation. For the environmental disturbances of the heading process, a NESO is designed for real-time estimation and compensated to the adaptive complementary sliding mode control law to improve the robustness of the system. The closed-loop stability is proved, and simulation results show that the control strategy effectively improves the tracking accuracy and robustness of the system.

Differential Flatness Based Unmanned Surface Vehicle Control: Planning and Conditional Disturbance-Compensation

To achieve precise control of the symmetrical unmanned surface vehicle (USV) under strong external disturbances, we propose a disturbance estimation and conditional disturbance compensation control (CDCC) scheme. First, the differential flatness method is applied to convert the underactuated model into a fully actuated one, simplifying the controller design. Then, a nonlinear disturbance observer (NDOB) is designed to estimate the lumped disturbance. Subsequently, a continuous disturbance characterization index (CDCI) is proposed, which not only indicates whether the disturbance is beneficial to the system stability but also makes the controller switch smoothly and suppresses the chattering phenomenon greatly. Indicated by the CDCI, the proposed CDCC method can not only utilize the beneficial disturbance but also compensate for the detrimental disturbance, which improves the USV’s control performance under strong external disturbances. Moreover, a trajectory-planning method is designed to generate an obstacle avoidance reference trajectory for the controller. Finally, simulations verify the feasibility of applying the proposed control method to USV.

Backstepping control of DFIG wind turbine system based rotor flux observer

This paper introduces a novel approach to controlling a wind energy system based on a doubly fed induction generator (DFIG) using backstepping control. The proposed control method allows for independent control of the active and reactive power of the stator. Unlike traditional methods that rely on vector control of the stator fluxes and neglect the stator resistance, this approach takes into account the nonlinearities and coupled nature of the system. By using a nonlinear model in the Park frame, the control is more accurate and closer to the behavior of a real machine. This method has yet to consider any estimation of the rotor flux model. Using a high-gain observer can resolve the issue of measuring rotor flux. The stability of the nonlinear observer is demonstrated through the application of Lyapunov theory. The simulation results indicate that the suggested control scheme has enhanced the dynamic performance of the system.

Output-feedback formation tracking control of autonomous surface vessels with collision avoidance

In this paper, a formation control problem with collision avoidance is investigated for underactuated surface vessels with position–heading measurements. Each vessels is subject to actuator magnitude and rate saturations. At first, an anti-saturation nonlinear extended state observer is developed to recover the linear velocity and yaw rate as well as unknown uncertainty and disturbances. Then, observer-based formation control laws are designed based on an artificial potential functions, obstacle avoidance yaw references and a backstepping technique. The stability of closed-loop formation control system is proved. The salient features of this paper are as follows. First, formation control with the capability of collision avoidance is achieved by using artificial potential functions and obstacle avoidance yaw references, which is more aggressive. Second, the proposed controller is able to deal with the magnitude and rate constraints of the actuator. Third, the proposed anti-saturation nonlinear extended state observer can achieve better estimation results for rapidly changing signals. Simulation results are given to substantiate the proposed formation control laws.