Quickest Change Detection in Adaptive Censoring Sensor Networks

The problem of quickest change detection with communication rate constraints is studied. A network of wireless sensors with limited computation capability monitors the environment and sends observations to a fusion center via wireless channels. At an unknown time instant, the distributions of observations at all the sensor nodes change simultaneously. Due to limited energy, the sensors cannot transmit at all the time instants. The objective is to detect the change at the fusion center as quickly as possible, subject to constraints on false detection and average communication rate between the sensors and the fusion center. A minimax formulation is proposed. The cumulative sum (CuSum) algorithm is used at the fusion center and censoring strategies are used at the sensor nodes. The censoring strategies, which are adaptive to the CuSum statistic, are fed back by the fusion center. The sensors only send observations that fall into prescribed sets to the fusion center. This CuSum adaptive censoring (CuSum-AC) algorithm is proved to be an equalizer rule and to be globally asymptotically optimal for any positive communication rate constraint, as the average run length to false alarm goes to infinity. It is also shown, by numerical examples, that the CuSum-AC algorithm provides a suitable trade-off between the detection performance and the communication rate.Comment: 12 pages, 6 figures, to appear in IEEE Transactions on Control of Network System

Infinite Horizon Optimal Transmission Power Control for Remote State Estimation over Fading Channels

Jointly optimal transmission power control and remote estimation over an infinite horizon is studied. A sensor observes a dynamic process and sends its observations to a remote estimator over a wireless fading channel characterized by a time-homogeneous Markov chain. The successful transmission probability depends on both the channel gains and the transmission power used by the sensor. The transmission power control rule and the remote estimator should be jointly designed, aiming to minimize an infinite-horizon cost consisting of the power usage and the remote estimation error. A first question one may ask is: Does this joint optimization problem have a solution? We formulate the joint optimization problem as an average cost belief-state Markov decision process and answer the question by proving that there exists an optimal deterministic and stationary policy. We then show that when the monitored dynamic process is scalar, the optimal remote estimates depend only on the most recently received sensor observation, and the optimal transmission power is symmetric and monotonically increasing with respect to the innovation error

Fully Finite Element Adaptive Algebraic Multigrid Method for Time-Space Caputo-Riesz Fractional Diffusion Equations

The paper aims to establish a fully discrete finite element (FE) scheme and provide cost-effective solutions for one-dimensional time-space Caputo-Riesz fractional diffusion equations on a bounded domain $\Omega$. Firstly, we construct a fully discrete scheme of the linear FE method in both temporal and spatial directions, derive many characterizations on the coefficient matrix and numerically verify that the fully FE approximation possesses the saturation error order under $L^2(\Omega)$ norm. Secondly, we theoretically prove the estimation $1+\mathcal{O}(\tau^\alpha h^{-2\beta})$ on the condition number of the coefficient matrix, in which $\tau$ and $h$ respectively denote time and space step sizes. Finally, on the grounds of the estimation and fast Fourier transform, we develop and analyze an adaptive algebraic multigrid (AMG) method with low algorithmic complexity, reveal a reference formula to measure the strength-of-connection tolerance which severely affect the robustness of AMG methods in handling fractional diffusion equations, and illustrate the well robustness and high efficiency of the proposed algorithm compared with the classical AMG, conjugate gradient and Jacobi iterative methods.Comment: 26 pages, 2 figure

Time-space Finite Element Adaptive AMG for Multi-term Time Fractional Advection Diffusion Equations

In this study we construct a time-space finite element (FE) scheme and furnish cost-efficient approximations for one-dimensional multi-term time fractional advection diffusion equations on a bounded domain $\Omega$. Firstly, a fully discrete scheme is obtained by the linear FE method in both temporal and spatial directions, and many characterizations on the resulting matrix are established. Secondly, the condition number estimation is proved, an adaptive algebraic multigrid (AMG) method is further developed to lessen computational cost and analyzed in the classical framework. Finally, some numerical experiments are implemented to reach the saturation error order in the $L^2(\Omega)$ norm sense, and present theoretical confirmations and predictable behaviors of the proposed algorithm.Comment: 27 pages, 2 figure

Parallel-in-Time with Fully Finite Element Multigrid for 2-D Space-fractional Diffusion Equations

The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions. We firstly obtain a fully discrete scheme via using the linear finite element method to discretize spatial and temporal derivatives to propagate solutions. Next, we present a non-intrusive time-parallelization and its two-level convergence analysis, where we algorithmically and theoretically generalize the MGRIT to time-dependent fine time-grid propagators. Finally, numerical illustrations show that the obtained numerical scheme possesses the saturation error order, theoretical results of the two-level variant deliver good predictions, and significant speedups can be achieved when compared to parareal and the sequential time-stepping approach.Comment: 20 pages, 4 figures, 8 table

