Nonlinear Observer Research Articles

A differentiable perturbation-based weak lensing shear estimator

ABSTRACT Upcoming imaging surveys will use weak gravitational lensing to study the large-scale structure of the Universe, demanding sub-per cent accuracy for precise cosmic shear measurements. We present a new differentiable implementation of our perturbation-based shear estimator (fpfs), using jax, which is publicly available as part of a new suite of analytic shear algorithms called anacal. This code can analytically calibrate the shear response of any non-linear observable constructed with the fpfs shapelets and detection modes utilizing autodifferentiation (ad), generalizing the formalism to include a family of shear estimators with corrections for detection and selection biases. Using the ad capability of jax, it calculates the full Hessian matrix of the non-linear observables, which improves the previously presented second-order noise bias correction in the shear estimation. As an illustration of the power of the new anacal framework, we optimize the effective galaxy number density in the space of the generalized shear estimators using an LSST-like galaxy image simulation for the 10 yr LSST. For the generic shear estimator, the magnitude of the multiplicative bias |m| is below 3 × 10−3 (99.7 per cent confidence interval), and the effective galaxy number density is improved by 5 per cent . We also discuss some planned future additions to the anacal software suite to extend its applicability beyond the fpfs measurements.

Reconstruction of incidence reporting rate for SARS-CoV-2 Delta variant of COVID-19 pandemic in the US

In recent years, advanced regularization techniques have emerged as a powerful tool aimed at stable estimation of infectious disease parameters that are crucial for future projections, prevention, and control. Unlike other system parameters, i.e., incubation and recovery rates, the case reporting rate, Ψ, and the time-dependent effective reproduction number, Re(t), are directly influenced by a large number of factors making it impossible to pre-estimate these parameters in any meaningful way. In this study, we propose a novel iteratively-regularized trust-region optimization algorithm, combined with SuSvIuIvRD compartmental model, for stable reconstruction of Ψ and Re(t) from reported epidemic data on vaccination percentages, incidence cases, and daily deaths. The innovative regularization procedure exploits (and takes full advantage of) a unique structure of the Jacobian and Hessian approximation for the nonlinear observation operator. The proposed inversion method is thoroughly tested with synthetic and real SARS-CoV-2 Delta variant data for different regions in the United States of America from July 9, 2021, to November 25, 2021. Our study shows that case reporting rate during the Delta wave of COVID-19 pandemic in the US is between 12% and 37%, with most states being in the range from 15% to 25%. This confirms earlier accounts on considerable under-reporting of COVID-19 cases due to the impact of ”silent spreaders” and the limitations of testing.

Evaluation of earthquake-related damages on masonry structures due to the 6 February 2023 Kahramanmaraş-Türkiye earthquakes: A case study for Hatay Governorship Building

The present study contributes to enriching the sparse literature on the seismic analysis of historical masonry buildings through field observations and advanced computational tools. To do this, the findings from field observations in the area affected by the February 6th, 2023, Kahramanmaraş earthquakes (Mw = 7.7 and Mw = 7.6) are evaluated to point out the possible reasons for damages occurred in masonry buildings. Further, numerical simulations of a historical building in Hatay which has a significant amount of historical masonry building stock in the region. Comparisons of the results obtained from non-linear finite element analyses and field observations are made to explain the crack patterns occurred and damage mechanisms. Nonlinear finite element analyses confirmed that the considered structure did not collapse despite being seriously damaged in the first two earthquakes (Mw = 7.7 and Mw = 7.6), but a part of it completely collapsed because of the third earthquake (Mw = 6.4) on February 20th, 2023, in Defne district. The damage patterns observed in the field are also obtained exactly by the numerical simulations. Some retrofitting proposals are given to assist the authorities in charge of the reconstruction and rehabilitation programs to account for a better interpretation and understanding of the seismic performance of masonry buildings.

