Probabilistic robust control : theory and applications

In this work, the development of a probabilistic approach to robust control is motivated by structural control applications in civil engineering. Often in civil structural applications, a system's performance is specified in terms of its reliability. In addition, the model and input uncertainty for the system may be described most appropriately using probabilistic or "soft" bounds on the model and input sets. The probabilistic robust control methodology contrasts with existing H∞/μ robust control methodologies that do not use probability information for the model and input uncertainty sets, yielding only the guaranteed (i.e., "worst-case") system performance, and no information about the system's probable performance which would be of interest to civil engineers.

The design objective for the probabilistic robust controller is to maximize the reliability of the uncertain structure/controller system for a probabilistically-described uncertain excitation. The robust performance is computed for a set of possible models by weighting the conditional performance probability for a particular model by the probability of that model, then integrating over the set of possible models. This integration is accomplished efficiently using an asymptotic approximation. The probable performance can be optimized numerically over the class of allowable controllers to find the optimal controller. Also, if structural response data becomes available from a controlled structure, its probable performance can easily be updated using Bayes's Theorem to update the probability distribution over the set of possible models. An updated optimal controller can then be produced, if desired, by following the original procedure. Thus, the probabilistic framework integrates system identification and robust control in a natural manner.

The probabilistic robust control methodology is applied to two systems in this thesis. The first is a high-fidelity computer model of a benchmark structural control laboratory experiment. For this application, uncertainty in the input model only is considered. The probabilistic control design minimizes the failure probability of the benchmark system while remaining robust with respect to the input model uncertainty. The performance of an optimal low-order controller compares favorably with higher-order controllers for the same benchmark system which are based on other approaches. The second application is to the Caltech Flexible Structure, which is a light-weight aluminum truss structure actuated by three voice coil actuators. A controller is designed to minimize the failure probability for a nominal model of this system. Furthermore, the method for updating the model-based performance calculation given new response data from the system is illustrated.

Structure-Guided Design and Biophysical Characterization of Novel Anti-HIV Reagents

Despite over 30 years of effort, an HIV-1 vaccine that elicits protective antibodies still does not exist. Recent clinical studies have identified that during natural infection about 20% of the population is capable of mounting a potent and protective antibody response. Closer inspection of these individuals reveal that a subset of these antibodies, recently termed potent VRC01-like (PVL), derive exclusively from a single human germline heavy chain gene. Induced clonal expansion of the B cell encoding this gene is the first step through which PVL antibodies may be elicited. Unfortunately, naturally occurring HIV gp120s fail to bind to this germline, and as a result cannot be used as the initial prime for a vaccine regimen. We have determined the crystal structure of an important germline antibody that is a promising target for vaccine design efforts, and have set out to engineer a more likely candidate using computationally-guided rational design.

In addition to prevention efforts on the side of vaccine design, recently characterized broadly neutralizing anti-HIV antibodies have excellent potential for use in gene therapy and passive immunotherapy. The separation distance between functional Fabs on an antibody is important due to the sparse distribution of envelop spikes on HIV compared to other viruses. We set out to build and characterize novel antibody architectures by incorporating structured linkers into the hinge region of an anti-HIV antibody b12. The goal was to observe whether these linkers increased the arm-span of the IgG dimer. When incorporated, flexible Gly4Ser repeats did not result in detectable extensions of the IgG antigen binding domains, by contrast to linkers including more rigid domains such as β2-microglobulin, Zn-α2-glycoprotein, and tetratricopeptide repeats (TPRs). This study adds an additional set of linkers with varying lengths and rigidities to the available linker repertoire, which may be useful for the modification and construction of antibodies and other fusion proteins.

Part I. Approximate Hartree-Fock wavefunctions one-electron properties and electronic structure of the water molecule. Part II. Perturbation-variational calculation of the nuclear spin-spin isotope coupling constant in HD

Part I

Several approximate Hartree-Fock SCF wavefunctions for the ground electronic state of the water molecule have been obtained using an increasing number of multicenter s, p, and d Slater-type atomic orbitals as basis sets. The predicted charge distribution has been extensively tested at each stage by calculating the electric dipole moment, molecular quadrupole moment, diamagnetic shielding, Hellmann-Feynman forces, and electric field gradients at both the hydrogen and the oxygen nuclei. It was found that a carefully optimized minimal basis set suffices to describe the electronic charge distribution adequately except in the vicinity of the oxygen nucleus. Our calculations indicate, for example, that the correct prediction of the field gradient at this nucleus requires a more flexible linear combination of p-orbitals centered on this nucleus than that in the minimal basis set. Theoretical values for the molecular octopole moment components are also reported.

Part II

The perturbation-variational theory of R. M. Pitzer for nuclear spin-spin coupling constants is applied to the HD molecule. The zero-order molecular orbital is described in terms of a single 1s Slater-type basis function centered on each nucleus. The first-order molecular orbital is expressed in terms of these two functions plus one singular basis function each of the types e^-r/r and e^-r ln r centered on one of the nuclei. The new kinds of molecular integrals were evaluated to high accuracy using numerical and analytical means. The value of the HD spin-spin coupling constant calculated with this near-minimal set of basis functions is J_HD = +96.6 cps. This represents an improvement over the previous calculated value of +120 cps obtained without using the logarithmic basis function but is still considerably off in magnitude compared with the experimental measurement of J_HD = +43 0 ± 0.5 cps.