In this paper, we consider a numerical homogenization of the poroelasticity problem with stochastic properties. The proposed method based on the construction of the deep neural network (DNN) for fast calculation of the effective properties for a coarse grid approximation of the problem. We train neural networks on the set of the selected realizations of the local microscale stochastic fields and macroscale characteristics (permeability and elasticity tensors). We construct a deep learning method through convolutional neural network (CNN) to learn a map between stochastic fields and effective properties. Numerical results are presented for two and three-dimensional model problems and show that proposed method provide fast and accurate effective property predictions.

In this paper, we address the risk estimation problem where one aims at estimating the probability of violation of safety constraints for a robot in the presence of bounded uncertainties with arbitrary probability distributions. In this problem, an unsafe set is described by level sets of polynomials that is, in general, a non-convex set. Uncertainty arises due to the probabilistic parameters of the unsafe set and probabilistic states of the robot. To solve this problem, we use a moment-based representation of probability distributions. We describe upper and lower bounds of the risk in terms of a linear weighted sum of the moments. Weights are coefficients of a univariate Chebyshev polynomial obtained by solving a sum-of-squares optimization problem in the offline step. Hence, given a finite number of moments of probability distributions, risk can be estimated in real-time. We demonstrate the performance of the provided approach by solving probabilistic collision checking problems where we aim to find the probability of collision of a robot with a non-convex obstacle in the presence of probabilistic uncertainties in the location of the robot and size, location, and geometry of the obstacle.

This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques, possibly combined with random sampling. A multilevel coarsening technique is proposed which utilizes a hypergraph associated with the data matrix and a graph coarsening strategy based on column matching. Theoretical results are established that characterize the quality of the dimension reduction achieved by a coarsening step, when a proper column matching strategy is employed. We consider a number of standard applications of this technique as well as a few new ones. Among the standard applications we first consider the problem of computing the partial SVD for which a combination of sampling and coarsening yields significantly improved SVD results relative to sampling alone. We also consider the Column subset selection problem, a popular low rank approximation method used in data related applications, and show how multilevel coarsening can be adapted for this problem. Similarly, we consider the problem of graph sparsification and show how coarsening techniques can be employed to solve it. Numerical experiments illustrate the performances of the methods in various applications.

In this paper, we study the control design of an automatic crosswind stabilization system for a novel, buoyantly-assisted aerial transportation vehicle. This vehicle has several advantages over other aircraft including the ability to take-off and land in very short distances and without the need for roads or runways. Despite these advantages, the large surface area of the vehicle's wing makes it more susceptible to wind, which introduces undesirable roll angle motions. The role of the automatic crosswind stabilization system is to detect the roll angle deviation, and then use motors at the wingtips to counteract the wind effect. However, due to the relatively large inertia of the wing compared to small-size unmanned aerial vehicles and additional input time delays, an automatic crosswind stabilization system based on traditional control algorithms such as the proportional-integral-derivative (PID) controller results in a response time that is too slow. Another challenge is the lack of high-accuracy wind sensors that can be mounted on the vehicle's wing. Therefore, we first design a wind torque estimator that relies on inertial measurements, and then use feed-forward compensation to directly correct for the wind torque, resulting in a significantly faster response. We second combine the proposed estimator with a model predictive controller (MPC), and compare constrained MPC with unconstrained MPC for the considered application. Experimental results show that our proposed estimation-based MPC strategy reduces the response time of the system by around 80-90% compared to a standard PID controller, without the need for adding wind sensors or changing the hardware of the stabilization system.

Learning algorithms have shown considerable prowess in simulation by allowing robots to adapt to uncertain environments and improve their performance. However, such algorithms are rarely used in practice on safety-critical systems, since the learned policy typically does not yield any safety guarantees. That is, the required exploration may cause physical harm to the robot or its environment. In this paper, we present a method to learn accurate safety certificates for nonlinear, closed-loop dynamical systems. Specifically, we construct a neural network Lyapunov function and a training algorithm that adapts it to the shape of the largest safe region in the state space. The algorithm relies only on knowledge of inputs and outputs of the dynamics, rather than on any specific model structure. We demonstrate our method by learning the safe region of attraction for a simulated inverted pendulum. Furthermore, we discuss how our method can be used in safe learning algorithms together with statistical models of dynamical systems.