Robust Direct Power Flow Control of Voltage Source Converters

In this study, a disturbance observer-based power control system is developed for voltage source converters (VSC) to achieve smooth power delivery to the grid. Firstly, modeling of grid connected converter which is used for power delivery in terms of frequency and current dynamics is executed under consideration of modelling errors and uncertainties. This disturbance effects are mainly consist of frequency and amplitude variations, output impedance aging, large dc-link voltage ripple A second order nonlinear observer is integrated into the designed control to reject with model uncertainty and disturbances. Due to the objective of the proposed controller is power regulation, there is no need a voltage and current compensator. Comperative simulations are carried out to verify the robustness of the proposed controller. Also effectiveness of the proposed approach is tested under different grid scenarios (e.g., weak grid, dc-link variation, frequency deviation)

Adaptive sliding mode tracking control of underwater vehicle-manipulator systems considering dynamic disturbance

This paper proposes an adaptive sliding mode tracking control method with a nonlinear disturbance observer (NDO-ASMTC) to solve the trajectory tracking problem of the underwater vehicle-manipulator system (UVMS) in the presence of large dynamic uncertainties and severe external disturbances. The proposed NDO-ASMTC method employs an adaptive control law, an improved fractional-order sliding mode, and a nonlinear disturbance observer to achieve excellent tracking performance of the UVMS. To obtain a fast response speed in the sliding mode phase and eliminate static error in the reaching phase, a modified fractional-order sliding mode control scheme is proposed. An adaptive auto-tuning law of switching gains is presented to overcome the problem that the fixed switching gain may lead to obvious tracking performance degradation under lumped uncertainty. In addition, a nonlinear disturbance observer is implemented to maintain the robustness and stability of the control scheme under severe disturbances. Moreover, the proposed adaptive control scheme has been proved to be stable using the Lyapunov theorem. Simulations and experiments show that the proposed control scheme can meet the design requirements of the UVMS in terms of tracking accuracy, system stability, and interference attenuation under the application of external disturbances.

On error-driven nonlinear ESO based control design with application to air–fuel ratio control of engines

In this paper, the tracking control problem of the uncertain control system is studied in the frame of uncertainties estimation and compensation. To eliminate the influence of external disturbances and internal uncertainties on the control system, the error-driven nonlinear extended state observer (EDN-ESO), whose gain is set as an increasing function with respect to the absolute value of estimation error of the system output, is proposed to improve the estimation performance for the “total disturbance”. Next, both the estimation error of proposed ESO and the tracking error of system output are proven to be bounded by selecting the lower bound and variation range of ESO’s bandwidth. Moreover, the convergence of the estimation error as well as the tracking error to zero is proven under certain conditions. Finally, the proposed design method is applied to the air–fuel ratio control system of gasoline engines, and the experimental results show that the proposed EDN-ESO can effectively adjust the observer gain, so as to enhance the tracking performance.

Performance Improvement of Nonlinear Flux Observer for Sensorless Control of PMSM

The effectiveness of nonlinear flux observer has been validated in practical application. However, it is not easy to tune the gradient search gain. The observer is sensitive to the parameter variation and also the stability can be greatly affected by the gradient search gain. This paper proposes an improved nonlinear flux observer to enhance the performance. The proposed method utilizes the gradient search for both magnitude and phase of the rotor, which changes the error dynamic equations. Further, it brings the benefits of smaller estimation error and quicker dynamic responses, since the convergence path is more reasonable. In addition, it has the advantages of better steady-state performance, robustness against parameter variation and stronger stability against larger observer gain value. By comparisons of simulations and experiments, the superiority is demonstrated.

