Unknown Terms Research Articles

Finite-time path following control for UUV with unknown model constraints

ABSTRACT This paper focuses on the path-following problem of an underactuated unmanned underwater vehicle (UUV) affected by external time-varying disturbances and unknown model constraints. A control strategy integrating the finite-time line-of-sight method (FTLOS), radial basis function (RBF) neural network and switching nonsingular terminal sliding mode (SNTSMC) is proposed. Initially, the FTLOS formulates the path following guidance law, making position errors converge to a small area near zero in finite time. The SNTSMC stabilizes velocity errors, ensuring they converge to zero vicinity more precisely. Next, the RBF neural network approximates the combined unknown term, which consists of unknown model constraints and external time-varying disturbances. The approximation term is then compensated into the control force and torque. Finally, a simulation experiment is conducted on the NUTU UUV. The results verify that the UUV can follow the desired path within a finite time and stay on it.

Physiology-informed regularisation enables training of universal differential equation systems for biological applications.

Systems biology tackles the challenge of understanding the high complexity in the internal regulation of homeostasis in the human body through mathematical modelling. These models can aid in the discovery of disease mechanisms and potential drug targets. However, on one hand the development and validation of knowledge-based mechanistic models is time-consuming and does not scale well with increasing features in medical data. On the other hand, data-driven approaches such as machine learning models require large volumes of data to produce generalisable models. The integration of neural networks and mechanistic models, forming universal differential equation (UDE) models, enables the automated learning of unknown model terms with less data than neural networks alone. Nevertheless, estimating parameters for these hybrid models remains difficult with sparse data and limited sampling durations that are common in biological applications. In this work, we propose the use of physiology-informed regularisation, penalising biologically implausible model behavior to guide the UDE towards more physiologically plausible regions of the solution space. In a simulation study we show that physiology-informed regularisation not only results in a more accurate forecasting of model behaviour, but also supports training with less data. We also applied this technique to learn a representation of the rate of glucose appearance in the glucose minimal model using meal response data measured in healthy people. In that case, the inclusion of regularisation reduces variability between UDE-embedded neural networks that were trained from different initial parameter guesses.

Dynamic behavior of multi-dimensional chaotic systems based on state variables and unknown parameters with applications in image encryption

Abstract To explore the impact of unknown terms and parameters on chaotic characteristics in chaotic systems, this paper examines the effects of state variables and unknown parameters. The study focuses on different combinations of linear, nonlinear, and constant terms It primarily investigates the role of multi-order state variables and their application to chaotic system models of varying dimensions. Firstly, by simulating a three-dimensional chaotic system, the paper analyzes how different combinations of nonlinear terms and initial conditions affect the system's chaotic behavior. Secondly, it evaluates the chaotic characteristics of a four-dimensional system, combining nonlinear terms with unknown parameters, using tools such as Lyapunov index diagrams, sample entropy, and dynamic trajectory plots. Finally, the paper integrates the constructed chaotic system with chaotic mapping to develop a two-level key chaotic image encryption system, thoroughly assessing its security and resistance to interference.

Fixed-time event-triggered distributed formation control for underactuated USVs considering actuator saturation

This paper proposes an event-triggered fixed-time containment control strategy (FTETCCS) to address the distributed formation control (DFC) problem of multiple underactuated surface vessels (USVs). By integrating fixed-time control (FTC) with event-triggered control (ETC), this strategy achieves fixed-time stability while reducing the usage of communication resources within the system. Initially, the fixed-time containment control law is utilized to compute the desired virtual target points for the followers. Subsequently, to facilitate future real-world experiments, an event-triggered fixed-time containment control guidance law is developed. This law computes the desired heading angle and forward speed derived from the virtual target points. The resulting values are then accurately tracked using a fixed-time controller. Furthermore, this study tackles the challenges posed by lumped unknown terms and actuator saturation during USV navigation. To address these issues, a fixed-time disturbance observer and a fixed-time auxiliary saturation system are designed. The effectiveness and superiority of the proposed FTETCCS are validated through theoretical analysis and simulation studies, with an analysis of the Zeno phenomenon confirming that the event-triggered mechanism does not lead to Zeno phenomena. Additionally, real ship experiments demonstrate the practical applicability of the proposed event-triggered fixed-time containment control guidance law.

