Attitude Synchronization of Spacecraft Formation with Optimization and Adaptation of Consensus Penalty Terms

The contribution of this thesis is on the temporal adjustment of the consensus weights, as applied to spacecraft formation control. Such an objective is attained by dynamically enforcing attitude synchronization via coupling terms included in each spacecraft controller. It is assumed that each spacecraft has identical dynamics but with unknown inertia parameters and external disturbances. By augmenting a standard adaptive controller that accounts for the unknown parameters, made feasible via an assumption on parameterization, with adaptation of the consensus weights, one opts to improve spacecraft synchronization. The coupling terms, responsible for enforcing synchronization amongst spacecraft, are weighted dynamically in proportion to the disagreement between the states of the spacecraft. The time adjustment of edge-dependent gains as well as the special cases of node-dependent and agent-independent constant gains are derived using Lyapunov redesign methods. The proposed adaptive control architectures which allow for adaptation of both parameter uncertainties and consensus penalty terms are demonstrated via extensive numerical studies of spacecraft networks with limited connectivity. By considering the sum of deviation-from-the-mean and rotational kinetic energy as appropriate metrics for synchronization and controller performance, the numerical studies also provide insights on the choice of optimal consensus gains

Élaboration d'une plate-forme informatique des systèmes commandés du point de vue d'asservissement en temps réel

Dans ce projet de mémoire, on tente de définir une commande nouvelle d’un système modélisé à paramètres variables. La commande par mode glissant définie dans le plan de phase constitue la base de la transformation afin de trouver la nouvelle commande recherchée. Celle-ci est effectivement optimale en minimisant le temps de la réponse temporelle en plus de s'assurer de la stabilité du système. Utilisant la transformation, il a été possible de prédire les trajectoires dans le plan d’état. De ce cas, une commande glissante en forme explicite est obtenue. Une plate-forme mobile de soudage (PFM) est choisie comme le système étudié pour appliquer ces commandes. Par ailleurs, une plate-forme informatique aux trois niveaux est construite pour faire la transformation et la visualisation d’application des commandes proposées ci-dessus. Mots clés : variables d’état, plan de phase, plan d’état, commande par mode glissante, commande glissante.In this thesis a new control method have been defined to apply in the variable parameters model system. A sliding mode control defined in the phase plane is the basis of the transformation for finding this new desired control. The sliding mode control is an optimal method for both minimizing the response time and ensuring the stability of system. With this transformation, it is possible to predict the trajectories in the state plan. In this case, a sliding control with an explicit form can be obtained in the state plan. A mobile platform of welding (PFM) is chosen as example for applying the sliding mode controls and the sliding control. Furthermore, an IT platform with three levels is built up to do the transformation and visualize the application of those controls mentioned above. Key words : variables states, phase plane, state plan, sliding mode control, sliding control

Improved bounds for the sunflower lemma

A sunflower with $r$ petals is a collection of $r$ sets so that the intersection of each pair is equal to the intersection of all. Erd\H{o}s and Rado proved the sunflower lemma: for any fixed $r$, any family of sets of size $w$, with at least about $w^w$ sets, must contain a sunflower. The famous sunflower conjecture is that the bound on the number of sets can be improved to $c^w$ for some constant $c$. In this paper, we improve the bound to about $(\log w)^w$. In fact, we prove the result for a robust notion of sunflowers, for which the bound we obtain is tight up to lower order terms.Comment: Revised preprint, added sections on applications and rainbow sunflower

Penetration of hydroxyl radicals in the aqueous phase surrounding a cavitation bubble

In the sonochemical degradation of nonvolatile compounds, the free radicals must be delivered into the aqueous solution from the cavitation bubble to initiate reduction–oxidation reactions. The penetration depth in the liquid becomes an important parameter that influences the radical delivery efficiency and eventual treatment performance. However, the transport of radicals in the liquid phase is not well understood yet. In this paper, we focus on the most reactive OH radical and numerically simulate its penetration behavior. This is realized by solving the coupled equations of bubble dynamics, intracavity chemistry, and radical dispersion in the aqueous phase. The results present both the local and global penetration patterns for the OH radicals. By performing simulations over a wide range of acoustic parameters, we find an undesirable phenomenon that the penetration can be adversely suppressed when strengthening the radical production. A mechanistic analysis attributes this to the excessively vigorous recombination reactions associated with high radical concentrations near the bubble interface. In this circumstance, the radicals are massively consumed and converted into molecular species before they can appreciably diffuse away. Our study sheds light on the interplay between radical production inside the bubble and dispersion in the outside liquid. The derived conclusions provide guides for sonochemical applications from a new perspective

Indole-3-acetate induces apoptosis and stimulates phosphorylation of p65NF-κB in 143B and HOS osteosarcoma cells