In this paper, we are concerned with the 2D and 3D geometric shape generation by prescribing a set of characteristic values of a specific geometric body. One of the major motivations of our study is the 3D human body generation in various applications. We develop a novel method that can generate the desired body with customized characteristic values. The proposed method follows a machine-learning flavour that generates the inferred geometric body with the input characteristic parameters from a training dataset. One of the critical ingredients and novelties of our method is the borrowing of inverse scattering techniques in the theory of wave propagation to the body generation. This is done by establishing a delicate one-to-one correspondence between a geometric body and the far-field pattern of a source scattering problem governed by the Helmholtz system. It in turn enables us to establish a one-to-one correspondence between the geometric body space and the function space defined by the far-field patterns. Hence, the far-field patterns can act as the shape generators. The shape generation with prescribed characteristic parameters is achieved by first manipulating the shape generators and then reconstructing the corresponding geometric body from the obtained shape generator by a stable multiple-frequency Fourier method. Our method is easy to implement and produces more efficient and stable body generations. We provide both theoretical analysis and extensive numerical experiments for the proposed method. The study is the first attempt to introduce inverse scattering approaches in combination with machine learning to the geometric body generation and it opens up many opportunities for further developments.

In this paper we show how the stochastic heavy ball method (SHB) -- a popular method for solving stochastic convex and non-convex optimization problems --operates as a randomized gossip algorithm. In particular, we focus on two special cases of SHB: the Randomized Kaczmarz method with momentum and its block variant. Building upon a recent framework for the design and analysis of randomized gossip algorithms, [Loizou Richtarik, 2016] we interpret the distributed nature of the proposed methods. We present novel protocols for solving the average consensus problem where in each step all nodes of the network update their values but only a subset of them exchange their private values. Numerical experiments on popular wireless sensor networks showing the benefits of our protocols are also presented.

We introduce a ranking model for temporal multi-dimensional weighted and directed networks based on the Perron eigenvector of a multi-homogeneous order-preserving map. The model extends to the temporal multilayer setting the HITS algorithm and defines five centrality vectors: two for the nodes, two for the layers, and one for the temporal stamps. Nonlinearity is introduced in the standard HITS model in order to guarantee existence and uniqueness of these centrality vectors for any network, without any requirement on its connectivity structure. We introduce a globally convergent power iteration like algorithm for the computation of the centrality vectors. Numerical experiments on real-world networks are performed in order to assess the effectiveness of the proposed model and showcase the performance of the accompanying algorithm.

Surface registration is one of the most fundamental problems in geometry processing. Many approaches have been developed to tackle this problem in cases where the surfaces are nearly isometric. However, it is much more challenging to compute correspondence between surfaces which are intrinsically less similar. In this paper, we propose a variational model to align the Laplace-Beltrami (LB) eigensytems of two non-isometric genus zero shapes via conformal deformations. This method enables us compute to geometric meaningful point-to-point maps between non-isometric shapes. Our model is based on a novel basis pursuit scheme whereby we simultaneously compute a conformal deformation of a 'target shape' and its deformed LB eigensytem. We solve the model using an proximal alternating minimization algorithm hybridized with the augmented Lagrangian method which produces accurate correspondences given only a few landmark points. We also propose a reinitialization scheme to overcome some of the difficulties caused by the non-convexity of the variational problem. Intensive numerical experiments illustrate the effectiveness and robustness of the proposed method to handle non-isometric surfaces with large deformation with respect to both noise on the underlying manifolds and errors within the given landmarks.

Series elastic actuators (SEA) are playing an increasingly important role in the fields of physical human-robot interaction. This paper focuses on the modeling and control of a cable-driven SEA. First, the scheme of the cable-driven SEA has been proposed, and a velocity controlled DC motor has been used as its power source. Based on this, the model of the cable-driven SEA has been built up. Further, a two degrees of freedom (2-DOF) control approach has been employed to control the output torque. Simulation results have shown that the 2-DOF method has achieved better robust performance than the PD method.