Enhancing students’ comprehension of metaphoric terms in physics

This paper aims to dwell on students’ perceptions and attitudes towards metaphoric terms and some approaches that contribute to the comprehension and acquisition of basic physics metaphoric terminology for 1st-year undergraduate engineering students. Physics English terminology comprehension and acquisition is of great importance when it comes to these students. Being the lingua franca of today, mastering the basic terminology of the respective field of interest in English is demanding for everyone who aspires to have a deep understanding of their field of interest and a prosperous career in the future. To have an effective input and output in the teaching/learning process a collaboration among professionals of STEM (science, technology, engineering, and mathematics) and ESP (English for Specific Purposes) is necessitated. Physics is fundamentally dependent on abstract notions that frequently lack tangible counterparts, such as in these metaphoric terms "tunneling effect" or "black hole". Concepts expressed through such metaphoric terms assist students to envision, conceive, and acquire the latter, but can also hinder their understanding of concepts. To conduct this research, a semi–structured questionnaire was handed to 100 students of Polytechnic University of Tirana to investigate their beliefs towards these terms and to determine different approaches that will contribute to their understanding of the above-mentioned terms. The results concluded that students face challenges in comprehending a metaphoric unknown term. Nevertheless, the results indicated that the most used and preferred approaches to learning these terms are related to the professor’s assistance with explanation, analogy with everyday experiences, and visual aids, videos mainly. This study highlights the importance of collaboration between STEM and ESP in combining the linguistic-semantic nature of terms and their practical application in the function of students’ terminology acquisition.

Adaptive practical prescribed-time control for uncertain nonlinear systems with time-varying parameters

In this paper, adaptive practical prescribed-time (PPT) control is proposed for a class of uncertain nonlinear systems with time-varying parameters and unmodeled dynamics. By constructing a novel time-varying scaling function and utilizing nonlinear mapping, the PPT control is successfully resolved. The dynamical uncertainties resulting from unmodeled dynamics are estimated by employing an auxiliary available signal, and the unknown continuous terms are handled by the aid of radial basis function neural networks (RBFNNs). A novel adaptive control method is developed by introducing the compensating signals and dynamic surface control as well as practical prescribed-time control. All the signals involved are proved to be semi-globally uniformly ultimately bounded, and the tracking error could enter the pre-specified convergence region within a pre-specified time. The robotic manipulator system is used to demonstrate the effectiveness of the proposed control approach.

Event-Triggered Adaptive Preassigned Finite-Time Consensus Control for Multiagent Systems With Nonlinear Faults.

This article investigates a novel neuro-adaptive barrier Lyapunov function (BLF)-based event-triggered preassigned finite-time consensus control with asymptotic tracking for the nonlinear multiagent systems. The proposed approach is designed to broaden the scope of application by considering the high-order nonstrict-feedback dynamics of each agent with dynamic uncertainties subject to external disturbances and nonaffine nonlinear faults. A neural network (NN) is employed to approximate the unknown nonlinear terms. By fusing the NNs and Butterworth low-pass filter technique, the issues arising from the nonaffine nonlinear fault are addressed. To save the communication resources, a novel dynamic event-triggered mechanism based on an enhanced switching threshold is suggested. Additionally, a novel concept called the preassigned finite-time performance function (PFTPF) is defined to improve the transient and steady-state performances as well as providing faster response. The key feature of the proposed adaptive BLF-based control based on the bound estimation method is the introduction of a smooth function with decreasing variable which not only ensures that all the signals remain bounded and the synchronization errors are restricted within the PFTPF but also guarantees that the tracking errors asymptotically converge to zero. Finally, an illustrative example is provided to verify the feasibility of the proposed control approach.

Scalable learning of potentials to predict time-dependent Hartree–Fock dynamics

We propose a framework to learn the time-dependent Hartree–Fock (TDHF) inter-electronic potential of a molecule from its electron density dynamics. Although the entire TDHF Hamiltonian, including the inter-electronic potential, can be computed from first principles, we use this problem as a testbed to develop strategies that can be applied to learn a priori unknown terms that arise in other methods/approaches to quantum dynamics, e.g., emerging problems such as learning exchange–correlation potentials for time-dependent density functional theory. We develop, train, and test three models of the TDHF inter-electronic potential, each parameterized by a four-index tensor of size up to 60 × 60 × 60 × 60. Two of the models preserve Hermitian symmetry, while one model preserves an eight-fold permutation symmetry that implies Hermitian symmetry. Across seven different molecular systems, we find that accounting for the deeper eight-fold symmetry leads to the best-performing model across three metrics: training efficiency, test set predictive power, and direct comparison of true and learned inter-electronic potentials. All three models, when trained on ensembles of field-free trajectories, generate accurate electron dynamics predictions even in a field-on regime that lies outside the training set. To enable our models to scale to large molecular systems, we derive expressions for Jacobian-vector products that enable iterative, matrix-free training.