Fast Charging Control Method for Electric Vehicle-to-Vehicle Energy Interaction Devices

In order to reduce energy consumption and alleviate environmental pollution, the number of electric vehicles is increasing. But people are still worried about the choice of electric vehicles because of the problems of battery charging and duration. Therefore, a vehicle-to-vehicle energy interaction converter device is proposed in this paper, which has the characteristics of high-power, high-gain and small-volume. Based on the characteristics of this device, this paper uses modularized boost converter (MBC) to design this device. However, the electric vehicle battery can be divided into constant resistance loads and constant power loads (CPLs). Therein, the CPLs are very easy to cause the instability of the charging device. Therefore, a nonlinear controller combining an external nonlinear disturbance observer and an adaptive backstepping algorithm is proposed in this paper. In the first place, the high order MBC model is reduced to Brunovsky’s canonical form by using accurate feedback linearization technology in this paper. Afterwards, a nonlinear disturbance observer is designed to speed up the dynamic response of the system. At the same time, an adaptive backstepping controller is designed to ensure the stability of the output voltage in the sense of large signal by using the output of nonlinear disturbance observer. In the end, simulation and experiment results illustrate the correctness and feasibility of the converter device.

Distributed Coordinated Control for Stabilization of Multi-Inverter Power Plant

For a power plant integrated with multiple parallel inverters, the impedance variation of the power grid and the natural plug-and-play property of the inverters bring stability challenges. One of the issues is nonlinear wideband oscillations of the grid current and voltage. This paper proposes a distributed coordinated control for the stabilization of the multi-inverter power plant. The passivity-based control (PBC) scheme designs the controller of a single grid-connected inverter from the perspective of energy reshaping, which ensures the stability of the entire system when it is extended to multiple inverters in parallel. A nonlinear observer is proposed to discover the changeable frequency drifting of wideband oscillations so that the PBC scheme can adapt to nonlinear disturbances, such as inverter plug-and-play and fluctuated grid impedance. Moreover, to achieve mutual coordination and distributed control of damping characteristics among multi-inverters to ensure the good dynamic performance of the system, an adaptive dynamic coordination loop based on grid impedance identification is incorporated in the PBC scheme. The Lyapunov stability of the system with the proposed PBC controller is proven in the paper. The effectiveness of the proposed scheme is verified by simulation and experimental results.

Nonlinear observer with reduced sensors for WECS involving Vienna rectifiers — Theoretical design and experimental evaluation

Nonlinear observer with reduced sensors for WECS involving Vienna rectifiers — Theoretical design and experimental evaluation

One new composite control based smooth nonlinear fractional order sliding mode algorithm and disturbance compensation for PMSM with parameter uncertainties

To achieve high-quality control of PMSM with parameter uncertainties, a nonlinear smooth fractional order sliding mode composite control (NSFOSMCC) strategy is designed in this paper. This approach incorporates a novel nonlinear smooth fractional order sliding mode controller, a novel adaptive super-twisting (AST) algorithm, and a modified nonlinear extended state observer (ESO) to achieve enhanced motor performance. To effectively overcome the disadvantages of simplicity and toughness associated with the conventional fractional order sliding mode controller, a novel nonlinear smooth fractional order sliding mode controller is designed. A novel AST technique is introduced to effectively weaken chattering issues. The modified nonlinear ESO is used to estimate the uncertainty parameters of the PMSM. By combining the modified nonlinear ESO with the latest sliding mode controller, a new composite controller called NSFOSMCC strategy is developed for PMSM. The proposed NSFOSMCC strategy, utilizing a combination of “feedforward plus feedback,” is implemented for PMSM with parameter uncertainties. The reliability and stability of the controller are thoroughly established through the utilization of the Lyapunov stability theorem. Furthermore, comparative results show strong evidence supporting the effectiveness of the novel composite control strategy.

Beyond Battery State of Charge Estimation: Observer for Electrode-Level State and Cyclable Lithium With Electrolyte Dynamics

