Performance Bounds for the Scenario Approach and an Extension to a Class of Non-convex Programs

We consider the Scenario Convex Program (SCP) for two classes of optimization problems that are not tractable in general: Robust Convex Programs (RCPs) and Chance-Constrained Programs (CCPs). We establish a probabilistic bridge from the optimal value of SCP to the optimal values of RCP and CCP in which the uncertainty takes values in a general, possibly infinite dimensional, metric space. We then extend our results to a certain class of non-convex problems that includes, for example, binary decision variables. In the process, we also settle a measurability issue for a general class of scenario programs, which to date has been addressed by an assumption. Finally, we demonstrate the applicability of our results on a benchmark problem and a problem in fault detection and isolation.Comment: 19 pages, revised versio

Isospectral flows on a class of finite-dimensional Jacobi matrices

We present a new matrix-valued isospectral ordinary differential equation that asymptotically block-diagonalizes $n\times n$ zero-diagonal Jacobi matrices employed as its initial condition. This o.d.e.\ features a right-hand side with a nested commutator of matrices, and structurally resembles the double-bracket o.d.e.\ studied by R.W.\ Brockett in 1991. We prove that its solutions converge asymptotically, that the limit is block-diagonal, and above all, that the limit matrix is defined uniquely as follows: For $n$ even, a block-diagonal matrix containing $2\times 2$ blocks, such that the super-diagonal entries are sorted by strictly increasing absolute value. Furthermore, the off-diagonal entries in these $2\times 2$ blocks have the same sign as the respective entries in the matrix employed as initial condition. For $n$ odd, there is one additional $1\times 1$ block containing a zero that is the top left entry of the limit matrix. The results presented here extend some early work of Kac and van Moerbeke.Comment: 19 pages, 3 figures, conjecture from previous version is added as assertion (iv) of the main theorem including a proof; other major change

From Infinite to Finite Programs: Explicit Error Bounds with Applications to Approximate Dynamic Programming

We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite convex programs in which the performance of the approximation is quantified explicitly. To this end, we adopt the recent developments in two areas of randomized optimization and first order methods, leading to a priori as well as a posterior performance guarantees. We illustrate the generality and implications of our theoretical results in the special case of the long-run average cost and discounted cost optimal control problems for Markov decision processes on Borel spaces. The applicability of the theoretical results is demonstrated through a constrained linear quadratic optimal control problem and a fisheries management problem.Comment: 30 pages, 5 figure

Multidisciplinary analysis of actively controlled large flexible spacecraft

The control of Flexible Structures (COFS) program has supported the development of an analysis capability at the Langley Research Center called the Integrated Multidisciplinary Analysis Tool (IMAT) which provides an efficient data storage and transfer capability among commercial computer codes to aid in the dynamic analysis of actively controlled structures. IMAT is a system of computer programs which transfers Computer-Aided-Design (CAD) configurations, structural finite element models, material property and stress information, structural and rigid-body dynamic model information, and linear system matrices for control law formulation among various commercial applications programs through a common database. Although general in its formulation, IMAT was developed specifically to aid in the evaluation of the structures. A description of the IMAT system and results of an application of the system are given

Structurally adaptive space crane concept for assembling space systems on orbit

Many future human space exploration missions will probably require large vehicles that must be assembled on orbit. Thus, a device that can move, position, and assemble large and massive spacecraft components on orbit becomes essential for these missions. A concept is described for such a device: a space crane concept that uses erectable truss hardware to achieve high-stiffness and low-mass booms and uses articulating truss joints that can be assembled on orbit. The hardware has been tested and shown to have linear load-deflection response and to be structurally predictable. The hardware also permits the crane to be reconfigured into different geometries to satisfy future assembly requirements. A number of articulating and rotary joint concepts have been sized and analyzed, and the results are discussed. Two strategies were proposed to suppress motion-induced vibration: placing viscous dampers in selected truss struts and preshaping motion commands. Preliminary analyses indicate that these techniques have the potential to greatly enhance structural damping

Novel opportunities for sub-meV inelastic X-ray scattering at high-repetition rate self-seeded X-ray free-electron lasers

Inelastic X-ray scattering (IXS) is an important tool for studies of equilibrium dynamics in condensed matter. A new spectrometer recently proposed for ultra-high-resolution IXS (UHRIX) has achieved 0.6~meV and 0.25~nm$^{-1}$ spectral and momentum transfer resolutions, respectively. However, further improvements down to 0.1~meV and 0.02~nm$^{-1}$ are required to close the gap in energy-momentum space between high and low frequency probes. We show that this goal can be achieved by further optimizing the X-ray optics and by increasing the spectral flux of the incident X-ray pulses. UHRIX performs best at energies from 5 to 10 keV, where a combination of self-seeding and undulator tapering at the SASE-2 beamline of the European XFEL promises up to a hundred-fold increase in average spectral flux compared with nominal SASE pulses at saturation, or three orders of magnitude more than possible with storage-ring based radiation sources. Wave-optics propagation shows that about $7\times 10^{12}$~ph/s in a $90$-$\mu$eV bandwidth can be achieved on the sample. This will provide unique new possibilities for dynamics studies by IXS.Comment: 17 pages, 14 figure

Long term isothermal aging and thermal analysis of N-CYCAP polyimides

The N-CYCAP polyimides utilize a (2,2) paracyclophane endcap that polymerizes and does not generate volatile gases during the cure process. These polyimides have both high glass temperatures (390 C) and an onset of decomposition in air of 560 C. Thermal oxidative stability (TOS) weight loss studies show that replacing 25 percent by weight of the paraphenylene diamine in the polymer backbone with metaphenylene diamine improves the weight loss characteristics. N-CYCAP neat resin samples performed better than PMR-II-50 when exposed at 343 and 371 C in air for up to 1000 hours. Preliminary composite studies show that both PMR-II-50 and N-CYCAP have better thermal stability when fabricated on T-40R. Higher isothermal aging temperatures of longer aging times are needed to determine the differences in TOS between composite samples of PMR-II-50 and N-CYCAP polyimides