1,153 research outputs found
Sensor Scheduling for Optimal Observability Using Estimation Entropy
We consider sensor scheduling as the optimal observability problem for
partially observable Markov decision processes (POMDP). This model fits to the
cases where a Markov process is observed by a single sensor which needs to be
dynamically adjusted or by a set of sensors which are selected one at a time in
a way that maximizes the information acquisition from the process. Similar to
conventional POMDP problems, in this model the control action is based on all
past measurements; however here this action is not for the control of state
process, which is autonomous, but it is for influencing the measurement of that
process. This POMDP is a controlled version of the hidden Markov process, and
we show that its optimal observability problem can be formulated as an average
cost Markov decision process (MDP) scheduling problem. In this problem, a
policy is a rule for selecting sensors or adjusting the measuring device based
on the measurement history. Given a policy, we can evaluate the estimation
entropy for the joint state-measurement processes which inversely measures the
observability of state process for that policy. Considering estimation entropy
as the cost of a policy, we show that the problem of finding optimal policy is
equivalent to an average cost MDP scheduling problem where the cost function is
the entropy function over the belief space. This allows the application of the
policy iteration algorithm for finding the policy achieving minimum estimation
entropy, thus optimum observability.Comment: 5 pages, submitted to 2007 IEEE PerCom/PerSeNS conferenc
Space-Time Sampling for Network Observability
Designing sparse sampling strategies is one of the important components in
having resilient estimation and control in networked systems as they make
network design problems more cost-effective due to their reduced sampling
requirements and less fragile to where and when samples are collected. It is
shown that under what conditions taking coarse samples from a network will
contain the same amount of information as a more finer set of samples. Our goal
is to estimate initial condition of linear time-invariant networks using a set
of noisy measurements. The observability condition is reformulated as the frame
condition, where one can easily trace location and time stamps of each sample.
We compare estimation quality of various sampling strategies using estimation
measures, which depend on spectrum of the corresponding frame operators. Using
properties of the minimal polynomial of the state matrix, deterministic and
randomized methods are suggested to construct observability frames. Intrinsic
tradeoffs assert that collecting samples from fewer subsystems dictates taking
more samples (in average) per subsystem. Three scalable algorithms are
developed to generate sparse space-time sampling strategies with explicit error
bounds.Comment: Submitted to IEEE TAC (Revised Version
Sequential Detection with Mutual Information Stopping Cost
This paper formulates and solves a sequential detection problem that involves
the mutual information (stochastic observability) of a Gaussian process
observed in noise with missing measurements. The main result is that the
optimal decision is characterized by a monotone policy on the partially ordered
set of positive definite covariance matrices. This monotone structure implies
that numerically efficient algorithms can be designed to estimate and implement
monotone parametrized decision policies.The sequential detection problem is
motivated by applications in radar scheduling where the aim is to maintain the
mutual information of all targets within a specified bound. We illustrate the
problem formulation and performance of monotone parametrized policies via
numerical examples in fly-by and persistent-surveillance applications involving
a GMTI (Ground Moving Target Indicator) radar
Optimal Drive-by Sensing in Urban Road Networks with Large-scale Ridesourcing Vehicles
The sensing and monitoring of the urban road network contribute to the
efficient operation of the urban transportation system and the functionality of
urban systems. However, traditional sensing methods, such as inductive loop
sensors, roadside cameras, and crowdsourcing data from massive urban travelers
(e.g., Google Maps), are often hindered by high costs, limited coverage, and
low reliability. This study explores the potential of drive-by sensing, an
innovative approach that employs large-scale ridesourcing vehicles (RVs) for
urban road network monitoring. We first evaluate RV sensing performance by
coverage and reliability through historical road segment visits. Next, we
propose an optimal trip-based RV rerouting model to maximize the sensing
coverage and reliability while preserving the same level of service for the
RVs' mobility service. Furthermore, a scalable column generation-based
heuristic is designed to guide the cruising trajectory of RVs, assuming trip
independence. The effectiveness of the proposed model is validated through
experiments and sensitivity analyses using real-world RV trajectory data of
over 20,000 vehicles in New York City. The optimized rerouting strategy has
yielded significantly improved results, elevating explicit sensing coverage of
the road network by 15.0\% to 17.3\% (varies by time of day) and achieving an
impressive enhancement in sensing reliability by at least 24.6\% compared to
historical records. Expanding the path-searching space further improved sensing
coverage of up to 4.5\% and reliability of over 4.2\%. Moreover, considering
incentives for RV drivers, the enhanced sensing performance comes at a
remarkably low cost of \$0.10 per RV driver, highlighting its
cost-effectiveness
Resilient Submodular Maximization For Control And Sensing
Fundamental applications in control, sensing, and robotics, motivate the design of systems by selecting system elements, such as actuators or sensors, subject to constraints that require the elements not only to be a few in number, but also, to satisfy heterogeneity or interdependency constraints (called matroid constraints). For example, consider the scenarios:
- (Control) Actuator placement: In a power grid, how should we place a few generators both to guarantee its stabilization with minimal control effort, and to satisfy interdependency constraints where the power grid must be controllable from the generators?
