Asymptotic Disturbance Rejection for Hammerstein Positive Real Systems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57797/1/HarshadHammerPRTCST2003.pd

Nonholonomic Motion Planning as Efficient as Piano Mover's

We present an algorithm for non-holonomic motion planning (or 'parking a car') that is as computationally efficient as a simple approach to solving the famous Piano-mover's problem, where the non-holonomic constraints are ignored. The core of the approach is a graph-discretization of the problem. The graph-discretization is provably accurate in modeling the non-holonomic constraints, and yet is nearly as small as the straightforward regular grid discretization of the Piano-mover's problem into a 3D volume of 2D position plus angular orientation. Where the Piano mover's graph has one vertex and edges to six neighbors each, we have three vertices with a total of ten edges, increasing the graph size by less than a factor of two, and this factor does not depend on spatial or angular resolution. The local edge connections are organized so that they represent globally consistent turn and straight segments. The graph can be used with Dijkstra's algorithm, A*, value iteration or any other graph algorithm. Furthermore, the graph has a structure that lends itself to processing with deterministic massive parallelism. The turn and straight curves divide the configuration space into many parallel groups. We use this to develop a customized 'kernel-style' graph processing method. It results in an N-turn planner that requires no heuristics or load balancing and is as efficient as a simple solution to the Piano mover's problem even in sequential form. In parallel form it is many times faster than the sequential processing of the graph, and can run many times a second on a consumer grade GPU while exploring a configuration space pose grid with very high spatial and angular resolution. We prove approximation quality and computational complexity and demonstrate that it is a flexible, practical, reliable, and efficient component for a production solution.Comment: 34 pages, 37 figures, 9 tables, 4 graphs, 8 insert

Disturbance Rejection Using Self-Tuning ARMARKOV Adaptive Control with Simultaneous Identification

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57807/1/HarshadSimultIDTCST2001.pd

Trions in a periodic potential

The group-theoretical classification of trion states is presented. It is based on considerations of products of irreducible representations of the 2D translation group. For a given BvK period N degeneracy of obtained states is N^2. Trions consist of two identical particles so the symmetrization of states with respect to particles transposition is considered. Completely antisymmetric states can be constructed by introducing antisymmetric spin functions. Two symmetry adapted bases are considered. The third possibility is postponed for the further investigations.Comment: revtex, 5 p., sub. to Physica

State Space and Transfer Function Modeling of Evanescent Waves in Two-Dimensional Acoustics

Abstract With intense current interest in active noise control, it is desirable to develop models of acoustic phenomena that are useful for state-space-based control methodologies. Consequently, this paper extends the one-dimensional modeling of acoustic transfer functions developed in earlier work to the case of two-dimensional acoustics. This extension must therefore account for the phenomenon of evanescent waves, which are non-propagating and thus affect only the near field. While evanescent waves are well understood within the context of wave models, their presence is less apparent in state space-based model modals. This paper thus presents a derivation of state space models for two-dimensional acoustics which are shown to predict the presence of evanescent waves

Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks

Improving women’s diet quality pre-conceptionally and during gestation: effects on birth weight and prevalence of low birth weight; a randomized controlled efficacy trial in India (Mumbai Maternal Nutrition Project)

BACKGROUND: Low birth weight (LBW) is an important public health problem in undernourished populations.OBJECTIVE: We tested whether improving women's dietary micronutrient quality before conception and throughout pregnancy increases birth weight in a high-risk Indian population.DESIGN: The study was a nonblinded, individually randomized controlled trial. The intervention was a daily snack made from green leafy vegetables, fruit, and milk (treatment group) or low-micronutrient vegetables (potato and onion) (control group) from ? 90 d before pregnancy until delivery in addition to the usual diet. Treatment snacks contained 0.69 MJ of energy (controls: 0.37 MJ) and 10-23% of WHO Reference Nutrient Intakes of ?-carotene, riboflavin, folate, vitamin B-12, calcium, and iron (controls: 0-7%). The primary outcome was birth weight.RESULTS: Of 6513 women randomly assigned, 2291 women became pregnant, 1962 women delivered live singleton newborns, and 1360 newborns were measured. In an intention-to-treat analysis, there was no overall increase in birth weight in the treatment group (+26 g; 95% CI: -15, 68 g; P = 0.22). There was an interaction (P &lt; 0.001) between the allocation group and maternal prepregnant body mass index (BMI; in kg/m(2)) [birth-weight effect: -23, +34, and +96 g in lowest (&lt;18.6), middle (18.6-21.8), and highest (&gt;21.8) thirds of BMI, respectively]. In 1094 newborns whose mothers started supplementation ? 90 d before pregnancy (per-protocol analysis), birth weight was higher in the treatment group (+48 g; 95% CI: 1, 96 g; P = 0.046). Again, the effect increased with maternal BMI (-8, +79, and +113 g; P-interaction = 0.001). There were similar results for LBW (intention-to-treat OR: 0.83; 95% CI: 0.66, 1.05; P = 0.10; per-protocol OR = 0.76; 95% CI: 0.59, 0.98; P = 0.03) but no effect on gestational age in either analysis.CONCLUSIONS: A daily snack providing additional green leafy vegetables, fruit, and milk before conception and throughout pregnancy had no overall effect on birth weight. Per-protocol and subgroup analyses indicated a possible increase in birth weight if the mother was supplemented ? 3 mo before conception and was not underweight. This trial was registered at www.controlled-trials.com/isrctn/ as ISRCTN62811278<br/

