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.

Temporal Control of Ion Channel Activation

Ion channels are a large class of integral membrane proteins that allow for the diffusion of ions across a cellular membrane and are found in all forms of life. Pentameric ligand-gated ion channels (pLGICs) comprise a large family of proteins that include the nicotinic acetylcholine receptor (nAChR) and the γ-aminobutyric acid (GABA) receptor. These ion channels are responsible for the fast synaptic transmission that occurs in humans and as a result are of fundamental biological importance. pLGICs bind ligands (neurotransmitters), and upon ligand-binding undergo activation. The activation event causes an ion channel to enter a new physical state that is able to conduct ions. Ion channels allow for the flux of ions across the membrane through a pore that is formed upon ion channel activation. For pLGICs to function properly both ligand-binding and ion channel activation must occur. The ligand-binding event has been studied extensively over the past few decades, and a detailed mechanism of binding has emerged. During activation the ion channel must undergo structural rearrangements that allow the protein to enter a conformation in which ions can flow through. Despite this great and ubiquitous importance, a fundamental understanding of the ion channel activation mechanism and kinetics, as well as concomitant structural arrangements, remains elusive.

This dissertation describes efforts that have been made to temporally control the activation of ligand-gated ion channels. Temporal control of ion channel activation provides a means by which to activate ion channels when desired. The majority of this work examines the use of light to activate ion channels. Several photocages were examined in this thesis; photocages are molecules that release a ligand under irradiation, and, for the work described here, the released ligand then activates the ion channel. First, a new water-soluble photoacid was developed for the activation of proton-sensitive ion channels. Activation of acid-sensing ion channels, ASIC2a and GLIC, was observed only upon irradiation. Next, a variety of Ru²⁺ photocages were also developed for the release of amine ligands. The Ru²⁺ systems interacted in a deleterious manner with a representative subset of biologically essential ion channels. The rapid mixing of ion channels with agonist was also examined. A detection system was built to monitor ion channels activation in the rapid mixing experiments. I have shown that liposomes, and functionally-reconstituted ELIC, are not destroyed during the mixing process. The work presented here provides the means to deliver agonist to ligand-gated ion channels in a controlled fashion.