Compartmental models based on tracer mass balance are extensively used in clinical and pre-clinical nuclear medicine in order to obtain quantitative information on tracer metabolism in the biological tissue. This paper is the second of a series of two that deal with the problem of tracer coefficient estimation via compartmental modelling in an inverse problem framework. While the previous work was devoted to the discussion of identifiability issues for 2, 3 and n-dimension compartmental systems, here we discuss the problem of numerically determining the tracer coefficients by means of a general regularized Multivariate Gauss Newton scheme. In this paper, applications concerning cerebral, hepatic and renal functions are considered, involving experimental measurements on FDG-PET data on different set of murine models.

This paper presents the generalized optimal sub-pattern assignment (GOSPA) metric on the space of finite sets of targets. Compared to the well-established optimal sub-pattern assignment (OSPA) metric, GOSPA is unnormalized as a function of the cardinality and it penalizes cardinality errors differently, which enables us to express it as an optimisation over assignments instead of permutations. An important consequence of this is that GOSPA allows us to penalize localization errors for detected targets and the errors due to missed and false targets, as indicated by traditional multiple target tracking (MTT) performance measures, in a sound manner. In addition, we extend the GOSPA metric to the space of random finite sets, which is important to evaluate MTT algorithms via simulations in a rigorous way.

Insightful visualization of multidimensional scalar fields, in particular parameter spaces, is key to many fields in computational science and engineering. We propose a principal component-based approach to visualize such fields that accurately reflects their sensitivity to input parameters. The method performs dimensionality reduction on the vast $L^2$ Hilbert space formed by all possible partial functions (i.e., those defined by fixing one or more input parameters to specific values), which are projected to low-dimensional parameterized manifolds such as 3D curves, surfaces, and ensembles thereof. Our mapping provides a direct geometrical and visual interpretation in terms of Sobol's celebrated method for variance-based sensitivity analysis. We furthermore contribute a practical realization of the proposed method by means of tensor decomposition, which enables accurate yet interactive integration and multilinear principal component analysis of high-dimensional models.

For large-scale industrial processes under closed-loop control, process dynamics directly resulting from control action are typical characteristics and may show different behaviors between real faults and normal changes of operating conditions. However, conventional distributed monitoring approaches do not consider the closed-loop control mechanism and only explore static characteristics, which thus are incapable of distinguishing between real process faults and nominal changes of operating conditions, leading to unnecessary alarms. In this regard, this paper proposes a distributed monitoring method for closed-loop industrial processes by concurrently exploring static and dynamic characteristics. First, the large-scale closed-loop process is decomposed into several subsystems by developing a sparse slow feature analysis (SSFA) algorithm which capture changes of both static and dynamic information. Second, distributed models are developed to separately capture static and dynamic characteristics from the local and global aspects. Based on the distributed monitoring system, a two-level monitoring strategy is proposed to check different influences on process characteristics resulting from changes of the operating conditions and control action, and thus the two changes can be well distinguished from each other. Case studies are conducted based on both benchmark data and real industrial process data to illustrate the effectiveness of the proposed method.

Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate singular value decompositions of large matrices. Similar ideas were used to solve least squares regression problems. In this paper, we show how matrices from error correcting codes can be used to find such low rank approximations and matrix decompositions, and extend the framework to linear least squares regression problems. The benefits of using these code matrices are the following: (i) They are easy to generate and they reduce randomness significantly. (ii) Code matrices with mild properties satisfy the subspace embedding property, and have a better chance of preserving the geometry of an entire subspace of vectors. (iii) For parallel and distributed applications, code matrices have significant advantages over structured random matrices and Gaussian random matrices. (iv) Unlike Fourier or Hadamard transform matrices, which require sampling $O(k\log k)$ columns for a rank-$k$ approximation, the log factor is not necessary for certain types of code matrices. That is, $(1+ε)$ optimal Frobenius norm error can be achieved for a rank-$k$ approximation with $O(k/ε)$ samples. (v) Fast multiplication is possible with structured code matrices, so fast approximations can be achieved for general dense input matrices. (vi) For least squares regression problem $\min\|Ax-b\|_2$ where $A\in \mathbb{R}^{n\times d}$, the $(1+ε)$ relative error approximation can be achieved with $O(d/ε)$ samples, with high probability, when certain code matrices are used.

