pwc-archive/papers-with-abstracts huggingface dataset:
The Level Set Kalman Filter for State Estimation of Continuous-discrete Systems
Authors: Ningyuan Wang, Daniel B. Forger
Date: 2021-03-20 00:00:00
Tasks: State Estimation, State Space Models

We propose a new extension of Kalman filtering for continuous-discrete systems with nonlinear state-space models that we name as the level set Kalman filter (LSKF). The LSKF assumes the probability distribution can be approximated as a Gaussian, and updates the Gaussian distribution through a time-update step and a measurement-update step. The LSKF improves the time-update step when compared to existing methods, such as the continuous-discrete cubature Kalman filter (CD-CKF) by reformulating the underlying Fokker-Planck equation as an ordinary differential equation for the Gaussian, thereby avoiding expansion in time. Together with a carefully picked measurement-update method, numerical experiments show that the LSKF has a consistent performance improvement over CD-CKF for a range of parameters, while also simplifies the implementation, as no user-defined timestep subdivision between measurements is required, and the spatial derivatives of the drift function are not explicitly needed.
In-Field Gyroscope Autocalibration with Iterative Attitude Estimation
Authors: Li Wang, Rob Duffield, Deborah Fox, Athena Hammond, Andrew J. Zhang, Wei Xing Zheng, Steven W. Su
Date: 2021-03-20 00:00:00
Tasks: Experimental Design, parameter estimation

This paper presents an efficient in-field calibration method tailored for low-cost triaxial MEMS gyroscopes often used in healthcare applications. Traditional calibration techniques are challenging to implement in clinical settings due to the unavailability of high-precision equipment. Unlike the auto-calibration approaches used for triaxial MEMS accelerometers, which rely on local gravity, gyroscopes lack a reliable reference since the Earth's self-rotation speed is insufficient for accurate calibration. To address this limitation, we propose a novel method that uses manual rotation of the MEMS gyroscope to a specific angle (360{\deg}) as the calibration reference. This approach iteratively estimates the sensor's attitude without requiring any external equipment. Numerical simulations and empirical tests validate that the calibration error is low and that parameter estimation is unbiased. The method can be implemented in real-time on a low-energy microcontroller and completed in under 30 seconds. Comparative results demonstrate that the proposed technique outperforms existing state-of-the-art methods, achieving scale factor and bias errors of less than $2.5\times10^{-2}$ for LSM9DS1 and less than $1\times10^{-2}$ for ICM20948.
Model-free LQR based PID controller for trajectory tracking of 2-DoF helicopter: comparison and experimental results
Authors: Nouha Rouis, Ibrahima N'Doye, Taous-Meriem Laleg-Kirati
Date: 2021-03-19 00:00:00

This paper studies the performance of a model-free LQR based PID (i-LQR-PID) controller designed for tracking control problem of a 2-DoF laboratory helicopter. The control problem addressed in 2-DoF helicopter system aims to track the desired pitch and yaw axes trajectories despite disturbed operating conditions. In addition to the unpredictable variations, the 2-DoF helicopter dynamic is highly nonlinear with having strong cross-couplings in their models as well as being open loop unstable system. Thus, we propose a model-free LQR based PID control strategy in order to achieve better trajectory tracking control objectives. Robustness tests are performed experimentally to show the effectiveness of the model-free control.
Incremental Stability and Performance Analysis of Discrete-Time Nonlinear Systems using the LPV Framework
Authors: Patrick J. W. Koelewijn, Roland Tóth
Date: 2021-03-19 00:00:00