This paper presents a provably convergent battery estimation scheme based on a single particle model with electrolyte dynamics (SPMe), by proposing a systematic methodology to estimate critical information such as electrode-level states, electrolyte dynamics, and cyclable lithium. Electrode-level state estimation suffers from weak observability originating from two standalone electrode dynamics, which is then aggravated by the addition of electrolyte dynamics. This lack of observability can be alleviated by exploiting lithium inventory conservation enabled by Kalman decomposition, allowing one to separate out the unobservable subspace. Assuming the knowledge of cyclable lithium, a nonlinear state observer with provable convergence can be constructed for the SPMe model, using voltage and current measurements. To relax this strong assumption, a sensitivity-based parameter estimation scheme is also deployed to track cyclable lithium – a crucial physical variable for capacity fade. Ultimately, the estimation framework can perform finer monitoring and diagnosis of battery charge and health down to the level of individual electrode and the electrolyte. Experimental validation demonstrates <1% estimation error for cyclable lithium inventory. Solid phase lithium concentration estimates, especially in the negative electrode, can be sensitive to disturbances in cyclable lithium.

Adaptive Dynamic Surface Control With Disturbance Observers for Battery/Supercapacitor-Based Hybrid Energy Sources in Electric Vehicles

The underlying control in the hybrid energy source system (HESS) of an electric vehicle plays a pivotal role. Uncertainty is unavoidable in system modeling owing to variations in electrical parameters and unknown external disturbances, which inevitably deteriorate the control performance of the HESS. In this study, an innovative adaptive dynamic surface control with disturbance observers (ADSCDOB) is adopted as a control scheme for underlying tracking in the HESS to counteract the adverse effects and improve control accuracy. First, disturbance observers are designed by employing a nonlinear disturbance observer and an extreme learning machine approximator to estimate the mismatched and matched uncertainties. Subsequently, the proposed ADSCDOB scheme integrates the adaptive dynamic surface technique and second-order differentiators to achieve robust control, in which voltage/current references are obtained through the rule-based energy management strategy. The established ADSCDOB obviates the “differential explosion” problem and ensures that the closed-loop system is semi-globally and uniformly bounded. Comprehensive simulations and prototype experiments prove the effectiveness of the ADSCDOB, confirming its satisfactory performance in terms of a fast response, reduced error, and robust stability under hybrid driving conditions.

Nonlinear Extended State Observer Based Super-Twisting Terminal Sliding Mode Synchronous Control for Parallel Drive Systems

Addressing the issue to restrain the nonlinear coupling disturbance in the multimotor parallel drive system and acquiring perfect driving control performance, a novel super-twisting terminal sliding mode synchronous control (STSC) is proposed. In this control scheme, a lumped error (LE) with a synchronization coefficient is designed to transform coupled control into LE convergence. Then, a recursive terminal sliding mode function with two layers is introduced. Based on this sliding mode function, the STSC scheme is proposed, and it can guarantee the LE finite-time convergence and the continuous control action in nature. A nonlinear extended state observer (NESO) is introduced to enhance robustness. Moreover, the NESO not only provides an estimation of disturbance but also provides a smooth velocity signal. Therefore, differential operations and filtering operations are avoided. Finally, a compound control scheme is obtained. Compared with conventional super-twisting algorithm (STA), the robustness is enhanced by embedding NESO-based disturbance compensation, and the advantage of continuous control action is inherited. The major advantages of this scheme are characterized by output-based information only used, good model adaptability, and strong disturbance rejection ability. Experimental results show the effectiveness of the proposed control law.

Active fault-tolerant control for the dual-valve hydraulic system with unknown dead-zone

This paper proposes a method for high-performance motion control of the dual-valve hydraulic system subject to parameter and model uncertainties, unknown proportional valve dead-zone, and servo valve fault. By constructing a detailed dual-valve fault system model (DFSM), a disturbance observer-based adaptive robust fault-tolerant controller is proposed via the backstepping method. This controller integrates a model-based fault detection algorithm for real-time fault monitoring and subsequent controller reconfiguration. Additionally, the DFSM-based adaptive robust control (ARC) technique is applied to handle the unknown dead-zone problem and other nonlinearities, ensuring precise control. Once the servo valve fault occurs, a nonlinear observer estimates the fault and collaborates with the ARC to establish a reconfigured controller, thereby maintaining motion control. The effectiveness of the proposed method has been experimentally verified.