Connected and automated vehicles (CAVs) have the potential to address the safety, mobility and sustainability issues of our current transportation systems. Cooperative adaptive cruise control (CACC), for example, is one promising technology to allow CAVs to be driven in a cooperative manner and introduces system-wide benefits. In this paper, we review the progress achieved by researchers worldwide regarding different aspects of CACC systems. Literature of CACC system architectures are reviewed, which explain how this system works from a higher level. Different control methodologies and their related issues are reviewed to introduce CACC systems from a lower level. Applications of CACC technology are demonstrated with detailed literature, which draw an overall landscape of CACC, point out current opportunities and challenges, and anticipate its development in the near future.

In this paper we study models and coordination policies for intermodal Autonomous Mobility-on-Demand (AMoD), wherein a fleet of self-driving vehicles provides on-demand mobility jointly with public transit. Specifically, we first present a network flow model for intermodal AMoD, where we capture the coupling between AMoD and public transit and the goal is to maximize social welfare. Second, leveraging such a model, we design a pricing and tolling scheme that allows to achieve the social optimum under the assumption of a perfect market with selfish agents. Finally, we present a real-world case study for New York City. Our results show that the coordination between AMoD fleets and public transit can yield significant benefits compared to an AMoD system operating in isolation.

Nowadays, companies such as Amazon, Alibaba, and even pizza chains are pushing forward to use drones, also called UAVs (Unmanned Aerial Vehicles), for service provision, such as package and food delivery. As governments intend to use these immense economic benefits that UAVs have to offer, urban planners are moving forward to incorporate so-called UAV flight zones and UAV highways in their smart city designs. However, the high-speed mobility and behavior dynamics of UAVs need to be monitored to detect and, subsequently, to deal with intruders, rogue drones, and UAVs with a malicious intent. This paper proposes a UAV defense system for the purpose of intercepting and escorting a malicious UAV outside the flight zone. The proposed UAV defense system consists of a defense UAV swarm, which is capable to self-organize its defense formation in the event of intruder detection, and chase the malicious UAV as a networked swarm. Modular design principles have been used for our fully localized approach. We developed an innovative auto-balanced clustering process to realize the intercept- and capture-formation. As it turned out, the resulting networked defense UAV swarm is resilient against communication losses. Finally, a prototype UAV simulator has been implemented. Through extensive simulations, we show the feasibility and performance of our approach.

The minimization of a nonconvex composite function can model a variety of imaging tasks. A popular class of algorithms for solving such problems are majorization-minimization techniques which iteratively approximate the composite nonconvex function by a majorizing function that is easy to minimize. Most techniques, e.g. gradient descent, utilize convex majorizers in order to guarantee that the majorizer is easy to minimize. In our work we consider a natural class of nonconvex majorizers for these functions, and show that these majorizers are still sufficient for a globally convergent optimization scheme. Numerical results illustrate that by applying this scheme, one can often obtain superior local optima compared to previous majorization-minimization methods, when the nonconvex majorizers are solved to global optimality. Finally, we illustrate the behavior of our algorithm for depth super-resolution from raw time-of-flight data.

How can we find patterns and anomalies in a tensor, or multi-dimensional array, in an efficient and directly interpretable way? How can we do this in an online environment, where a new tensor arrives each time step? Finding patterns and anomalies in a tensor is a crucial problem with many applications, including building safety monitoring, patient health monitoring, cyber security, terrorist detection, and fake user detection in social networks. Standard PARAFAC and Tucker decomposition results are not directly interpretable. Although a few sampling-based methods have previously been proposed towards better interpretability, they need to be made faster, more memory efficient, and more accurate. In this paper, we propose CTD, a fast, accurate, and directly interpretable tensor decomposition method based on sampling. CTD-S, the static version of CTD, provably guarantees a high accuracy that is 17 ~ 83x more accurate than that of the state-of-the-art method. Also, CTD-S is made 5 ~ 86x faster, and 7 ~ 12x more memory-efficient than the state-of-the-art method by removing redundancy. CTD-D, the dynamic version of CTD, is the first interpretable dynamic tensor decomposition method ever proposed. Also, it is made 2 ~ 3x faster than already fast CTD-S by exploiting factors at previous time step and by reordering operations. With CTD, we demonstrate how the results can be effectively interpreted in the online distributed denial of service (DDoS) attack detection.

