Matching Items (8)

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An Assessment of the Performance of Machine Learning Techniques When Applied to Trajectory Optimization

Description

Prior research has confirmed that supervised learning is an effective alternative to computationally costly numerical analysis. Motivated by NASA's use of abort scenario matrices to aid in mission operations and planning, this paper applies supervised learning to trajectory optimization in

Prior research has confirmed that supervised learning is an effective alternative to computationally costly numerical analysis. Motivated by NASA's use of abort scenario matrices to aid in mission operations and planning, this paper applies supervised learning to trajectory optimization in an effort to assess the accuracy of a less time-consuming method of producing the magnitude of delta-v vectors required to abort from various points along a Near Rectilinear Halo Orbit. Although the utility of the study is limited, the accuracy of the delta-v predictions made by a Gaussian regression model is fairly accurate after a relatively swift computation time, paving the way for more concentrated studies of this nature in the future.

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Date Created
2018-05

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A Space Elevator to Mars: Calculating Space Flight Trajectories

Description

Human habitation of other planets requires both cost-effective transportation and low time-of-flight for human passengers and critical supplies. The current methods for interplanetary orbital transfers, such as the Hohmann transfer, require either expensive, high fuel maneuvers or extended space travel.

Human habitation of other planets requires both cost-effective transportation and low time-of-flight for human passengers and critical supplies. The current methods for interplanetary orbital transfers, such as the Hohmann transfer, require either expensive, high fuel maneuvers or extended space travel. However, by utilizing the high velocities of a super-geosynchronous space elevator, spacecraft released from an apex anchor could achieve interplanetary transfers with minimal Delta V fuel and time of flight requirements. By using Lambert’s Problem and Free Release propagation to determine the minimal fuel transfer from a terrestrial space elevator to Mars under a variety of initial conditions and time-of-flight constraints, this paper demonstrates that the use of a space elevator release can address both needs by dramatically reducing the time-of-flight and the fuel budget.

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Date Created
2020-05

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Parallel optimization of polynomials for large-scale problems in stability and control

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

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.

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Date Created
2016

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A convex approach for stability analysis of partial differential equations

Description

A computational framework based on convex optimization is presented for stability analysis of systems described by Partial Differential Equations (PDEs). Specifically, two forms of linear PDEs with spatially distributed polynomial coefficients are considered.

The first class includes linear coupled PDEs

A computational framework based on convex optimization is presented for stability analysis of systems described by Partial Differential Equations (PDEs). Specifically, two forms of linear PDEs with spatially distributed polynomial coefficients are considered.

The first class includes linear coupled PDEs with one spatial variable. Parabolic, elliptic or hyperbolic PDEs with Dirichlet, Neumann, Robin or mixed boundary conditions can be reformulated in order to be used by the framework. As an example, the reformulation is presented for systems governed by Schr¨odinger equation, parabolic type, relativistic heat conduction PDE and acoustic wave equation, hyperbolic types. The second form of PDEs of interest are scalar-valued with two spatial variables. An extra spatial variable allows consideration of problems such as local stability of fluid flows in channels and dynamics of population over two dimensional domains.

The approach does not involve discretization and is based on using Sum-of-Squares (SOS) polynomials and positive semi-definite matrices to parameterize operators which are positive on function spaces. Applying the parameterization to construct Lyapunov functionals with negative derivatives allows to express stability conditions as a set of LinearMatrix Inequalities (LMIs). The MATLAB package SOSTOOLS was used to construct the LMIs. The resultant LMIs then can be solved using existent Semi-Definite Programming (SDP) solvers such as SeDuMi or MOSEK. Moreover, the proposed approach allows to calculate bounds on the rate of decay of the solution norm.

The methodology is tested using several numerical examples and compared with the results obtained from simulation using standard methods of numerical discretization and analytic solutions.

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Date Created
2016

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Implementation and Comparison of H∞ Observers for Time-Delay Systems

Description

In this thesis, different H∞ observers for time-delay systems are implemented and

their performances are compared. Equations that can be used to calculate observer gains are mentioned. Different methods that can be used to implement observers for time-delay systems are illustrated.

In this thesis, different H∞ observers for time-delay systems are implemented and

their performances are compared. Equations that can be used to calculate observer gains are mentioned. Different methods that can be used to implement observers for time-delay systems are illustrated. Various stable and unstable systems are used and H∞ bounds are calculated using these observer designing methods. Delays are assumed to be known constants for all systems. H∞ gains are calculated numerically using disturbance signals and performances of observers are compared.

The primary goal of this thesis is to implement the observer for Time Delay Systems designed using SOS and compare its performance with existing H∞ optimal observers. These observers are more general than other observers for time-delay systems as they make corrections to the delayed state as well along with the present state. The observer dynamics can be represented by an ODE coupled with a PDE. Results shown in this thesis show that this type of observers performs better than other H∞ observers. Sub-optimal observer-based state feedback system is also generated and simulated using the SOS observer. The simulation results show that the closed loop system converges very quickly, and the observer can be used to design full state-feedback closed loop system.

