Autonomous Trajectory Planning by Convex Optimization

The objective of this dissertation is to use second-order cone programming (SOCP) for autonomous trajectory planning of optimal control problems arisen from aerospace applications. Rendezvous and proximity operations (RPO) of spacecraft in any general orbit include various constraints on acquisition of docking axis point, approach corridor, plume impingement inhibition, relative velocity, and rate of change of thrust. By a lossless relaxation technique, this highly constrained RPO problem (non-convex) is transformed into a relaxed problem the solution of which is proven to be the same as that of the original problem. Then a novel successive approximation method, forming a sequence of subproblems with linear and time-varying dynamics, is applied to solve the relaxed problem. Each subproblem is a SOCP problem which can be solved by state-of-the-art primal-dual interior point method. Constraints on collision avoidance, or more generally concave inequality state constraints, from any aerospace application also make a problem non-convex. A successive linearization method is employed to linearize the concave inequality constraints. It is proven that the successive solutions from this method globally converge to the solution of the original problem and the converged solution has no conservativeness. Further non-convex constraints include nonlinear terminal constraints which are handled by first approximated with first-order expansions, and then compensated with second-order corrections to improve the robustness of the approach. The effectiveness of the methodology proposed in this dissertation is supported by various applications in highly constrained RPO, finite-thrust orbital transfers, and optimal launch ascent

DEVELOPMENT OF Liriodendron EST-SSR MARKERS AND GENETIC COMPOSITION OF TWO Liriodendron tulipifera L. ORCHARDS

Liriodendron tulipifera L., commonly known as yellow-poplar, is a fast-growing hardwood tree species with great ecological and economic value and is native to eastern North America. Liriodendron occupies an important phylogenetic position as a basal angiosperm and has been used in studies of the evolution of flowering plants. Genomic resources, such as Expressed Sequence Taq (EST) databases and Bacterial Artificial Chromosome (BAC) libraries, have been developed for this species. However, no genetic map is available for Liriodendron, and very few molecular markers have been developed. In this study, a total of 119 informative genomic SSR markers suitable were identified for genetic linkage map construction with an F1 progeny from #UT108A × #UT23 cross, that have been developed. The full-sibship of 213 seedlings were validated. These informative SSR markers and full-sib seedlings are essential in construction of linkage maps. Linkage map will enable molecular breeding and quantitative trait locus (QTL) mapping, and provide framework for sequencing the Liriodendron genome. In addition we characterized 20 EST-SSR markers with 174 trees from two yellow-poplar seed orchards (residing in Knoxville, Tennesse, and Clemson, South Carolina, respectively), and the US National Arboretum, and provided a first look at the genetic diversity and allele richness among selections of this unique native species. Analysis revealed only one locus significantly deviating from Hardy-Weinberg proportions in the Clemson population, and 10 loci in Knoxville population (p\u3e0.05). In addition, the Clemson orchard exhibited higher values of observed and effective number of alleles, observed heterozygosity, and Nei\u27s expected heterozygosity than the Knoxville orchard, revealing larger genetic diversity in the Clemson seed orchard

Sharp estimates on minimum travelling wave speed of reaction diffusion systems modelling autocatalysis

This article studies propagating wave fronts in an isothermal chemical reaction A + 2B - \u3e 3B involving two chemical species, a reactant A and an autocatalyst B, whose diffusion coefficients, D-A and D-B, are unequal due to different molecular weights and/or sizes. Explicit bounds v(*) and v* that depend on D-B/D-A are derived such that there is a unique travelling wave of every speed v \u3e = v* and there does not exist any travelling wave of speed v \u3c v*. New to the literature, it is shown that v(*) proportional to v* proportional to D-B/D-A when D-B = v(min). Estimates on v(min) significantly improve those of early works. The framework is built upon general isothermal autocatalytic chemical reactions A + nB - \u3e (n + 1)B of arbitrary order n \u3e = 1

Mass conserved Allen-Cahn equation and volume preserving mean curvature flow

We consider a mass conserved Allen-Cahn equation u_t=\Delta u+ \e^{-2} (f(u)-\e\lambda(t)) in a bounded domain with no flux boundary condition, where \e\lambda(t) is the average of $f(u(\cdot,t))$ and $-f$ is the derivative of a double equal well potential. Given a smooth hypersurface $\gamma_0$ contained in the domain, we show that the solution u^\e with appropriate initial data approaches, as \e\searrow0, to a limit which takes only two values, with the jump occurring at the hypersurface obtained from the volume preserving mean curvature flow starting from $\gamma_0$