Matching Items (3)
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- All Subjects: Control Theory
- Genre: Academic theses
- Creators: Artemiadis, Panagiotis
- Creators: Ilkturk, Utku
Description
Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition determining whether a finite number of measurements suffice to recover the initial state. However to employ observability for sensor scheduling, the binary definition needs to be expanded so that one can measure how observable a system is with a particular measurement scheme, i.e. one needs a metric of observability. Most methods utilizing an observability metric are about sensor selection and not for sensor scheduling. In this dissertation we present a new approach to utilize the observability for sensor scheduling by employing the condition number of the observability matrix as the metric and using column subset selection to create an algorithm to choose which sensors to use at each time step. To this end we use a rank revealing QR factorization algorithm to select sensors. Several numerical experiments are used to demonstrate the performance of the proposed scheme.
ContributorsIlkturk, Utku (Author) / Gelb, Anne (Thesis advisor) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Renaut, Rosemary (Committee member) / Armbruster, Dieter (Committee member) / Arizona State University (Publisher)
Created2015
Description
To achieve the ambitious long-term goal of a feet of cooperating Flexible Autonomous
Machines operating in an uncertain Environment (FAME), this thesis addresses several
critical modeling, design, control objectives for rear-wheel drive ground vehicles.
Toward this ambitious goal, several critical objectives are addressed. One central objective of the thesis was to show how to build low-cost multi-capability robot platform
that can be used for conducting FAME research.
A TFC-KIT car chassis was augmented to provide a suite of substantive capabilities.
The augmented vehicle (FreeSLAM Robot) costs less than $500 but offers the capability
of commercially available vehicles costing over $2000.
All demonstrations presented involve rear-wheel drive FreeSLAM robot. The following
summarizes the key hardware demonstrations presented and analyzed:
(1)Cruise (v, ) control along a line,
(2) Cruise (v, ) control along a curve,
(3) Planar (x, y) Cartesian Stabilization for rear wheel drive vehicle,
(4) Finish the track with camera pan tilt structure in minimum time,
(5) Finish the track without camera pan tilt structure in minimum time,
(6) Vision based tracking performance with different cruise speed vx,
(7) Vision based tracking performance with different camera fixed look-ahead distance L,
(8) Vision based tracking performance with different delay Td from vision subsystem,
(9) Manually remote controlled robot to perform indoor SLAM,
(10) Autonomously line guided robot to perform indoor SLAM.
For most cases, hardware data is compared with, and corroborated by, model based
simulation data. In short, the thesis uses low-cost self-designed rear-wheel
drive robot to demonstrate many capabilities that are critical in order to reach the
longer-term FAME goal.
Machines operating in an uncertain Environment (FAME), this thesis addresses several
critical modeling, design, control objectives for rear-wheel drive ground vehicles.
Toward this ambitious goal, several critical objectives are addressed. One central objective of the thesis was to show how to build low-cost multi-capability robot platform
that can be used for conducting FAME research.
A TFC-KIT car chassis was augmented to provide a suite of substantive capabilities.
The augmented vehicle (FreeSLAM Robot) costs less than $500 but offers the capability
of commercially available vehicles costing over $2000.
All demonstrations presented involve rear-wheel drive FreeSLAM robot. The following
summarizes the key hardware demonstrations presented and analyzed:
(1)Cruise (v, ) control along a line,
(2) Cruise (v, ) control along a curve,
(3) Planar (x, y) Cartesian Stabilization for rear wheel drive vehicle,
(4) Finish the track with camera pan tilt structure in minimum time,
(5) Finish the track without camera pan tilt structure in minimum time,
(6) Vision based tracking performance with different cruise speed vx,
(7) Vision based tracking performance with different camera fixed look-ahead distance L,
(8) Vision based tracking performance with different delay Td from vision subsystem,
(9) Manually remote controlled robot to perform indoor SLAM,
(10) Autonomously line guided robot to perform indoor SLAM.
For most cases, hardware data is compared with, and corroborated by, model based
simulation data. In short, the thesis uses low-cost self-designed rear-wheel
drive robot to demonstrate many capabilities that are critical in order to reach the
longer-term FAME goal.
ContributorsLu, Xianglong (Author) / Rodriguez, Armando Antonio (Thesis advisor) / Berman, Spring (Committee member) / Artemiadis, Panagiotis (Committee member) / Arizona State University (Publisher)
Created2016
Description
In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems - in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) - whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers - machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers.
We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to efficiently utilize hundreds and potentially thousands of processors, and analyze systems with 100+ dimensional state-space. Furthermore, we extend our algorithms to analyze robust stability over more complicated geometries such as hypercubes and arbitrary convex polytopes. Our algorithms can be readily extended to address a wide variety of problems in control such as Hinfinity synthesis for systems with parametric uncertainty and computing control Lyapunov functions.
We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to efficiently utilize hundreds and potentially thousands of processors, and analyze systems with 100+ dimensional state-space. Furthermore, we extend our algorithms to analyze robust stability over more complicated geometries such as hypercubes and arbitrary convex polytopes. Our algorithms can be readily extended to address a wide variety of problems in control such as Hinfinity synthesis for systems with parametric uncertainty and computing control Lyapunov functions.
ContributorsKamyar, Reza (Author) / Peet, Matthew (Thesis advisor) / Berman, Spring (Committee member) / Rivera, Daniel (Committee member) / Artemiadis, Panagiotis (Committee member) / Fainekos, Georgios (Committee member) / Arizona State University (Publisher)
Created2016