Unknown Velocity Research Articles

Finite-time output feedback path following control of underactuated MSV based on FTESO

The paper designs a finite-time output feedback path following control strategy of underactuated marine surface vehicle (MSV) with the unavailable velocity, the unknown dynamic and unknown external environment disturbances. Firstly, a new finite time extended state observer (FTESO) is devised to accurately observe the unknown velocity and unknown lumped disturbances within finite time. Secondly, depending on the output of FTESO, the velocity observation-based finite-time LOS guidance approach is raised to acquire the reference yaw angle. Thirdly, the finite-time output feedback path following controllers are constructed through the backstepping method to track the desired path with precise tracking performance. It has been demonstrated that the observation error of FTESO is capable of converging to zero and the path following error is able to converge to an arbitrarily small domain near zero in finite time according to the homogeneous theory and the Lyapunov theory. Simulation comparison researches are performed to demonstrate the availability of the designed finite-time output feedback path following strategy.

Optimal Localization With Sequential Pseudorange Measurements for Moving Users in a Time-Division Broadcast Positioning System

In a time division broadcast positioning system (TDBPS), a user device (UD) determines its position by obtaining sequential time-of-arrival (TOA) or pseudorange measurements from signals broadcast by multiple synchronized base stations (BSs). The existing localization method using sequential pseudorange measurements and a linear clock drift model for the TDPBS, namely LSPM-D, does not compensate the position displacement caused by the UD movement and will result in position error. In this paper, depending on the knowledge of the UD velocity, we develop a set of optimal localization methods for different cases. First, for known UD velocity, we develop the optimal localization method, namely LSPM-KVD, to compensate the movement-caused position error. We show that the LSPM-D is a special case of the LSPM-KVD when the UD is stationary with zero velocity. Second, for the case with unknown UD velocity, we develop a maximum likelihood (ML) method to jointly estimate the UD position and velocity, namely LSPM-UVD. Third, in the case that we have prior distribution information of the UD velocity, we present a maximum a posteriori (MAP) estimator for localization, namely LSPM-PVD. We derive the Cramer-Rao lower bound (CRLB) for all three estimators and analyze their localization error performance. We show that the position error of the LSPM-KVD increases as the assumed known velocity deviates from the true value. As expected, the LSPM-KVD has the smallest position error while the LSPM-PVD and the LSPM-UVD are more robust when the prior knowledge of the UD velocity is limited. Numerical results verify the theoretical analysis on the optimality and the positioning accuracy of the proposed methods.

Globally exponentially stable single beacon underwater navigation with unknown sound velocity estimation

Single beacon navigation methods with unknown effective sound velocity (ESV) have recently been proposed to solve the performance degeneration induced by ESV setting error. In these methods, a local linearization-based state estimator, which only exhibits local convergence, is adopted to estimate the navigation state. When the initial ESV setting error or vehicle initial position error is large, the local linearization-based state estimators have difficulty guaranteeing the filtering convergence. With this background, this paper proposes a linear time-varying single beacon navigation model with an unknown ESV that can realize global convergence under the condition of system observability. A Kalman filter is adopted to estimate the model state, and the corresponding stochastic model is inferred for the application of the Kalman filter. Numerical simulation confirms that the proposed linear time-varying single beacon navigation model can realize fast convergence in the case of a large initial error, and has superior steady-state performance compared with the existing methods.