We study the distribution of strategies in a large game that models how agents choose among different double auction markets. We classify the possible mean field Nash equilibria, which include potentially segregated states where an agent population can split into subpopulations adopting different strategies. As the game is aggregative, the actual equilibrium strategy distributions remain undetermined, however. We therefore compare with the results of Experience-Weighted Attraction (EWA) learning, which at long times leads to Nash equilibria in the appropriate limits of large intensity of choice, low noise (long agent memory) and perfect imputation of missing scores (fictitious play). The learning dynamics breaks the indeterminacy of the Nash equilibria. Non-trivially, depending on how the relevant limits are taken, more than one type of equilibrium can be selected. These include the standard homogeneous mixed and heterogeneous pure states, but also \emph{heterogeneous mixed} states where different agents play different strategies that are not all pure. The analysis of the EWA learning involves Fokker-Planck modeling combined with large deviation methods. The theoretical results are confirmed by multi-agent simulations.

The objective of this article is to optimize the overall traffic flow on freeways using multiple ramp metering controls plus its complementary Dynamic Speed Limits (DSLs). An optimal freeway operation can be reached when minimizing the difference between the freeway density and the critical ratio for maximum traffic flow. In this article, a Multi-Agent Reinforcement Learning for Freeways Control (MARL-FWC) system for ramps metering and DSLs is proposed. MARL-FWC introduces a new microscopic framework at the network level based on collaborative Markov Decision Process modeling (Markov game) and an associated cooperative Q-learning algorithm. The technique incorporates payoff propagation (Max-Plus algorithm) under the coordination graphs framework, particularly suited for optimal control purposes. MARL-FWC provides three control designs: fully independent, fully distributed, and centralized; suited for different network architectures. MARL-FWC was extensively tested in order to assess the proposed model of the joint payoff, as well as the global payoff. Experiments are conducted with heavy traffic flow under the renowned VISSIM traffic simulator to evaluate MARL-FWC. The experimental results show a significant decrease in the total travel time and an increase in the average speed (when compared with the base case) while maintaining an optimal traffic flow.

This note considers softmax parameter estimation when little/no labeled training data is available, but a priori information about the relative geometry of class label log-odds boundaries is available. It is shown that `data-free' softmax model synthesis corresponds to solving a linear system of parameter equations, wherein desired dominant class log-odds boundaries are encoded via convex polytopes that decompose the input feature space. When solvable, the linear equations yield closed-form softmax parameter solution families using class boundary polytope specifications only. This allows softmax parameter learning to be implemented without expensive brute force data sampling and numerical optimization. The linear equations can also be adapted to constrained maximum likelihood estimation in data-sparse settings. Since solutions may also fail to exist for the linear parameter equations derived from certain polytope specifications, it is thus also shown that there exist probabilistic classification problems over m convexly separable classes for which the log-odds boundaries cannot be learned using an m-class softmax model.

The Underactuated Lightweight Tensegrity Robotic Assistive Spine (ULTRA Spine) project is an ongoing effort to develop a flexible, actuated backbone for quadruped robots. In this work, model-predictive control is used to track a trajectory in the robot's state space, in simulation. The state trajectory used here corresponds to a bending motion of the spine, with translations and rotations of the moving vertebrae. Two different controllers are presented in this work: one that does not use a reference input but includes smoothing constrants, and a second one that uses a reference input without smoothing. For the smoothing controller, without reference inputs, the error converges to zero, while the simpler-to-tune controller with an input reference shows small errors but not complete convergence. It is expected that this controller will converge as it is improved further.

We study the game theoretic p-Laplacian for semi-supervised learning on graphs, and show that it is well-posed in the limit of finite labeled data and infinite unlabeled data. In particular, we show that the continuum limit of graph-based semi-supervised learning with the game theoretic p-Laplacian is a weighted version of the continuous p-Laplace equation. We also prove that solutions to the graph p-Laplace equation are approximately Holder continuous with high probability. Our proof uses the viscosity solution machinery and the maximum principle on a graph.

