A matlab-based toolbox for the simulation and design of L1 adaptive controllers

This thesis introduces the L1 Adaptive Control Toolbox, a set of tools implemented in Matlab that aid in the design process of an L1 adaptive controller and enable the user to construct simulations of the closed-loop system to verify its performance. Following a brief review of the existing theory on L1 adaptive controllers, the interface of the toolbox is presented, including a description of the functions accessible to the user. Two novel algorithms for determining the required sampling period of a piecewise constant adaptive law are presented and their implementation in the toolbox is discussed. The detailed description of the structure of the toolbox is provided as well as a discussion of the implementation of the creation of simulations. Finally, the graphical user interface is presented and described in detail, including the graphical design tools provided for the development of the filter C(s). The thesis closes with suggestions for further improvement of the toolbox.

Approximation Algorithms for Network Design and Orienteering

This thesis presents approximation algorithms for some NP-Hard combinatorial optimization problems on graphs and networks; in particular, we study problems related to Network Design. Under the widely-believed complexity-theoretic assumption that P is not equal to NP, there are no efficient (i.e., polynomial-time) algorithms that solve these problems exactly. Hence, if one desires efficient algorithms for such problems, it is necessary to consider approximate solutions: An approximation algorithm for an NP-Hard problem is a polynomial time algorithm which, for any instance of the problem, finds a solution whose value is guaranteed to be within a multiplicative factor of the value of an optimal solution to that instance. We attempt to design algorithms for which this factor, referred to as the approximation ratio of the algorithm, is as small as possible. The field of Network Design comprises a large class of problems that deal with constructing networks of low cost and/or high capacity, routing data through existing networks, and many related issues. In this thesis, we focus chiefly on designing fault-tolerant networks. Two vertices u,v in a network are said to be k-edge-connected if deleting any set of k − 1 edges leaves u and v connected; similarly, they are k-vertex connected if deleting any set of k − 1 other vertices or edges leaves u and v connected. We focus on building networks that are highly connected, meaning that even if a small number of edges and nodes fail, the remaining nodes will still be able to communicate. A brief description of some of our results is given below. We study the problem of building 2-vertex-connected networks that are large and have low cost. Given an n-node graph with costs on its edges and any integer k, we give an O(log n log k) approximation for the problem of finding a minimum-cost 2-vertex-connected subgraph containing at least k nodes. We also give an algorithm of similar approximation ratio for maximizing the number of nodes in a 2-vertex-connected subgraph subject to a budget constraint on the total cost of its edges. Our algorithms are based on a pruning process that, given a 2-vertex-connected graph, finds a 2-vertex-connected subgraph of any desired size and of density comparable to the input graph, where the density of a graph is the ratio of its cost to the number of vertices it contains. This pruning algorithm is simple and efficient, and is likely to find additional applications. Recent breakthroughs on vertex-connectivity have made use of algorithms for element-connectivity problems. We develop an algorithm that, given a graph with some vertices marked as terminals, significantly simplifies the graph while preserving the pairwise element-connectivity of all terminals; in fact, the resulting graph is bipartite. We believe that our simplification/reduction algorithm will be a useful tool in many settings. We illustrate its applicability by giving algorithms to find many trees that each span a given terminal set, while being disjoint on edges and non-terminal vertices; such problems have applications in VLSI design and other areas. We also use this reduction algorithm to analyze simple algorithms for single-sink network design problems with high vertex-connectivity requirements; we give an O(k log n)-approximation for the problem of k-connecting a given set of terminals to a common sink. We study similar problems in which different types of links, of varying capacities and costs, can be used to connect nodes; assuming there are economies of scale, we give algorithms to construct low-cost networks with sufficient capacity or bandwidth to simultaneously support flow from each terminal to the common sink along many vertex-disjoint paths. We further investigate capacitated network design, where edges may have arbitrary costs and capacities. Given a connectivity requirement R_uv for each pair of vertices u,v, the goal is to find a low-cost network which, for each uv, can support a flow of R_uv units of traffic between u and v. We study several special cases of this problem, giving both algorithmic and hardness results. In addition to Network Design, we consider certain Traveling Salesperson-like problems, where the goal is to find short walks that visit many distinct vertices. We give a (2 + epsilon)-approximation for Orienteering in undirected graphs, achieving the best known approximation ratio, and the first approximation algorithm for Orienteering in directed graphs. We also give improved algorithms for Orienteering with time windows, in which vertices must be visited between specified release times and deadlines, and other related problems. These problems are motivated by applications in the fields of vehicle routing, delivery and transportation of goods, and robot path planning.

Design of unique composites based on aromatic thermosetting copolyesters

Aromatic thermosetting copolyester (ATSP) has promise in high-temperature applications. It can be employed as a bulk polymer, as a coating and as a matrix for carbon fiber composites (ATSP/C composites). This work focuses on the applications of high performance ATSP/C composites. The morphology of the ATSP matrix in the presence of carbon fiber was studied. The effect of liquid crystalline character of starting oligomers used to prepare ATSP on the final crystal structure of the ATSP/C composite was evaluated. Matrices obtained by crosslinking of both liquid crystalline oligomers (ATSP2) and non-liquid crystalline oligomers (ATSP1) tend to crystallize in presence of carbon fibers. The crystallite size of ATSP2 is 4 times that of ATSP1. Composites made from ATSP2 yield tougher matrices compared to those made from ATSP1. Thus toughened matrices could be achieved without incorporating any additives by just changing the morphology of the final polymer. The flammability characteristics of ATSP were also studied. The limiting oxygen index (LOI) of bulk ATSP was found to be 40% whereas that of ATSP/C composites is estimated to be 85%. Thus, ATSP shows potential to be used as a flame resistant material, and also as an aerospace reentry shield. Mechanical properties of the ATSP/C composite were characterized. ATSP was observed to bond strongly with reinforcing carbon fibers. The tensile strength, modulus and shear modulus were comparable to those of conventionally used high temperature epoxy resins. ATSP shows a unique capability for healing of interlaminar cracks on application of heat and pressure, via the Interchain Transesterification Reaction (ITR). ITR can also be used for reduction in void volume and healing of microcracks. Thus, ATSP resin systems provide a unique intrinsic repair mechanism compared to any other thermosetting systems in use today. Preliminary studies on measurement of residual stresses for ATSP/C composites indicate that the stresses induced are much lower than that in epoxy/C composites. Thermal fatigue testing suggests that ATSP shows better resistance to microcracking compared to epoxy resins.