Adaptive stabilization and disturbance rejection for linear systems and Hammerstein systems.

In this dissertation we present control algorithms for stabilization and asymptotic disturbance rejection for Linear Systems and Hammerstein systems with positive-real linear dynamics. We present the novel idea of Lyapunov wells, which are scalar positive-valued continuously differentiable functions defined on open intervals on the real line. We introduce this concept with applications to plants that have a control input, a state or a parameter constrained to operate within an interval. Next, we consider the problem of adaptive stabilization of second-order minimum phase systems subjected to exogenous plant and measurement disturbances. This case is of particular interest as it has been shown that, in presence of exogenous disturbances several direct adaptive control schemes for minimum phase plants with relative degree 1 exhibit parameter divergence eventually leading to instability. The proof of convergence is based on a variation of Lyapunov's method in which the Lyapunov derivative is shown to be asymptotically nonpositive. Next, The technique of Lyapunov wells and the nonlinear controllers developed for Hammerstein systems are used to design control systems for electromagnetic oscillators which guarantee that the oscillator mass and the electromagnetic plates never make contact. We provide extensive numerical results for each theoretical result presented. The second part of the thesis develops an indirect extension of the ARMARKOV adaptive control algorithm with simultaneous identification. This algorithm requires a model of only the secondary path (control input to performance variable) transfer function which is identified on-line using the time-domain ARMARKOV/Toeplitz identification technique. For a 5-mode acoustic duct model, we present numerical as well as experimental results for single-tone, dual-tone, and broadband disturbance rejection.Ph.D.Aerospace engineeringApplied SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/126434/2/3016951.pd

Effect of a daily snack containing green leafy vegetables on women's fatty acid status: a randomized controlled trial in Mumbai, India

Background and Objectives: There are few data on the fatty acid status of non-pregnant Indian women. Our objective was to investigate the effect of a snack containing green leafy vegetables (GLVs) on women’s erythrocyte long chain polyunsaturated fatty acid status (LCPUFA). Methods and Study Design: Non-pregnant women (n=222) aged 14-35 years from Mumbai slums were randomized to consume a snack containing GLVs, fruit and milk (treatment) or a control snack containing foods of low micronutrient content such as potato and onion, daily under observation. One treatment snack contained a mean (SD) of 54.1 (33.7) mg alpha-linolenic acid (ALA) and one control snack contained 4.1 (3.4) mg ALA. Blood was collected at baseline (0 weeks) and after 12 weeks of supplementation. Erythrocyte fatty acids were analyzed using gas chromatography and expressed as g/100g fatty acids. Plasma malondialdehyde, homocysteine, and erythrocyte superoxide dismutase and glutathione peroxidase were measured. The effect of the treatment on 12 week LCPUFA was assessed using ANCOVA models. Results: Median (IQR) erythrocyte DHA in the treatment group increased from 1.50 (1.11, 2.03) at baseline to 1.86 (1.50, 2.43) (p&lt;0.001) at 12 weeks, and fell in controls from 1.78 (1.37, 2.32) to 1.60 (1.32, 2.04) (p&lt;0.001). The total n-3 fatty acids increased in the treatment group. There was no effect on malondialdehyde and antioxidant enzyme levels. Plasma homocysteine at 0 and 12 weeks was inversely associated with erythrocyte DHA at 12 weeks. Conclusion: Daily consumption of a snack containing GLV improved women’s erythrocyte DHA levels without increasing oxidative stress