ДОСЛІДЖЕННЯ ГІДРОПРУЖНИХ КОЛИВАНЬ ЕЛЕМЕНТІВ КОНСТРУКЦІЙ З ВИКОРИСТАННЯМ МЕТОДУ ГІПЕРСИНГУЛЯРНИХ РІВНЯНЬ

Створено методику визначення частот та форм власних коливань елементів конструкцій при двобічному контакті з рідиною. Вважається, що рідина є ідеальною і нестисливою, а її рух, індукований коливаннями конструктивного елементу є безвихровим. За цих умов існує потенціал швидкостей, який всюди в області, що зайнята рідиною, задовольняє рівнянню Лапласа. На поверхнях конструктивного елементу задається умова непротікання. Ця умова полягає в рівності нормальних компонент швидкостей рідини та конструкції. Для знаходження переміщень конструкції використовуються рівняння руху під дією навантаження, що обумовлене тиском рідини. Тиск рідини, в свою чергу, визначається з рівняння Лапласа, граничні умови для якого містять невідому швидкість конструкції. Тобто, отримано зв’язану задачу щодо визначення гідропружних коливань. Для розв’язання сформульованої задачі використано метод заданих форм. Спочатку визначаються частоти і форми коливань пружного елементу без урахування сили тиску з боку рідини. За отриманими формами будується подання переміщень конструкції, що взаємодіє з рідиною, у вигляді відповідного ряду. Далі розв’язується крайова задача Неймана для рівняння Лапласа, при цьому граничні умови містять відомі функції, а саме, форми коливань пружного елементу, що були отримані на першому етапі. Розв’язання цієї задачі виконано із застосуванням теорії потенціалу. Невідому функцію зображено у вигляді потенціалу подвійного шару. Граничні умови при цьому призводять до гіперсингулярного інтегрального рівняння відносно невідомої густини, яка й відображає тиск рідини. Надалі це двовимірне гіперснргулярне рівняння зводиться до одновимірного. Розроблено ефективний метод числового розв’язання цього рівняння. Здійснено порівняння отриманих числових результатів з відомими аналітичними розв’язками. Отримано добре узгодження результатів, що свідчить про вірогідність запропонованого методу. Після цього розроблений алгоритм побудови матриці приєднаних мас, що дало змогу знайти частоти власних коливань круглої пружної пластинки з урахуванням приєднаних мас рідини.

Joint Reconstruction of Conductivity and Velocity in Two-Phase Flows Using Electromagnetic Flow Tomography and Electrical Tomography: A Simulation Study

Characterization of two-phase flows is a common problem in the process industry. Due to complexity of flows, having accurate measurements of velocity fields, phase fractions, and the volumetric flow rates is challenging. Even though several approaches have been developed, accurate measurements of the flow quantities remain a challenge. Metering volumetric flow rate requires information on the local phase fraction and velocity field in the pipe cross section to be imaged. These data are commonly obtained using two individual measurement systems, the so-called dual-modality system. This article considers a dual-modality consisting of electromagnetic flow tomography (EMFT) and electrical tomography (ET) imaging, which provide information on the velocity field and electrical conductivity distribution, respectively; the combination of EMFT and ET reconstruction can be further used for inferring the volumetric flow rate. The aim of this article is to improve the accuracy of the EMFT and ET reconstructions—and the resulting flow rate estimate—by enhanced modeling of the unknown velocity and conductivity fields. More specifically, the proposed approach is based on modeling the joint statistics of the velocity and conductivity with a cross-covariance matrix which is based on a representative ensemble of velocity–conductivity image pairs obtained, for example, from fluid dynamical modeling or empirically. The cross-covariance matrix is incorporated in the joint reconstruction within the Bayesian inverse problems framework as an additional prior model. The proposed image reconstruction approach is tested with a set of numerical simulations. The results show that the joint reconstruction approach (JRA) with a cross-covariance model is capable of improving the accuracy of the estimates compared to the approaches that are currently in use.

Određivanje brzina i ubrzanja u mrtvom položaju zglavkastog četvorougla metodom zaustavljanja

The paper studies a plane four-bar mechanism in a dead, kinematically indeterminate position. From that position, the mechanism could continue to move, continuously, or the driven lever would stop and move backwards. But, if we eliminate this second possibility, the position of the mechanism is no longer indeterminate and it would be logical that we can determine unknown speeds and accelerations by some kinematic method. The authors of this paper, applying the stopping method, came up with analytical expressions for determining unknown velocities and accelerations in the dead position of an four-bar mechanism.

A spatial epidemic model with a moving boundary.