- (Sensing) Sensor placement: In medical brain-wearable devices, how should we place a few sensors to ensure smoothing estimation capabilities?
- (Robotics) Sensor scheduling: At a team of mobile robots, which few on-board sensors should we activate at each robot ---subject to heterogeneity constraints on the number of sensors that each robot can activate at each time--- so both to maximize the robots\u27 battery life, and to ensure the robots\u27 capability to complete a formation control task?
In the first part of this thesis we motivate the above design problems, and propose the first algorithms to address them. In particular, although traditional approaches to matroid-constrained maximization have met great success in machine learning and facility location, they are unable to meet the aforementioned problem of actuator placement. In addition, although traditional approaches to sensor selection enable Kalman filtering capabilities, they do not enable smoothing or formation control capabilities, as required in the above problems of sensor placement and scheduling. Therefore, in the first part of the thesis we provide the first algorithms, and prove they achieve the following characteristics: provable approximation performance: the algorithms guarantee a solution close to the optimal; minimal running time: the algorithms terminate with the same running time as state-of-the-art algorithms for matroid-constrained maximization; adaptiveness: where applicable, at each time step the algorithms select system elements based on both the history of selections. We achieve the above ends by taking advantage of a submodular structure of in all aforementioned problems ---submodularity is a diminishing property for set functions, parallel to convexity for continuous functions.
But in failure-prone and adversarial environments, sensors and actuators can fail; sensors and actuators can get attacked. Thence, the traditional design paradigms over matroid-constraints become insufficient, and in contrast, resilient designs against attacks or failures become important. However, no approximation algorithms are known for their solution; relevantly, the problem of resilient maximization over matroid constraints is NP-hard.
In the second part of this thesis we motivate the general problem of resilient maximization over matroid constraints, and propose the first algorithms to address it, to protect that way any design over matroid constraints, not only within the boundaries of control, sensing, and robotics, but also within machine learning, facility location, and matroid-constrained optimization in general.
In particular, in the second part of this thesis we provide the first algorithms, and prove they achieve the following characteristics: resiliency: the algorithms are valid for any number of attacks or failures; adaptiveness: where applicable, at each time step the algorithms select system elements based on both the history of selections, and on the history of attacks or failures; provable approximation guarantees: the algorithms guarantee for any submodular or merely monotone function a solution close to the optimal; minimal running time: the algorithms terminate with the same running time as state-of-the-art algorithms for matroid-constrained maximization. We bound the performance of our algorithms by using notions of curvature for monotone (not necessarily submodular) set functions, which are established in the literature of submodular maximization.
In the third and final part of this thesis we apply our tools for resilient maximization in robotics, and in particular, to the problem of active information gathering with mobile robots. This problem calls for the motion-design of a team of mobile robots so to enable the effective information gathering about a process of interest, to support, e.g., critical missions such as hazardous environmental monitoring, and search and rescue. Therefore, in the third part of this thesis we aim to protect such multi-robot information gathering tasks against attacks or failures that can result to the withdrawal of robots from the task. We conduct both numerical and hardware experiments in multi-robot multi-target tracking scenarios, and exemplify the benefits, as well as, the performance of our approach
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