A Discrete Sine‐Cosine Transforms Galerkin Method for the Conductivity of Heterogeneous Materials With Mixed Dirichlet/Neumann Boundary Conditions

ABSTRACTThis work aims at developing a numerical method for conductivity problems in heterogeneous media subjected to mixed Dirichlet/Neumann boundary conditions. The method relies on a fixed‐point iterative solution of an auxiliary problem obtained by a Galerkin discretization using an approximation space spanned by mixed cosine‐sine series. The solution field is written as a known term verifying the boundary conditions and an unknown term described by cosine‐sine series, having no contribution on the boundary. Discrete sine‐cosine transforms, of Type I and III depending on the boundary conditions, are used to approximate the elementary integrals involved in the Galerkin formulation, which makes the method relying on the numerical complexity of fast Fourier transforms. The method is finally assessed in a problem of a composite material.

Uniqueness, stability and algorithm for an inverse wave-number-dependent source problem

Abstract This paper is concerned with an inverse wave-number-/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but independent on one spatial variable. The dependence of the source function on wave-number/frequency is supposed to be unknown. Based on the Fourier-transform and Dirichlet-Laplacian methods, we develop two efficient non-iterative numerical algorithms to recover the wave-number-dependent source. Uniqueness proof and increasing stability analysis are carried out if the boundary measurement data of Dirichlet kind are available. Numerical experiments are conducted to illustrate the effectiveness and efficiency of the proposed methods.

Adaptive neural control for a class of random nonlinear Markov jump multi-agent systems with full state constraints

This paper proposes a consensus control protocol based on the adaptive backstepping technique for a class of random Markov jump multi-agent systems (MASs) with full state constraints. Each agent is described by the high-order random nonlinear uncertain system driven by random differential equations, where the random noise is the second-order stationary stochastic process. First, a distributed tracking controller is designed for Markov jump MASs, effectively handling the interaction and coupling terms between agents. Second, an appropriate tan-type barrier Lyapunov function is selected to keep the agents’ states from the violation of constraint boundaries, and the unknown nonlinear terms with Markov jump parameters are approximated by neural networks (NNs) theory. Moreover, to address the differential explosion problem, the extended state observer (ESO) is first introduced instead of employing NNs approximation or command filtering techniques. Finally, the exponentially noise-to-state stability in mean square is proved rigorously through the Lyapunov method, which guarantees all signals of the closed-loop system are bounded in probability and the tracking error converges to a small neighborhood around zero. Simulations are given to demonstrate the feasibility of theoretical results.

Physics-informed and graph neural networks for enhanced inverse analysis

PurposeThis paper presents an original approach for learning models, partially known, of particular interest when performing source identification or structural health monitoring. The proposed procedures employ some amount of knowledge on the system under scrutiny as well as a limited amount of data efficiently assimilated.Design/methodology/approachTwo different formulations are explored. The first, based on the use of informed neural networks, leverages data collected at specific locations and times to determine the unknown source term of a parabolic partial differential equation. The second procedure, more challenging, involves learning the unknown model from a single measured field history, enabling the localization of a region where material properties differ.FindingsBoth procedures assume some kind of sparsity, either in the source distribution or in the region where physical properties differ. This paper proposed two different neural approaches able to learn models in order to perform efficient inverse analyses.Originality/valueTwo original methodologies are explored to identify hidden property that can be recovered with the right usage of data. Both methodologies are based on neural network architecture.