We present a new mathematical model to investigate the spatial spread of an infectious disease. The model consists of a nonlinear PDE system with an unknown velocity field, defined on an epidemic domain that changes with time. The moving boundary of the domain represents the wavefront of the epidemic. We conduct an equilibrium analysis to the simplified models represented by ODE systems. We also perform a numerical study on the original PDE system for a range of scenarios, including one under a realistic epidemic setting.

Robust Adaptive Self-Structuring Neural Network Bounded Target Tracking Control of Underactuated Surface Vessels.

This paper studies the target-tracking problem of underactuated surface vessels with model uncertainties and external unknown disturbances. A composite robust adaptive self-structuring neural-network-bounded controller is proposed to improve system performance and avoid input saturation. An extended state observer is proposed to estimate the uncertain nonlinear term, including the unknown velocity of the tracking target, when only the measurement values of the line-of-sight range and angle can be obtained. An adaptive self-structuring neural network is developed to approximate model uncertainties and external unknown disturbances, which can effectively optimize the structure of the neural network to reduce the computational burden by adjusting the number of neurons online. The input-to-state stability of the total closed-loop system is analyzed by the cascade stability theorem. The simulation results verify the effectiveness of the proposed method.

Numerical approximation of the averaged controllability for the wave equation with unknown velocity of propagation

We propose a numerical method to approximate the exact averaged boundary control of a family of wave equations depending on an unknown parameter σ. More precisely the control, independent of σ, that drives an initial data to a family of final states at time t = T, whose average in σ is given. The idea is to project the control problem in the finite dimensional space generated by the first N eigenfunctions of the Laplace operator. When applied to a single (nonparametric) wave equation, the resulting discrete control problem turns out to be equivalent to the Galerkin approximation proposed by F. Bourquin et al. [C.R. Acad. Sci. Paris 313 I (1991) 757–760]. We give a convergence result of the discrete controls to the continuous one. The method is illustrated with several examples in 1-d and 2-d in a square domain and allows us to give some conjectures on the averaged controllability for the continuous problem.

Non-invasive inference of thrombus material properties with physics-informed neural networks

We employ physics-informed neural networks (PINNs) to infer properties of biological materials using synthetic data. In particular, we successfully apply PINNs to extract the permeability and viscoelastic modulus from thrombus deformation data, which can be described by the fourth-order Cahn–Hilliard and Navier–Stokes Equations. In PINNs, the partial differential equations are encoded into a loss function, where partial derivatives can be obtained through automatic differentiation (AD). To tackle the challenge of calculating the fourth-order derivative in the Cahn–Hilliard equation with AD, we introduce an auxiliary network along with the main neural network to approximate the second-derivative of the energy potential term. Our model can simultaneously predict unknown material parameters and velocity, pressure, and deformation gradient fields by merely training with partial information among all data, i.e., phase field and pressure measurements, while remaining highly flexible in sampling within the spatio-temporal domain for data acquisition. We validate our model by numerical solutions from the spectral/hp element method (SEM) and demonstrate its robustness by training it with noisy measurements. Our results show that PINNs can infer the material properties from noisy synthetic data ►and thus they have great potential for inferring these properties from experimental multi-modality and multi-fidelity data.

Joint Inversion of Audio-Magnetotelluric and Seismic Travel Time Data With Deep Learning Constraint

Deep learning is applied to assist the joint inversion for audio-magnetotelluric and seismic travel time data. More specifically, deep residual convolutional neural networks (DRCNNs) are designed to learn both structural similarity and resistivity-velocity relationships according to prior knowledge. During the inversion, the unknown resistivity and velocity are updated alternatingly with the Gauss-Newton method, based on the reference model generated by the trained DRCNNs. The workflow of this joint inversion scheme and the design of the DRCNNs are explained in detail. Compared with describing the resistivity-velocity relationship using empirical equations, this method can avoid the necessity in modeling the correlations in rigorous mathematical forms and extract more hidden prior information embedded in the training set, meanwhile preserving the structural similarity between different inverted models. Numerical tests show that the inverted resistivity and velocity have similar profiles, and their relationship can be kept consistent with the prior joint distribution. Furthermore, the convergence is faster, and final data misfits can be lower than separate inversion.