Purpose: To investigate the effect of indole-3-acetate (IAA) on the proliferation of 143B and HOS osteosarcoma cells, and its mechanism of action.Methods: Indole-3-acetate (IAA)-induced changes in cell proliferation and apoptosis were investigated using 3-(4, 5-dimethylthiazol-2-yl)-2, 5-diphenyltetrazolium bromide (MTT) assay and flow cytometry, respectively. The effects of IAA on expressions of mRNAs for phosphatase and tensin homolog (PTEN), fas ligand (FasL), and fas receptor (FasR) were evaluated using western blot assay.Results: Early apoptosis in 143B cell cultures due to addition of IAA (5 μM) was 34.67 %, relative to 2.82 % in untreated cultures. In HOS cells, IAA caused 39.21 % apoptosis, relative to 3.53 % apoptosis in control. The addition of IAA to the cell cultures significantly enhanced the expressions of mRNAs for PTEN, FasL and FasR, compared to untreated cells (p < 0.05). Western blot analysis showed that IAA caused a significant decrease in the level of IκBα expression in both cell lines (p < 0.05). In 143B and HOS cells, treatment with IAA led to accumulation of higher levels of NF-κB in the nucleus than in the cytosol. The levels of cytosolic NF-κB, and nuclear lamin B1 in IAA-treated cells were lower than the corresponding levels in untreated cells.Conclusion: These results indicate that IAA inhibits proliferation, and induces apoptosis in 143B and HOS cells via activation of NF-κB, and its translocation to the nucleus. Therefore, IAA may be a useful drug target in the treatment of osteosarcoma.Keywords: Indole-3-acetate, Phosphatase, Fas receptor, Translocation, Proliferation, Tumoricidal activit

Optimal Space-Depth Trade-Off of CNOT Circuits in Quantum Logic Synthesis

Due to the decoherence of the state-of-the-art physical implementations of quantum computers, it is essential to parallelize the quantum circuits to reduce their depth. Two decades ago, Moore et al. demonstrated that additional qubits (or ancillae) could be used to design "shallow" parallel circuits for quantum operators. They proved that any $n$-qubit CNOT circuit could be parallelized to $O(\log n)$ depth, with $O(n^2)$ ancillae. However, the near-term quantum technologies can only support limited amount of qubits, making space-depth trade-off a fundamental research subject for quantum-circuit synthesis. In this work, we establish an asymptotically optimal space-depth trade-off for the design of CNOT circuits. We prove that for any $m\geq0$, any $n$-qubit CNOT circuit can be parallelized to $O\left(\max \left\{\log n, \frac{n^{2}}{(n+m)\log (n+m)}\right\} \right)$ depth, with $O(m)$ ancillae. We show that this bound is tight by a counting argument, and further show that even with arbitrary two-qubit quantum gates to approximate CNOT circuits, the depth lower bound still meets our construction, illustrating the robustness of our result. Our work improves upon two previous results, one by Moore et al. for $O(\log n)$-depth quantum synthesis, and one by Patel et al. for $m = 0$: for the former, we reduce the need of ancillae by a factor of $\log^2 n$ by showing that $m=O(n^2/\log^2 n)$ additional qubits suffice to build $O(\log n)$-depth, $O(n^2/\log n)$ size --- which is asymptotically optimal --- CNOT circuits; for the later, we reduce the depth by a factor of $n$ to the asymptotically optimal bound $O(n/\log n)$. Our results can be directly extended to stabilizer circuits using an earlier result by Aaronson et al. In addition, we provide relevant hardness evidences for synthesis optimization of CNOT circuits in term of both size and depth.Comment: 25 pages, 5 figures. Fixed several minor typos and a mistake about CNOT+Rz circui

Determination of Electrical Parameters in Carbonates with Micro-CT, NMR and Gas Displacement Experiments

Understanding the electrical characteristics of carbonate formation and accurately determining the electrical parameters (cementation exponent m and saturation exponent n in Archie equation) are very important for carbonate formations evaluation. However, the study of electrical characteristics faces great challenge because of the variable pore types, the complicated pore structure and the big heterogeneity in carbonates. We selected representative carbonate cores to carry out experiment research based on newly developed technologies in digital core analysis and resistivity test. Three types of cores were selected: the void space is mainly intergranular and intercrystalline; the vugs are developed; the fractures are developed. Firstly, the porosity and permeability of the selected cores have been tested. Then micro-CT with high resolution is used to scan the cores and NMR T2 spectrums of the cores both in water-saturated state and in bound water state are obtained. Finally, the resistivity of the cores in different water saturation is tested by using gas displacement technology. The analysis results of the experimental data show that the intergranular and intercrystalline pore and the fracture both have great influence on R0 while the influence of secondary vug on R0 is slight. Cementation exponent m and saturation exponent n have great difference between different cores and there is no obvious relation between m, n and reservoir parameters (φ or K). However, if we classify the cores based on the pore type, and the values of both m and n have good relationship with bound water saturation