Control of dynamical systems with temporal logic specifications

This thesis is motivated by safety-critical applications involving autonomous air, ground, and space vehicles carrying out complex tasks in uncertain and adversarial environments. We use temporal logic as a language to formally specify complex tasks and system properties. Temporal logic specifications generalize the classical notions of stability and reachability that are studied in the control and hybrid systems communities. Given a system model and a formal task specification, the goal is to automatically synthesize a control policy for the system that ensures that the system satisfies the specification. This thesis presents novel control policy synthesis algorithms for optimal and robust control of dynamical systems with temporal logic specifications. Furthermore, it introduces algorithms that are efficient and extend to high-dimensional dynamical systems.

The first contribution of this thesis is the generalization of a classical linear temporal logic (LTL) control synthesis approach to optimal and robust control. We show how we can extend automata-based synthesis techniques for discrete abstractions of dynamical systems to create optimal and robust controllers that are guaranteed to satisfy an LTL specification. Such optimal and robust controllers can be computed at little extra computational cost compared to computing a feasible controller.

The second contribution of this thesis addresses the scalability of control synthesis with LTL specifications. A major limitation of the standard automaton-based approach for control with LTL specifications is that the automaton might be doubly-exponential in the size of the LTL specification. We introduce a fragment of LTL for which one can compute feasible control policies in time polynomial in the size of the system and specification. Additionally, we show how to compute optimal control policies for a variety of cost functions, and identify interesting cases when this can be done in polynomial time. These techniques are particularly relevant for online control, as one can guarantee that a feasible solution can be found quickly, and then iteratively improve on the quality as time permits.

The final contribution of this thesis is a set of algorithms for computing feasible trajectories for high-dimensional, nonlinear systems with LTL specifications. These algorithms avoid a potentially computationally-expensive process of computing a discrete abstraction, and instead compute directly on the system's continuous state space. The first method uses an automaton representing the specification to directly encode a series of constrained-reachability subproblems, which can be solved in a modular fashion by using standard techniques. The second method encodes an LTL formula as mixed-integer linear programming constraints on the dynamical system. We demonstrate these approaches with numerical experiments on temporal logic motion planning problems with high-dimensional (10+ states) continuous systems.

Temporal and spacial control of RNA stability in the early embryo of Drosophila melanogaster

Early embryogenesis in metazoa is controlled by maternally synthesized products. Among these products, the mature egg is loaded with transcripts representing approximately two thirds of the genome. A subset of this maternal RNA pool is degraded prior to the transition to zygotic control of development. This transfer of control of development from maternal to zygotic products is referred to as the midblastula transition (or MBT). It is believed that the degradation of maternal transcripts is required to terminate maternal control of development and to allow zygotic control of development to begin. Until now this process of maternal transcript degradation and the subsequent timing of the MBT has been poorly understood. I have demonstrated that in the early embryo there are two independent RNA degradation pathways, either of which is sufficient for transcript elimination. However, only the concerted action of both pathways leads to elimination of transcripts with the correct timing, at the MBT. The first pathway is maternally encoded, is triggered by egg activation, and is targeted to specific classes of mRNAs through cis-acting elements in the 3' untranslated region (UTR}. The second pathway is activated 2 hr after fertilization and functions together with the maternal pathway to ensure that transcripts are degraded by the MBT. In addition, some transcripts fail to degrade at select subcellular locations adding an element of spatial control to RNA degradation. The spatial control of RNA degradation is achieved by protecting, or masking, transcripts from the degradation machinery. The RNA degradation and protection events are regulated by distinct cis-elements in the 3' untranslated region (UTR). These results provide the first systematic dissection of this highly conserved process in development and demonstrate that RNA degradation is a novel mechanism used for both temporal and spatial control of development.

Characterization of detectors and instrument systematics for the SPIDER CMB polarimeter

We know from the CMB and observations of large-scale structure that the universe is extremely flat, homogenous, and isotropic. The current favored mechanism for generating these characteristics is inflation, a theorized period of exponential expansion of the universe that occurred shortly after the Big Bang. Most theories of inflation generically predict a background of stochastic gravitational waves. These gravitational waves should leave their unique imprint on the polarization of the CMB via Thompson scattering. Scalar perturbations of the metric will cause a pattern of polarization with no curl (E-mode). Tensor perturbations (gravitational waves) will cause a unique pattern of polarization on the CMB that includes a curl component (B-mode). A measurement of the ratio of the tensor to scalar perturbations (r) tells us the energy scale of inflation. Recent measurements by the BICEP2 team detect the B-mode spectrum with a tensor-to-scalar ratio of r = 0.2 (+0.05, −0.07). An independent confirmation of this result is the next step towards understanding the inflationary universe.

This thesis describes my work on a balloon-borne polarimeter called SPIDER, which is designed to illuminate the physics of the early universe through measurements of the cosmic microwave background polarization. SPIDER consists of six single-frequency, on-axis refracting telescopes contained in a shared-vacuum liquid-helium cryostat. Its large format arrays of millimeter-wave detectors and tight control of systematics will give it unprecedented sensitivity. This thesis describes how the SPIDER detectors are characterized and calibrated for flight, as well as how the systematics requirements for the SPIDER system are simulated and measured.