A Novel Adaptive Two-Stage Information Filter Approach for Deep-Sea USBL/DVL Integrated Navigation.

An accurate observation model and statistical model are critical in underwater integrated navigation. However, it is often the case that the statistical characteristics of noise are unknown through the ultra-short baseline (USBL) system/Doppler velocity log (DVL) integrated navigation in the deep-sea. Additionally, the velocity of underwater vehicles relative to the bottom of the sea or the currents is commonly provided by the DVL, and an adaptive filtering solution is needed to correctly estimate the velocity with unknown currents. This paper focuses on the estimation of unknown currents and measurement noise covariance for an underwater vehicle based on the USBL, DVL, and a pressure gauge (PG), and proposes a novel unbiased adaptive two-stage information filter (ATSIF) for the underwater vehicle (UV) with an unknown time-varying currents velocity. In the proposed algorithm, the adaptive filter is decomposed into a standard information filter and an unknown currents velocity information filter with interconnections, and the time-varying unknown ocean currents and measurement noise covariance are estimated. The simulation and experimental results illustrate that the proposed algorithm can make full use of high-precision observation information and has better robustness and navigation accuracy to deal with time-varying currents and measurement outliers than existing state-of-the-art algorithms.

Averaged null controllability for some hyperbolic equations depending on a parameter

The aim of this paper is to prove the averaged null controllability property for a wave equation with an unknown velocity of propagation parameter and for parameter-dependent vibrating plate equation under the effect of a boundary control. The choice of the Hilbert uniqueness method seems to be the best-adapted method to our theory, where the key point to prove the desired result is an averaged inverse inequality (averaged observability inequality). Consequently, we'll prove the desired property for a large time enough and we'll design a single control chosen independently of the parameter value transferring the average of the state to the origin.

Robust trajectory tracking control of a marine surface vessel using asymmetric error constraints and output feedback

SummaryThis article investigates the problem of robust trajectory tracking for a marine surface vessel in the presence of asymmetrical error time‐varying constraints and output feedback. To deal with system uncertainties, adaptive neural networks (NNs) are used to approximate unknown dynamics model parameters and external disturbances. To obtain unmeasured velocities, a predictive observer based on output feedback is developed to estimate unknown velocities. A tan‐type asymmetric barrier Lyapunov function is used to deal with asymmetric error time‐varying constraints. The high‐frequency robust adaptive law is used to compensate for parameter estimation errors. The kinematic controller is designed based on the barrier Lyapunov function method, and the kinetics controller is designed base on an observer, an adaptive NN and a robust high‐frequency control. All signals of the closed‐loop systems are proved to be semiglobally uniformly and ultimately bounded via Lyapunov analysis, and the asymmetrical error constraints are not violated. Simulations are performed, and synthetic comparison is used to verify the feasibility and robustness of the proposed control law.

Bayesian Rayleigh wave inversion with an unknown number of layers

Surface wave methods have received much attention due to their efficient, flexible and convenient characteristics. However, there are still critical issues regarding a key step in surface wave inversion. In most existing methods, the number of layers is assumed to be known prior to the process of inversion. However, improper assignment of this parameter leads to erroneous inversion results. A Bayesian nonparametric method for Rayleigh wave inversion is proposed herein to address this problem. In this method, each model class represents a particular number of layers with unknown S-wave velocity and thickness of each layer. As a result, determination of the number of layers is equivalent to selection of the most applicable model class. Regarding each model class, the optimization search of S-wave velocity and thickness of each layer is implemented by using a genetic algorithm. Then, each model class is assessed in view of its efficiency under the Bayesian framework and the most efficient class is selected. Simulated and actual examples verify that the proposed Bayesian nonparametric approach is reliable and efficient for Rayleigh wave inversion, especially for its capability to determine the number of layers.