Neural Adaptive H∞ Sliding-Mode Control for Uncertain Nonlinear Systems with Disturbances Using Adaptive Dynamic Programming.

This paper focuses on a neural adaptive H∞ sliding-mode control scheme for a class of uncertain nonlinear systems subject to external disturbances by the aid of adaptive dynamic programming (ADP). First, by combining the neural network (NN) approximation method with a nonlinear disturbance observer, an enhanced observer framework is developed for estimating the system uncertainties and observing the external disturbances simultaneously. Then, based on the reliable estimations provided by the enhanced observer, an adaptive sliding-mode controller is meticulously designed, which can effectively counteract the effects of the system uncertainties and the separated matched disturbances, even in the absence of prior knowledge regarding their upper bounds. While the remaining unmatched disturbances are attenuated by means of H∞ control performance on the sliding surface. Moreover, a single critic network-based ADP algorithm is employed to learn the cost function related to the Hamilton-Jacobi-Isaacs equation, and thus, the H∞ optimal control is obtained. An updated law for the critic NN is proposed not only to make the Nash equilibrium achieved, but also to stabilize the sliding-mode dynamics without the need for an initial stabilizing control. In addition, we analyze the uniform ultimate boundedness stability of the resultant closed-loop system via Lyapunov's method. Finally, the effectiveness of the proposed scheme is verified through simulations of a single-link robot arm and a power system.

A nonlinear disturbance observer for robotic manipulators without velocity and acceleration measurements

A nonlinear disturbance observer for robotic manipulators without velocity and acceleration measurements

Observer-Based Adaptive Control for Trajectory Tracking of AUVs with Input Saturation

In this paper, an observer-based adaptive control method is investigated for the horizontal trajectory tracking of autonomous underwater vehicles (AUV) with input saturation and system disturbances. Firstly, the desired surge speed and trajectory angle are established, which could decouple the tracking error subsystem and avoid the complex form. Secondly, the input saturation is approximated by a smooth function, and a nonlinear extended states observer (NESO) is designed for estimating system disturbances. Based on the command filtered backstepping technique, which can avoid the explosion caused by the derivative of the virtual control, an observer-based adaptive output feedback control method is developed, and an auxiliary system is applied to compensate for filtered tracking errors, input saturation bias, and observer errors. Finally, simulation results show the proposed method has good robustness in the face of system uncertainties, and the error is nearly 33.3% smaller than that of other control methods when meeting sudden trajectory changes. A good control performance is guaranteed.

Decentralized event-triggered estimation of nonlinear systems

We investigate the scenario where a perturbed nonlinear system transmits its output measurements to a remote observer via a packet-based communication network. The sensors are grouped into N nodes and each of these nodes decides when its measured data is transmitted over the network independently. The objective is to design both the observer and the local transmission policies in order to obtain accurate state estimates, while only sporadically using the communication network. In particular, given a general nonlinear observer designed in continuous-time satisfying an input-to-state stability property, we explain how to systematically design a dynamic event-triggering rule for each sensor node that avoids the use of a copy of the observer, thereby keeping local calculation simple. We prove the practical convergence property of the estimation error to the origin and we show that there exists a uniform strictly positive minimum inter-event time for each local triggering rule under mild conditions on the plant. The efficiency of the proposed techniques is illustrated on a numerical case study of a flexible robotic arm.

Output tracking for nonlinear stochastic systems driven by bounded and colored noises

In this paper, we consider practical tracking problem for a class of nonlinear stochastic systems driven by bounded and colored noises by means of active disturbance rejection control approach. The nonlinear extended state observer with homogeneous weighted functions is constructed to estimate in real time the unmeasurable state and the total stochastic disturbance that affects system performance. An observer-based output feedback is designed to guarantee the almost surely practical convergence of the tracking errors. The existence of the global weak solution of the closed-loop system is proved and the tracking convergence accuracy is shown to be higher than that of linear one under the same tuning parameters. Some numerical simulations are carried out to validate the effectiveness of the proposed controller.