Effect of Microstructural Interfaces on the Mechanical Response of Crystalline Metallic Materials

Advances in nano-scale mechanical testing have brought about progress in the understanding of physical phenomena in materials and a measure of control in the fabrication of novel materials. In contrast to bulk materials that display size-invariant mechanical properties, sub-micron metallic samples show a critical dependence on sample size. The strength of nano-scale single crystalline metals is well-described by a power-law function, σαD^-n, where D is a critical sample size and n is a experimentally-fit positive exponent. This relationship is attributed to source-driven plasticity and demonstrates a strengthening as the decreasing sample size begins to limit the size and number of dislocation sources. A full understanding of this size-dependence is complicated by the presence of microstructural features such as interfaces that can compete with the dominant dislocation-based deformation mechanisms. In this thesis, the effects of microstructural features such as grain boundaries and anisotropic crystallinity on nano-scale metals are investigated through uniaxial compression testing. We find that nano-sized Cu covered by a hard coating displays a Bauschinger effect and the emergence of this behavior can be explained through a simple dislocation-based analytic model. Al nano-pillars containing a single vertically-oriented coincident site lattice grain boundary are found to show similar deformation to single-crystalline nano-pillars with slip traces passing through the grain boundary. With increasing tilt angle of the grain boundary from the pillar axis, we observe a transition from dislocation-dominated deformation to grain boundary sliding. Crystallites are observed to shear along the grain boundary and molecular dynamics simulations reveal a mechanism of atomic migration that accommodates boundary sliding. We conclude with an analysis of the effects of inherent crystal anisotropy and alloying on the mechanical behavior of the Mg alloy, AZ31. Through comparison to pure Mg, we show that the size effect dominates the strength of samples below 10 μm, that differences in the size effect between hexagonal slip systems is due to the inherent crystal anisotropy, suggesting that the fundamental mechanism of the size effect in these slip systems is the same.

Lock Acquisition and Sensitivity Analysis of Advanced LIGO Interferometers

Laser interferometer gravitational wave observatory (LIGO) consists of two complex large-scale laser interferometers designed for direct detection of gravitational waves from distant astrophysical sources in the frequency range 10Hz - 5kHz. Direct detection of space-time ripples will support Einstein's general theory of relativity and provide invaluable information and new insight into physics of the Universe.

Initial phase of LIGO started in 2002, and since then data was collected during six science runs. Instrument sensitivity was improving from run to run due to the effort of commissioning team. Initial LIGO has reached designed sensitivity during the last science run, which ended in October 2010.

In parallel with commissioning and data analysis with the initial detector, LIGO group worked on research and development of the next generation detectors. Major instrument upgrade from initial to advanced LIGO started in 2010 and lasted till 2014.

This thesis describes results of commissioning work done at LIGO Livingston site from 2013 until 2015 in parallel with and after the installation of the instrument. This thesis also discusses new techniques and tools developed at the 40m prototype including adaptive filtering, estimation of quantization noise in digital filters and design of isolation kits for ground seismometers.

The first part of this thesis is devoted to the description of methods for bringing interferometer to the linear regime when collection of data becomes possible. States of longitudinal and angular controls of interferometer degrees of freedom during lock acquisition process and in low noise configuration are discussed in details.

Once interferometer is locked and transitioned to low noise regime, instrument produces astrophysics data that should be calibrated to units of meters or strain. The second part of this thesis describes online calibration technique set up in both observatories to monitor the quality of the collected data in real time. Sensitivity analysis was done to understand and eliminate noise sources of the instrument.

Coupling of noise sources to gravitational wave channel can be reduced if robust feedforward and optimal feedback control loops are implemented. The last part of this thesis describes static and adaptive feedforward noise cancellation techniques applied to Advanced LIGO interferometers and tested at the 40m prototype. Applications of optimal time domain feedback control techniques and estimators to aLIGO control loops are also discussed.

Commissioning work is still ongoing at the sites. First science run of advanced LIGO is planned for September 2015 and will last for 3-4 months. This run will be followed by a set of small instrument upgrades that will be installed on a time scale of few months. Second science run will start in spring 2016 and last for about 6 months. Since current sensitivity of advanced LIGO is already more than factor of 3 higher compared to initial detectors and keeps improving on a monthly basis, upcoming science runs have a good chance for the first direct detection of gravitational waves.