Joint Time Synchronization and Ranging for a Mobile Wireless Network

Time synchronization is a fundamental and paramount technology for a wireless network when a cooperative mission is performed. In this letter, the problem of how to achieve time synchronization and ranging for a mobile wireless network is addressed. The case of all nodes are in motion, equipped with a drifting clock, and capable of communicating with each other under unknown positions and velocities is handled. A network-wide model for synchronizing time-varying clocks and measuring relative distance is presented, from which the clock skews, clock offsets, and virtual polynomial coefficients related to the relative distances could be estimated. The Cramer-Rao Lower Bound (CRLB) is derived for the proposed model. The simulation results show that the proposed method is close to the best result of the existing available estimators and meets the CRLB. Furthermore, compared with the existing estimators, the proposed method is able to reduce the overall communication overheads and streamline the process.

Application of the collision mathematical model based on a BP neural network in railway vehicles

In order to enhance the learning performance of small-data-set models and improve the computation efficiency of finite element simulations of vehicle collision, the collision mathematical model (VCMM) based on the back-propagation (BP) neural network is established to predict the collision response data of a single car and marshalling cars at unknown velocities. The predicted results of VCMM were compared with the simulation results of the finite element method (FEM) to verify the model. The compared results show that the maximum relative errors of deformation, energy absorption and average interfacial force of a single vehicle are all below 8.5%, and the relative errors of the maximum compression of the C0 coupler and the internal energy of the A1 car among the marshalling cars are all less than 5%. In addition, the calculation time of the single car and marshalling cars collisions based on the VCMM are reduced by 24.36 and 61.8 times, respectively, compared with the FEM results, and the simulation calculation efficiency is greatly improved. The prediction result of VCMM will partially replace experimental and simulation results for crashworthiness and safety design of the vehicle structure in future studies.

A two-dimensional version of Newton’s cradle

Three billiard balls arranged in a triangle were impacted head-on by another billiard ball. Since there were more unknown velocities after the collision than the two conservation equations, several guesses of possible outcomes were explored. The same problem arises even if the three balls are arranged in a straight line, as they are in Newton’s cradle. One guess was found to be consistent with experimental results.

Finite-time velocity-free prescribed performance control for Halo orbit autonomous rendezvous

This paper studies the problem of autonomous rendezvous in the libration point orbit without relative velocity measurement information. The proposed rendezvous algorithm consists of the finite-time-convergent differentiator and the finite-time prescribed performance controller. Wherein, the differentiator is used to compute the unknown relative velocity between the target and the chaser spacecraft. The novel differentiator-based finite-time prescribed performance controller ensures that the rendezvous error converges to an arbitrarily small prescribed region in finite time in spite of the presence of additive bounded disturbances. Furthermore, the prescribed convergence rate can be also achieved simultaneously. The associated stability proof is constructive and accomplished by the development of a Lyapunov function candidate. Numerical simulations on a final rendezvous approach example are provided to demonstrate the effectiveness and robustness of the proposed control algorithm.

Robust trajectory tracking control of marine surface vessels with uncertain disturbances and input saturations

In this paper, a novel robust trajectory tracking control law is proposed for marine surface vessels with uncertain disturbances and input saturations using a tan-type barrier Lyapunov function and a backstepping technique. The low-frequency disturbances in kinetics from wind and waves are estimated by a nonlinear finite-time disturbance observer (FTDO). An adaptive estimation law is employed to estimate the unknown time-varying current velocities. A Gaussian error function-based continuous differentiable asymmetric saturation model is employed to handle the effect of nonsmooth asymmetric saturation nonlinearity using a backstepping technique, and auxiliary dynamic systems are used to compensate for the input saturation constraints on the actuators. Lyapunov stability analysis proves that all the signals of the closed-loop systems are guaranteed to be semi-globally uniformly ultimately bounded, and the tracking errors can converge to a small neighborhood of the origin by appropriately selecting the control parameters. Simulations and comparison results are presented to verify the effectiveness of the proposed method.