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Agent

Created

Date Created
2018

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Controllability and Stabilization of Kolmogorov Forward Equations for Robotic Swarms

Description

Numerous works have addressed the control of multi-robot systems for coverage, mapping, navigation, and task allocation problems. In addition to classical microscopic approaches to multi-robot problems, which model the actions and decisions of individual robots, lately, there has been a

Numerous works have addressed the control of multi-robot systems for coverage, mapping, navigation, and task allocation problems. In addition to classical microscopic approaches to multi-robot problems, which model the actions and decisions of individual robots, lately, there has been a focus on macroscopic or Eulerian approaches. In these approaches, the population of robots is represented as a continuum that evolves according to a mean-field model, which is directly designed such that the corresponding robot control policies produce target collective behaviours.

This dissertation presents a control-theoretic analysis of three types of mean-field models proposed in the literature for modelling and control of large-scale multi-agent systems, including robotic swarms. These mean-field models are Kolmogorov forward equations of stochastic processes, and their analysis is motivated by the fact that as the number of agents tends to infinity, the empirical measure associated with the agents converges to the solution of these models. Hence, the problem of transporting a swarm of agents from one distribution to another can be posed as a control problem for the forward equation of the process that determines the time evolution of the swarm density.

First, this thesis considers the case in which the agents' states evolve on a finite state space according to a continuous-time Markov chain (CTMC), and the forward equation is an ordinary differential equation (ODE). Defining the agents' task transition rates as the control parameters, the finite-time controllability, asymptotic controllability, and stabilization of the forward equation are investigated. Second, the controllability and stabilization problem for systems of advection-diffusion-reaction partial differential equations (PDEs) is studied in the case where the control parameters include the agents' velocity as well as transition rates. Third, this thesis considers a controllability and optimal control problem for the forward equation in the more general case where the agent dynamics are given by a nonlinear discrete-time control system. Beyond these theoretical results, this thesis also considers numerical optimal transport for control-affine systems. It is shown that finite-volume approximations of the associated PDEs lead to well-posed transport problems on graphs as long as the control system is controllable everywhere.

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Agent

Created

Date Created
2019

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Self-Organization of Multi-Agent Systems Using Markov Chain Models

Description

The problem of modeling and controlling the distribution of a multi-agent system has recently evolved into an interdisciplinary effort. When the agent population is very large, i.e., at least on the order of hundreds of agents, it is important that

The problem of modeling and controlling the distribution of a multi-agent system has recently evolved into an interdisciplinary effort. When the agent population is very large, i.e., at least on the order of hundreds of agents, it is important that techniques for analyzing and controlling the system scale well with the number of agents. One scalable approach to characterizing the behavior of a multi-agent system is possible when the agents' states evolve over time according to a Markov process. In this case, the density of agents over space and time is governed by a set of difference or differential equations known as a {\it mean-field model}, whose parameters determine the stochastic control policies of the individual agents. These models often have the advantage of being easier to analyze than the individual agent dynamics. Mean-field models have been used to describe the behavior of chemical reaction networks, biological collectives such as social insect colonies, and more recently, swarms of robots that, like natural swarms, consist of hundreds or thousands of agents that are individually limited in capability but can coordinate to achieve a particular collective goal.

This dissertation presents a control-theoretic analysis of mean-field models for which the agent dynamics are governed by either a continuous-time Markov chain on an arbitrary state space, or a discrete-time Markov chain on a continuous state space. Three main problems are investigated. First, the problem of stabilization is addressed, that is, the design of transition probabilities/rates of the Markov process (the agent control parameters) that make a target distribution, satisfying certain conditions, invariant. Such a control approach could be used to achieve desired multi-agent distributions for spatial coverage and task allocation. However, the convergence of the multi-agent distribution to the designed equilibrium does not imply the convergence of the individual agents to fixed states. To prevent the agents from continuing to transition between states once the target distribution is reached, and thus potentially waste energy, the second problem addressed within this dissertation is the construction of feedback control laws that prevent agents from transitioning once the equilibrium distribution is reached. The third problem addressed is the computation of optimized transition probabilities/rates that maximize the speed at which the system converges to the target distribution.

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Agent

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Date Created
2020

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Numerical Modeling and Stress Analysis of Space Elevator Tethers

Description

Two of the most fundamental barriers to the exploration of the solar system are the cost of transporting material to space and the time it takes to get to destinations beyond Earth’s sphere of influence. Space elevators can solve this

Two of the most fundamental barriers to the exploration of the solar system are the cost of transporting material to space and the time it takes to get to destinations beyond Earth’s sphere of influence. Space elevators can solve this problem by enabling extremely fast and propellant free transit to nearly any destination in the solar system. A space elevator is a structure that consists of an anchor on the Earth’s surface, a tether connected from the surface to a point well above geostationary orbit, and an apex counterweight anchor. Since the entire structure rotates at the same rate as the Earth regardless of altitude, gravity is the dominant force on structures below GEO while centripetal force is dominant above, allowing climber vehicles to accelerate from GEO along the tether and launch off from the apex with large velocities. The outcome of this project is the development of a MATLAB script that can design and analyze a space elevator tether and climber vehicle. The elevator itself is designed to require the minimum amount of material necessary to support a given climber mass based on provided material properties, while the climber is simulated separately. The climber and tether models are then combined to determine how the force applied by the climber vehicle changes the stress distribution inside the tether.

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Agent

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Date Created
2022-05