The dissipativity framework is widely used to analyze stability and performance of nonlinear systems. By embedding nonlinear systems in an LPV representation, the convex tools of the LPV framework can be applied to nonlinear systems for convex dissipativity based analysis and controller synthesis. However, as has been shown recently in literature, naive application of these tools to nonlinear systems for analysis and controller synthesis can fail to provide the desired guarantees. Namely, only performance and stability with respect to the origin is guaranteed. In this paper, inspired by the results for continuous-time nonlinear systems, the notion of incremental dissipativity for discrete-time nonlinear systems is proposed, whereby stability and performance analysis is done between trajectories. Furthermore, it is shown how, through the use of the LPV framework, convex conditions can be obtained for incremental dissipativity analysis of discrete-time nonlinear systems. The developed concepts and tools are demonstrated by analyzing incremental dissipativity of a controlled unbalanced disk system.
A Novel Approach to Disturbance Rejection in Constrained Model Predictive Control
Authors: Isah Abdulrasheed Jimoh
Date: 2021-03-17 00:00:00
Tasks: Model Predictive Control

This thesis is concerned with the rejection of time-varying disturbances in linear model predictive control of discrete-time systems. In the literature, disturbances are widely rejected by using velocity models, disturbance model with observer approach or a scheme that combines the compensation of a disturbance observer and the feedback regulation of MPC. Contrary to the widely used methods, the technique proposed in this research utilises the increment model of plants, with the assumption of fast-changing disturbances, to formulate a control law to reject the varying-disturbances. The uniqueness of the method stems from the compensation of the disturbance magnitude and rate of change. By proposing a cost function where the increment form of the system disturbance is taken as an optimisation variable, a control signal that is a function of a computed optimal disturbance increment is formulated to ensure that the plant is driven according to the minimisation of the cost function. The degree of freedom introduced by using the optimal disturbance in the control law was exploited to introduce the estimated disturbance increment into the control signal such that it is always in opposition to the external disturbance increment. Moreover, the proposed cost function provides a weighting matrix that can be used to manipulate the impacts of the exogenous disturbances on the response of the system. To estimate the unmeasurable disturbances, a combined state and disturbance observer is designed based on a convex optimisation stated in terms of an H2-minimisation problem. Simulations of three different systems are used to show the benefits of the proposed algorithm when compared with conventional offset-free MPC techniques. The results demonstrated that the proposed scheme can give significantly improved output tracking and regulation.
Robust state and protection-level estimation within tightly coupled GNSS/INS navigation system
Authors: Shuchen Liu, Kaizheng Wang, Dirk Abel
Date: 2021-03-19 00:00:00
Tasks: Fault Detection, State Estimation, valid

In autonomous applications for mobility and transport, a high-rate and highly accurate vehicle-state estimation is achieved by fusing measurements of global navigation satellite systems (GNSS) and inertial sensors. The state estimation and its protection-level generation often suffer from satellite-signal disturbances in urban environments and subsequent poor parametrization of the satellite observables. Thus, we propose an innovative scheme involving an extended H_infinity filter (EHF) for robust state estimation and zonotope for the protection-level generation. This scheme is shown as part of a tightly coupled navigation system based on an inertial navigation system and aided by the GPS/Galileo dual-constellation satellite navigation system. Specifically, GNSS pseudorange and deltarange observables are utilized. The experimental results of post-processing a real-world dataset show significant advantages of EHF against a conventional extended Kalman filter regarding the navigation accuracy and robustness under various GNSS-measurement parametrizations and environmental circumstances. The zonotope-based protection-level calculation is proven valid, computationally affordable, and feasible for real-time implementations.
Cooperative Formation of Autonomous Vehicles in Mixed Traffic Flow: Beyond Platooning
Authors: Keqiang Li, Jiawei Wang, Yang Zheng
Date: 2020-09-08 00:00:00
Tasks: Autonomous Vehicles

Cooperative formation and control of autonomous vehicles (AVs) promise increased efficiency and safety on public roads. In mixed traffic flow consisting of AVs and human-driven vehicles (HDVs), the prevailing platooning of multiple AVs is not the only choice for cooperative formation. In this paper, we investigate how different formations of AVs impact traffic performance from a set-function optimization perspective. We first reveal a stability invariance property and a diminishing improvement property of noncooperative formation when AVs adopt typical Adaptive Cruise Control (ACC) strategies. Then, we focus on the case of cooperative formation where the AV controllers are cooperatively designed %redesign the control strategies of AVs in different formations and investigate the optimal formation of multiple AVs using set-function optimization. Two predominant optimal formations, i.e., uniform distribution and platoon formation, emerge from extensive numerical experiments. Interestingly, platooning might have the least potential to improve traffic performance when HDVs have poor string stability behavior. These results suggest more opportunities for cooperative formation of AVs, beyond platooning, in practical mixed traffic flow.
Online power system parameter estimation and optimal operation
Authors: Xu Du, Alexander Engelmann, Timm Faulwasser, Boris Houska
Date: 2020-11-08 00:00:00
Tasks: parameter estimation

