6 research outputs found
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
Approximating the Held-Karp Bound for Metric TSP in Nearly Linear Time
We give a nearly linear time randomized approximation scheme for the
Held-Karp bound [Held and Karp, 1970] for metric TSP. Formally, given an
undirected edge-weighted graph on edges and , the
algorithm outputs in time, with high probability, a
-approximation to the Held-Karp bound on the metric TSP instance
induced by the shortest path metric on . The algorithm can also be used to
output a corresponding solution to the Subtour Elimination LP. We substantially
improve upon the running time achieved previously
by Garg and Khandekar. The LP solution can be used to obtain a fast randomized
-approximation for metric TSP which improves
upon the running time of previous implementations of Christofides' algorithm
Random Sampling and Greedy Sparsification for Matroid Optimization Problems.
Random sampling is a powerful tool for gathering information about a group by considering only a small part of it. We discuss some broadly applicable paradigms for using random sampling in combinatorial optimization, and demonstrate the effectiveness of these paradigms for two optimization problems on matroids: finding an optimum matroid basis and packing disjoint matroid bases. Applications of these ideas to the graphic matroid led to fast algorithms for minimum spanning trees and minimum cuts. An optimum matroid basis is typically found by a greedy algorithm that grows an independent set into an the optimum basis one element at a time. This continuous change in the independent set can make it hard to perform the independence tests needed by the greedy algorithm. We simplify matters by using sampling to reduce the problem of finding an optimum matroid basis to the problem of verifying that a given fixed basis is optimum, showing that the two problems can be solved in roughly the same ..
Problems in Control, Estimation, and Learning in Complex Robotic Systems
In this dissertation, we consider a range of different problems in systems, control, and learning theory and practice. In Part I, we look at problems in control of complex networks. In Chapter 1, we consider the performance analysis of a class of linear noisy dynamical systems. In Chapter 2, we look at the optimal design problems for these networks. In Chapter 3, we consider dynamical networks where interactions between the networks occur randomly in time. And in the last chapter of this part, in Chapter 4, we look at dynamical networks wherein coupling between the subsystems (or agents) changes nonlinearly based on the difference between the state of the subsystems. In Part II, we consider estimation problems wherein we deal with a large body of variables (i.e., at large scale). This part starts with Chapter 5, in which we consider the problem of sampling from a dynamical network in space and time for initial state recovery. In Chapter 6, we consider a similar problem with the difference that the observations instead of point samples become continuous observations that happen in Lebesgue measurable observations. In Chapter 7, we consider an estimation problem in which the location of a robot during the navigation is estimated using the information of a large number of surrounding features and we would like to select the most informative features using an efficient algorithm. In Part III, we look at active perception problems, which are approached using reinforcement learning techniques. This part starts with Chapter 8, in which we tackle the problem of multi-agent reinforcement learning where the agents communicate and classify as a team. In Chapter 9, we consider a single agent version of the same problem, wherein a layered architecture replaces the architectures of the previous chapter. Then, we use reinforcement learning to design the meta-layer (to select goals), action-layer (to select local actions), and perception-layer (to conduct classification)