Autonomous inspection of large geographical areas is a central requirement for efficient hazard detection and disaster management in future cyber-physical systems such as smart cities. In this regard, exploiting unmanned aerial vehicle (UAV) swarms is a promising solution to inspect vast areas efficiently and with low cost. In fact, UAVs can easily fly and reach inspection points, record surveillance data, and send this information to a wireless base station (BS). Nonetheless, in many cases, such as operations at remote areas, the UAVs cannot be guided directly by the BS in real-time to find their path. Moreover, another key challenge of inspection by UAVs is the limited battery capacity. Thus, realizing the vision of autonomous inspection via UAVs requires energy-efficient path planning that takes into account the energy constraint of each individual UAV. In this paper, a novel path planning algorithm is proposed for performing energy-efficient inspection, under stringent energy availability constraints for each UAV. The developed framework takes into account all aspects of energy consumption for a UAV swarm during the inspection operations, including energy required for flying, hovering, and data transmission. It is shown that the proposed algorithm can address the path planning problem efficiently in polynomial time. Simulation results show that the proposed algorithm can yield substantial performance gains in terms of minimizing the overall inspection time and energy. Moreover, the results provide guidelines to determine parameters such as the number of required UAVs and amount of energy, while designing an autonomous inspection system.

In this paper, a method to synthesize controllers using finite time convergence control barrier functions guided by linear temporal logic specifications for continuous time multi-agent dynamical systems is proposed. Finite time convergence to a desired set in the state space is guaranteed under the existence of a suitable finite time convergence control barrier function. In addition, these barrier functions also guarantee forward invariance once the system converges to the desired set. This allows us to formulate a theoretical framework which synthesizes controllers for the multi-agent system. These properties also enable us to solve the reachability problem in continuous time by formulating a theorem on the composition of multiple finite time convergence control barrier functions. This approach is more flexible than existing methods and also allows for a greater set of feasible control laws. Linear temporal logic is used to specify complex task specifications that need to be satisfied by the multi-agent system. With this solution methodology, a control law is synthesized that satisfies the given temporal logic task specification. Robotic experiments are provided which were performed on the Robotarium multi-robot testbed at Georgia Tech.

This paper presents a bionic reflex control strategy for a kinematically constrained robotic finger. Here, the bionic reflex is achieved through a force tracking impedance control strategy. The dynamic model of the finger is reduced subject to kinematic constraints. Thereafter, an impedance control strategy that allows exact tracking of forces is discussed. Simulation results for a single finger holding a rectangular object against a flat surface are presented. Bionic reflex response time is of the order of milliseconds.

In recent years, using a network of autonomous and cooperative unmanned aerial vehicles (UAVs) without command and communication from the ground station has become more imperative, in particular in search-and-rescue operations, disaster management, and other applications where human intervention is limited. In such scenarios, UAVs can make more efficient decisions if they acquire more information about the mobility, sensing and actuation capabilities of their neighbor nodes. In this paper, we develop an unsupervised online learning algorithm for joint mobility prediction and object profiling of UAVs to facilitate control and communication protocols. The proposed method not only predicts the future locations of the surrounding flying objects, but also classifies them into different groups with similar levels of maneuverability (e.g. rotatory, and fixed-wing UAVs) without prior knowledge about these classes. This method is flexible in admitting new object types with unknown mobility profiles, thereby applicable to emerging flying Ad-hoc networks with heterogeneous nodes.

Unmanned aerial vehicles (UAVs) have gained a lot of popularity in diverse wireless communication fields. They can act as high-altitude flying relays to support communications between ground nodes due to their ability to provide line-of-sight links. With the flourishing Internet of Things, several types of new applications are emerging. In this paper, we focus on bandwidth hungry and delay-tolerant applications where multiple pairs of transceivers require the support of UAVs to complete their transmissions. To do so, the UAVs have the possibility to employ two different bands namely the typical microwave and the high-rate millimeter wave bands. In this paper, we develop a generic framework to assign UAVs to supported transceivers and optimize their trajectories such that a weighted function of the total service time is minimized. Taking into account both the communication time needed to relay the message and the flying time of the UAVs, a mixed non-linear programming problem aiming at finding the stops at which the UAVs hover to forward the data to the receivers is formulated. An iterative approach is then developed to solve the problem. First, a mixed linear programming problem is optimally solved to determine the path of each available UAV. Then, a hierarchical iterative search is executed to enhance the UAV stops' locations and reduce the service time. The behavior of the UAVs and the benefits of the proposed framework are showcased for selected scenarios.