Model uncertainty quantification of a degradation model of miter gates using normalizing flow-based likelihood-free inference

Degradation modeling is essential for failure prognostics of miter gates and subsequent risk-informed maintenance or operational decision-making. Typically, degradation models are formulated based on certain assumptions and simplifications and may not fully capture the complexity of underlying degradation mechanisms. Even minor errors in such models may lead to significant discrepancies in failure prognostics due to error accumulation over time. Aiming to improve the accuracy of the degradation model and ensure reliable failure prognostics, this article proposes a degradation model updating framework for miter gates using normalizing flow-based likelihood-free inference, accounting for both model parameter uncertainty and model form uncertainty (i.e., model bias). The proposed work consists of two phases: the offline training phase and the online updating phase. During the offline training phase, the unknown model bias term is modeled as a random noise with uncertain standard deviation. Synthetic data are then generated using a physical model based on prior knowledge of the uncertain model parameters and model bias. The synthetic data are utilized to train an inference model, which has a summary network for data compression and a conditional invertible neural network for parameter estimation. In the online updating phase, the trained inference model uses strain observations to obtain posterior samples. The Gaussian mixture model and dual particle filter techniques are utilized to recursively update posterior samples, thereby improving the estimation accuracy. Subsequently, model bias is inversely estimated using the degradation model, which uses the updated model parameters and the gap length from the inference model. Following that, a regression model is constructed to correct the biases inherent in the simplified degradation model. This process is implemented iteratively over time to perform continuous model updating and failure prognostics. Results of a case study demonstrate the efficacy of the proposed framework in reducing both model parameter uncertainty and recovering model biases and thereby improving the accuracy of failure prognostics of miter gates.

Robust bilinear tracking control of a parabolic trough solar collector via saturation

This paper investigates the problem of robust tracking control of heat transport in a Parabolic Trough Solar Collector (PTSC), where the output has to track a desired reference trajectory. In this work, the PTSC is modeled by state-space bilinear dynamics. The manipulated variable is the pump volumetric flow rate, and the source term, i.e., solar irradiance, is assumed to be unmeasured. In addition, the actuator’s physical constraints induce saturation bounds on the manipulated variable and need to be considered explicitly in the controller design. To deal with these challenges, we first propose a saturated state-feedback law that meets the control objectives. Then, we reconstruct the unknown time-varying source term using an adaptive estimator. Later, through Lyapunov stability analysis, we prove that the closed-loop system and the output tracking error are uniformly ultimately stable. Numerical simulations attest to the performance of the proposed control strategy.

Numerical Tests to Evaluate the Effect of Constraining the Spectral Shape of Reference Events on Source Parameter Scaling

ABSTRACT Extracting source parameters from recorded spectra requires correction for attenuation effects. In consideration of the trade-off between source and propagation effects, various strategies have been proposed to constrain the inverse problem with a priori assumptions. The objective of this study is to assess the impact of constraining the source spectra of reference earthquakes in an attempt to remove a common unknown term from the spectral decomposition results. We perform numerical analyses to simulate the outcomes of the decomposition by generating source spectra for different stress drop versus seismic moment scaling, considering a large population of earthquakes with moment magnitudes between 1.8 and 6.5. Following the strategy of constraining the corner frequency of reference events, we evaluate the error of the retrieved source parameters when the applied constraint shows different levels of discrepancy with respect to the assumption used to generate the synthetics. The numerical tests show that an assumption that differs from the correct one can introduce a magnitude-dependent bias that could alter the scaling of the corner frequency with earthquake size. Furthermore, the source spectral shape for large events is also influenced by the constraints applied to the reference earthquakes. As a consequence, inferences about the self-similarity of the rupture process across the scales, or the selection of the most appropriate source model based on the goodness of the spectral fit, may be strongly biased by the constraint imposed on the reference earthquakes.

Study of a non-linear Volterra integro-differential equation with a non-linear unknown source term

In this paper, we propose a new class of integro-differential nonlinear Volterra equations with a non-linear unknown source term. Our study focuses on both theoretical analysis and numerical approximation of solutions to these equations. In the theoretical analysis partition, we define the specific assumptions on the integral kernel's characteristics, on the source term function and also on the derivative of the solutions of equations, under which the Krasnoselskii's fixed point theorem can be applied and in order to ensures the existence and uniqueness of solutions to the proposed integro-differential equations. In the numerical approximation partition, we use a well-known numerical technique for solving integral equations called Nyström method. This method allows us to get an approximate solutions of the proposed equations. Furthermore, we provide some illustrative examples and according to the numerical method described in this paper we approach them, where the comparison results between the exact and approximate solutions of these examples confirm the effectiveness of the numerical Nyström method for approaching the solutions of this class of integro-differential equations.