The integration of renewables into electrical grids calls for optimization-based control schemes requiring reliable grid models. Classically, parameter estimation and optimization-based control is often decoupled, which leads to high system operation cost in the estimation procedure. The present work proposes a method for simultaneously minimizing grid operation cost and optimally estimating line parameters based on methods for the optimal design of experiments. This method leads to a substantial reduction in cost for optimal estimation and in higher accuracy in the parameters compared with standard Optimal Power Flow and maximum-likelihood estimation. We illustrate the performance of the proposed method on a benchmark system.
Improving the Fidelity of Mixed-Monotone Reachable Set Approximations via State Transformations
Authors: Matthew Abate, Samuel Coogan
Date: 2020-10-02 00:00:00

Mixed-monotone systems are separable via a decomposition function into increasing and decreasing components, and this decomposition function allows for embedding the system dynamics in a higher-order monotone embedding system. Embedding the system dynamics in this way facilitates the efficient over-approximation of reachable sets with hyperrectangles, however, unlike the monotonicity property, which can be applied to compute, e.g., the tightest hyperrectangle containing a reachable set, the application of the mixed-monotonicity property generally results in conservative reachable set approximations. In this work, explore conservatism in the method and we consider, in particular, embedding systems that are monotone with respect to an alternative partial order. This alternate embedding system is constructed with a decomposition function for a related system, formed via a linear transformation of the initial state-space. We show how these alternate embedding systems allow for computing reachable sets with improved fidelity, i.e., reduced conservatism.
Evolution and mass extinctions as lognormal stochastic processes
Authors: Claudio Maccone
Date: 2021-03-20 00:00:00

In a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical picture, concisely called Evo-SETI. The relevant mathematical tools are: (1) Geometric Brownian motion (GBM), the stochastic process representing evolution as the stochastic increase of the number of species living on Earth over the last 3.5 billion years. This GBM is well known in the mathematics of finances (Black-Sholes models). (2) The probability distributions known as b-lognormals, i.e. lognormals starting at a certain positive instant b>0 rather than at the origin. In the framework of Darwinian Evolution, the resulting mathematical construction was shown to be what evolutionary biologists call Cladistics. (3) The (Shannon) entropy of such b-lognormals is then seen to represent the 'degree of progress' reached by each living organism or by each big set of living organisms, like historic human civilizations. (4) All these results also match with SETI in that the statistical Drake equation (generalization of the ordinary Drake equation to encompass statistics) leads just to the lognormal distribution as the probability distribution for the number of extra-terrestrial civilizations existing in the Galaxy. (5) The well-known 'Molecular Clock of Evolution', namely the 'constant rate of Evolution at the molecular level' as shown by Kimura's Neutral Theory of Molecular Evolution, identifies with growth rate of the entropy of our Evo-SETI model. (6) Furthermore, we apply our Evo-SETI model to lognormal stochastic processes other than GBMs. For instance, we provide two models for the mass extinctions that occurred in the past. (7) Finally, we show that the Markov & Korotayev model for Darwinian Evolution identifies with an Evo-SETI model.
Gauging diffraction patterns: field of view and bandwidth estimation in lensless holography
Authors: Ferréol Soulez
Date: 2021-03-22 00:00:00
Tasks: Super-Resolution