Learning Optimal Scheduling Policy for Remote State Estimation under Uncertain Channel Condition

We consider optimal sensor scheduling with unknown communication channel statistics. We formulate two types of scheduling problems with the communication rate being a soft or hard constraint, respectively. We first present some structural results on the optimal scheduling policy using dynamic programming and assuming the channel statistics is known. We prove that the Q-factor is monotonic and submodular, which leads to the threshold-like structures in both types of problems. Then we develop a stochastic approximation and parameter learning frameworks to deal with the two scheduling problems with unknown channel statistics. We utilize their structures to design specialized learning algorithms. We prove the convergence of these algorithms. Performance improvement compared with the standard Q-learning algorithm is shown through numerical examples.Comment: Full Versio

Algebraic multigrid block preconditioning for multi-group radiation diffusion equations

The paper focuses on developing and studying efficient block preconditioners based on classical algebraic multigrid for the large-scale sparse linear systems arising from the fully coupled and implicitly cell-centered finite volume discretization of multi-group radiation diffusion equations, whose coefficient matrices can be rearranged into the $(G+2)\times(G+2)$ block form, where $G$ is the number of energy groups. The preconditioning techniques are based on the monolithic classical algebraic multigrid method, physical-variable based coarsening two-level algorithm and two types of block Schur complement preconditioners. The classical algebraic multigrid is applied to solve the subsystems that arise in the last three block preconditioners. The coupling strength and diagonal dominance are further explored to improve performance. We use representative one-group and twenty-group linear systems from capsule implosion simulations to test the robustness, efficiency, strong and weak parallel scaling properties of the proposed methods. Numerical results demonstrate that block preconditioners lead to mesh- and problem-independent convergence, and scale well both algorithmically and in parallel

Max-Min Fair Sensor Scheduling: Game-theoretic Perspective and Algorithmic Solution

We consider the design of a fair sensor schedule for a number of sensors monitoring different linear time-invariant processes. The largest average remote estimation error among all processes is to be minimized. We first consider a general setup for the max-min fair allocation problem. By reformulating the problem as its equivalent form, we transform the fair resource allocation problem into a zero-sum game between a "judge" and a resource allocator. We propose an equilibrium seeking procedure and show that there exists a unique Nash equilibrium in pure strategy for this game. We then apply the result to the sensor scheduling problem and show that the max-min fair sensor scheduling policy can be achieved

Quickest Change Detection with a Censoring Sensor in the Minimax Setting

The problem of quickest change detection with a wireless sensor node is studied in this paper. The sensor that is deployed to monitor the environment has limited energy constraint to the classical quickest change detection problem. We consider the "censoring" strategy at the sensor side, i.e., the sensor selectively sends its observations to the decision maker. The quickest change detection problem is formulated in a minimax way. In particular, our goal is to find the optimal censoring strategy and stopping time such that the detection delay is minimized subject to constraints on both average run length (ARL) and average energy cost before the change. We show that the censoring strategy that has the maximal post-censoring Kullback-Leibler (K-L) divergence coupled with Cumulative Sum (CuSum) and Shiryaev-Roberts-Pollak (SRP) detection procedure is asymptotically optimal for the Lorden's and Pollak's problem as the ARL goes to infinity, respectively. We also show that the asymptotically optimal censoring strategy should use up the available energy and has a very special structure, i.e., the likelihood ratio of the no send region is a single interval, which can be utilized to significantly reduce the computational complexity. Numerical examples are shown to illustrate our results

Fast-Learning Grasping and Pre-Grasping via Clutter Quantization and Q-map Masking

Grasping objects in cluttered scenarios is a challenging task in robotics. Performing pre-grasp actions such as pushing and shifting to scatter objects is a way to reduce clutter. Based on deep reinforcement learning, we propose a Fast-Learning Grasping (FLG) framework, that can integrate pre-grasping actions along with grasping to pick up objects from cluttered scenarios with reduced real-world training time. We associate rewards for performing moving actions with the change of environmental clutter and utilize a hybrid triggering method, leading to data-efficient learning and synergy. Then we use the output of an extended fully convolutional network as the value function of each pixel point of the workspace and establish an accurate estimation of the grasp probability for each action. We also introduce a mask function as prior knowledge to enable the agents to focus on the accurate pose adjustment to improve the effectiveness of collecting training data and, hence, to learn efficiently. We carry out pre-training of the FLG over simulated environment, and then the learnt model is transferred to the real world with minimal fine-tuning for further learning during actions. Experimental results demonstrate a 94% grasp success rate and the ability to generalize to novel objects. Compared to state-of-the-art approaches in the literature, the proposed FLG framework can achieve similar or higher grasp success rate with lesser amount of training in the real world. Supplementary video is available at https://youtu.be/e04uDLsxfDg