Finite-Time Adaptive Control for Electro-Hydraulic Braking Gear Transmission Mechanism with Unilateral Dead Zone Nonlinearity

Autonomous vehicles require more precise and reliable braking control, and electro-hydraulic braking (EHB) systems are better adapted to the development of autonomous driving. However, EHB systems inevitably suffer from unilateral dead zone nonlinearity, which adversely affects the position tracking control. Therefore, a finite-time adaptive control strategy was designed for unilateral dead zone nonlinearity. Initially, the unilateral dead zone nonlinearity was reformulated into a matched disturbance term and an unmatched disturbance term to reduce the adverse effects of disturbances, thereby enhancing system controllability. Then, the “complexity explosion” in the design of the control strategy was avoided by command filtering, and the design process of the controller was simplified. Furthermore, the finite-time control theory was employed to boost the system’s convergence speed, thereby enhancing control performance. In order to ensure the stability of the system under the dead zone disturbance, the unknown disturbance terms were estimated. The stability of the control strategy was validated through the finite-time stability theorem and the Lyapunov function. Eventually, simulations and hardware-in-the-loop (HIL) experiments validated the feasibility and availability of the finite-time adaptive control strategy.

Sparse regression for discovery of constitutive models from oscillatory shear measurements

We propose sparse regression as an alternative to neural networks for the discovery of parsimonious constitutive models (CMs) from oscillatory shear experiments. Symmetry and frame invariance are strictly imposed by using tensor basis functions to isolate and describe unknown nonlinear terms in the CMs. We generate synthetic experimental data using the Giesekus and Phan-Thien Tanner CMs and consider two different scenarios. In the complete information scenario, we assume that the shear stress, along with the first and second normal stress differences, is measured. This leads to a sparse linear regression problem that can be solved efficiently using l1 regularization. In the partial information scenario, we assume that only shear stress data are available. This leads to a more challenging sparse nonlinear regression problem, for which we propose a greedy two-stage algorithm. In both scenarios, the proposed methods fit and interpolate the training data remarkably well. Predictions of the inferred CMs extrapolate satisfactorily beyond the range of training data for oscillatory shear. They also extrapolate reasonably well to flow conditions like startup of steady and uniaxial extension that are not used in the identification of CMs. We discuss ramifications for experimental design, potential algorithmic improvements, and implications of the non-uniqueness of CMs inferred from partial information.

A stable difference scheme for the solution of a source identification problem for telegraph-parabolic equations

In the present paper, we construct a first order of accuracy difference scheme for the approximate solution of the inverse problem for telegraph-parabolic equations with an unknown spacewise dependent source term. The unique solvability of constructed difference scheme and the stability estimates for its solution were obtained. The proofs are based on the spectral representation of the self-adjoint positive definite operator in a Hilbert space.

Efficient Approximation Algorithms for Minimum Cost Seed Selection with Probabilistic Coverage Guarantee

Given a social network G , a cost associated with each user, and an influence threshold η, the minimum cost seed selection problem (MCSS) aims to find a set of seeds that minimizes the total cost to reach η users. Existing works are mainly devoted to providing an <u>e</u>xpected <u>c</u>overage <u>g</u>uarantee on reaching η, classified as MCSS-ECG, where their solutions either rely on an impractical influence oracle or cannot attain the expected influence threshold. More importantly, due to the expected coverage guarantee, the actual influence in a campaign may drift from the threshold evidently. Thus, the advertisers would like to request for a probability guarantee of reaching η. This motivates us to further solve the MCSS problem with a <u>p</u>robabilistic <u>c</u>overage <u>g</u>uarantee, termed MCSS-PCG. In this paper, we first propose our algorithm CLEAR to solve MCSS-ECG, which reaches the expected influence threshold without any influence oracle or influence shortfall but a practical approximation ratio. However, the ratio involves an unknown term (i.e., the optimal cost). Thus, we further devise the STAR method to derive a lower bound of the optimal cost and then obtain the first explicit approximation ratio for MCSS-ECG. In MCSS-PCG, it is necessary to estimate the probability that the current seeds reach η, to decide when to stop seed selection. To achieve this, we design a new technique named MRR, which provides efficient probability estimation with a theoretical guarantee. With MRR in hand, we propose our algorithm SCORE for MCSS-PCG, whose performance guarantee is derived by measuring the gap between MCSS-ECG and MCSS-PCG, and applying the theoretical results in MCSS-ECG. Finally, extensive experiments demonstrate that our algorithms achieve up to two orders of magnitude speed-up compared to alternatives while meeting the requirement of MCSS-PCG with the smallest cost.