The purpose of this work is to provide theoretically grounded assessment on both the field-of-view and the bandwidth of a lensless holographic setup. Indeed, while previous works have presented results with super-resolution and field-of-view extrapolation, there is no well established rules to determine them. We show that the theoretical field of view can be hugely large with a spatial-frequency bandwidth only limited by the wavelength leading to an unthinkable number of degrees of freedom. To keep a realistic field of view and bandwidth, we propose several practical bounds based on few setup properties: namely the noise level and the spatio-temporal coherence of the source.
Laser Inter-Satellite Links in a Starlink Constellation
Authors: Aizaz U. Chaudhry, Halim Yanikomeroglu
Date: 2021-02-26 00:00:00

Laser inter-satellite links (LISLs) are envisioned between satellites in upcoming satellite constellations, such as Phase I of SpaceX's Starlink. Within a constellation, satellites can establish LISLs with other satellites in the same orbital plane or in different orbital planes. We present a classification of LISLs based on the location of satellites within a constellation and the duration of LISLs. Then, using satellite constellation for Phase I of Starlink, we study the effect of varying a satellite's LISL range on the number of different types of LISLs it can establish with other satellites. In addition to permanent LISLs, we observe a significant number of temporary LISLs between satellites in crossing orbital planes. Such LISLs can play a vital role in achieving low-latency paths within next-generation optical wireless satellite networks.
Efficient generative modeling of protein sequences using simple autoregressive models
Authors: Jeanne Trinquier, Guido Uguzzoni, Andrea Pagnani, Francesco Zamponi, Martin Weigt
Date: 2021-03-04 00:00:00
Tasks: Protein Design

Generative models emerge as promising candidates for novel sequence-data driven approaches to protein design, and for the extraction of structural and functional information about proteins deeply hidden in rapidly growing sequence databases. Here we propose simple autoregressive models as highly accurate but computationally efficient generative sequence models. We show that they perform similarly to existing approaches based on Boltzmann machines or deep generative models, but at a substantially lower computational cost (by a factor between $10^2$ and $10^3$). Furthermore, the simple structure of our models has distinctive mathematical advantages, which translate into an improved applicability in sequence generation and evaluation. Within these models, we can easily estimate both the probability of a given sequence, and, using the model's entropy, the size of the functional sequence space related to a specific protein family. In the example of response regulators, we find a huge number of ca. $10^{68}$ possible sequences, which nevertheless constitute only the astronomically small fraction $10^{-80}$ of all amino-acid sequences of the same length. These findings illustrate the potential and the difficulty in exploring sequence space via generative sequence models.
Three-dimensional Coherent X-ray Diffraction Imaging via Deep Convolutional Neural Networks
Authors: Longlong Wu, Shinjae Yoo, Ana F. Suzana, Tadesse A. Assefa, Jiecheng Diao, Ross J. Harder, Wonsuk Cha, Ian K. Robinson
Date: 2021-02-26 00:00:00
Tasks: Retrieval, Transfer Learning

As a critical component of coherent X-ray diffraction imaging (CDI), phase retrieval has been extensively applied in X-ray structural science to recover the 3D morphological information inside measured particles. Despite meeting all the oversampling requirements of Sayre and Shannon, current phase retrieval approaches still have trouble achieving a unique inversion of experimental data in the presence of noise. Here, we propose to overcome this limitation by incorporating a 3D Machine Learning (ML) model combining (optional) supervised learning with transfer learning. The trained ML model can rapidly provide an immediate result with high accuracy which could benefit real-time experiments, and the predicted result can be further refined with transfer learning. More significantly, the proposed ML model can be used without any prior training to learn the missing phases of an image based on minimization of an appropriate 'loss function' alone. We demonstrate significantly improved performance with experimental Bragg CDI data over traditional iterative phase retrieval algorithms.
EEGs disclose significant brain activity correlated with synaptic fickleness
Authors: Jorge Pretel, Joaquin J. Torres, J. Marro
Date: 2021-02-14 00:00:00
Tasks: EEG, Electroencephalogram (EEG)

We here study a network of synaptic relations mingling excitatory and inhibitory neuron nodes that displays oscillations quite similar to electroencephalogram (EEG) brain waves, and identify abrupt variations brought about by swift synaptic mediations. We thus conclude that corresponding changes in EEG series surely come from the slowdown of the activity in neuron populations due to synaptic restrictions. The latter happens to generate an imbalance between excitation and inhibition causing a quick explosive increase of excitatory activity, which turns out to be a (first-order) transition among dynamic mental phases. Besides, near this phase transition, our model system exhibits waves with a strong component in the so-called \textit{delta-theta domain} that coexist with fast oscillations. These findings provide a simple explanation for the observed \textit{delta-gamma} and \textit{theta-gamma modulation} in actual brains, and open a serious and versatile path to understand deeply large amounts of apparently erratic, easily accessible brain data.
Behavioural Movement Strategies in Cyclic Models
Authors: B. Moura, J. Menezes
Date: 2021-03-21 00:00:00

The spatial segregation of species is fundamental to ecosystem formation and stability. Behavioural strategies may determine where species are located and how their interactions change the local environment arrangement. In response to stimuli in the environment, individuals may move in a specific direction instead of walking randomly. This behaviour can be innate or learned from experience, and allow the individuals to conquer or the maintain territory, foraging or taking refuge. We study a generalisation of the spatial rock-paper-scissors model where individuals of one out of the species may perform directional movement tactics. Running a series of stochastic simulations, we investigate the effects of the behavioural tactics on the spatial pattern formation and the maintenance of the species diversity. We also explore a more realistic scenario, where not all individuals are conditioned to perform the behavioural strategy or have different levels of neighbourhood perception. Our outcomes show that self-preservation behaviour is more profitable in terms of territorial dominance, with the best result being achieved when all individuals are conditioned and have a long-range vicinity perception. On the other hand, invading is more advantageous if part of individuals is conditioned and if they have short-range neighbourhood perception. Finally, our findings reveal that the self-defence strategy is the least jeopardising to biodiversity which can help biologists to understand population dynamics in a setting where individuals may move strategically.
Fixation and Fluctuations in Two-Species Cooperation
Authors: Jordi Piñero, S. Redner, Ricard Solé
Date: 2021-03-19 00:00:00
Tasks: Vocal Bursts Valence Prediction

Cooperative interactions pervade in a broad range of many-body populations, such as ecological communities, social organizations, and economic webs. We investigate the dynamics of a population of two equivalent species A and B that are driven by cooperative and symmetric interactions between these species. For an isolated population, we determine the probability to reach fixation, where only one species remains, as a function of the initial concentrations of the two species, as well as the time to reach fixation. The latter scales exponentially with the population size. When members of each species migrate into the population at rate $\lambda$ and replace a randomly selected individual, surprisingly rich dynamics ensues. Ostensibly, the population reaches a steady state, but the steady-state population distribution undergoes a unimodal to trimodal transition as the migration rate decreases below a critical value $\lambda_c$. In the low-migration regime, $\lambda<\lambda_c$, the steady state is not truly steady, but instead strongly fluctuates between near-fixation states, where the population consists of mostly A's or of mostly B's. The characteristic time scale of these fluctuations diverges as $\lambda^{-1}$. Thus in spite of the cooperative interaction, a typical snapshot of the population will contain almost all A's or almost all B's.
Search and localization dynamics of the CRISPR/Cas9 system
Authors: Qiao Lu, Deepak Bhat, Darya Stepanenko, Simone Pigolotti
Date: 2021-03-19 00:00:00

The CRISPR/Cas9 system acts as the prokaryotic immune system and has important applications in gene editing. The protein Cas9 is one of its crucial components. The role of Cas9 is to search for specific target sequences on the DNA and cleave them. In this Letter, we introduce a model of facilitated diffusion for Cas9 and fit its parameters to single-molecule experiments. Our model confirms that Cas9 search for targets by sliding, but shows that its sliding length is rather short. We then investigate how Cas9 explores a long stretch of DNA containing randomly placed targets. We solve this problem by mapping it into the theory of Anderson localization in condensed matter physics. Our theoretical approach rationalizes experimental evidences on the distribution of Cas9 molecules along the DNA.