Management of Biesboch reservoirs for quality control with special reference to eutrophication

The three Biesbosch Reservoirs are pumped storage reservoirs, fed with rather polluted and highly eutrophic water from the River Meuse. Air injection at the bottom of the reservoirs prevents thermal stratification, which would otherwise result in serious water quality deterioration. Reservoir mixing also serves as an economic algal control measure; mixing over sufficient depth causes light to play the role of limiting factor and this, combined with zooplankton grazing, keeps the biomass of phytoplankton at acceptable levels. Special problems are caused by benthic, geosmin-producing Oscillatoria species growing on the inner embankment. Rooting up the bottom with a harrow is used as the method of control, based on underwater observations by biological staff trained as SCUBA-divers. With regard to pollutant behaviour the three reservoirs act as a series of fully mixed reactors. This enables the application of kinetic models to describe their behaviour and allows the use of a selective intake policy, e.g. for suspended solids with associated contaminants, ammonia and polynuclear aromatic hydrocarbons. A combination of selective intake and self- purification processes - enhanced by the compartmentalisation of the storage volume in three reservoirs - leads to a striking improvement for many water-quality parameters.

Re-estimation of small-scale fishery catches for U.S. flag-associated island areas in the western Pacific: the last 50 years

Nearshore fisheries in the tropical Pacific play an important role, both culturally and as a reliable source of food security, but often remain under-reported in statistics, leading to undervaluation of their importance to communities. We re-estimated nonpelagic catches for Guam and the Commonwealth of the Northern Mariana Islands (CNMI), and summarize previous work for American Samoa for 1950−2002. For all islands combined, catches declined by 77%, contrasting with increasing trends indicated by reported data. For individual island entities, re-estima-tion suggested declines of 86%, 54%, and 79% for Guam, CNMI, and American Samoa, respectively. Except for Guam, reported data primarily represented commercial catches, and hence under-represented contributions by subsistence and recreational fisheries. Guam’s consistent use of creel surveys for data collection resulted in the most reliable reported catches for any of the islands considered. Our re-estimation makes the scale of under-reporting of total catches evident, and provides valuable baselines of likely historic patterns in fisheries catches.

The cost of quinine Cinchona pubescens control on Santa Cruz Island, Galapagos

We analyse the cost of controlling the invasive quinine tree Cinchona pubescens Vahl in the highlands of Santa Cruz Island, Galapagos. Control costs in ten 400 m2 plots formed the basis for estimating the cost of control over the whole island. In the plots, densities were 2100–24,000 stems/ha (stems >150 cm tall) and 55,000–138,000 stems/ha (all size classes combined). Control involved uprooting small plants, and applying of a mix of metsulfuron methyl and picloram to cut stumps or to machete cuts in the bark of larger trees. These methods are presently used by Galapagos National Park field crews to control quinine. Costs (in man hours, herbicide and US$) were related to stem density; the density of stems summed across four height classes was a better predictor of costs than density of any one size class. Regressions (on all size classes combined) formed the basis for predictive models of costs. Costs ranged from $14 to $2225 per ha depending on stem density. The amount of herbicide (active ingredient/ha) that must be applied to high density stands of quinine is higher than typical rates of application in an agricultural setting. The cost of treating all existing plants once across quinine’s known range on Santa Cruz Island (c. 11,000 ha) was estimated at c. US$1.65 million. CDF Contribution Number 1013.

Patterns of scale-dependency and the influence of map resolution on the seascape ecology of reef fish

Detection and perception of ecological relationships between biota and their surrounding habitats is sensitive to analysis scale and resolution of habitat data. We measured strength of univariate linear correlations between reef fish and seascape variables at multiple spatial scales (25 to 800 m). Correlation strength was used to identify the scale that best associates fish to their surrounding habitat. To evaluate the influence of map resolution, seascape variables were calculated based on 4 separate benthic maps produced using 2 levels of spatial and thematic resolution, respectively. Individual seascape variables explained only 25% of the variability in fish distributions. Length of reef edge was correlated with more aspects of the fish assemblage than other features. Area of seagrass and bare sand correlated with distribution of many fish, not just obligate users. No fish variables correlated with habitat diversity. Individual fish species achieved a wider range of correlations than mobility guilds or the entire fish assemblage. Scales of peak correlation were the same for juveniles and adults in a majority of comparisons. Highly mobile species exhibited broader scales of peak correlation than either resident or moderately mobile fish. Use of different input maps changed perception of the strength and even the scale of peak correlations for many comparisons involving hard bottom edge length and area of sand, whereas results were consistent regardless of map type for comparisons involving area of seagrass and habitat diversity.

Experimental investigation of 3D shock / boundary layer interaction control in transonic flows

A novel supersonic wind tunnel setup is proposed to enable the investigation of control on a normal shock wave. Previous experimental arrangements were found to suffer from shock instability. Wind tunnel tests with and without control have confirmed the capability of the new setup to stabilise a shock structure at a target position without changing the nature of the shock wave / boundary layer interaction flow at M∞ = 1.3 and M ∞ = 1.5. Flow visualisation and pressure measurements with the new setup have revealed detailed characteristics of shock wave / boundary layer interactions and a λ-shock structure as well as benefits of control in total drag reduction in the presence of 3D bump control.

Feedback control and the arrow of time

The purpose of this paper is to highlight the central role that the time asymmetry of stability plays in feedback control. We show that this provides a new perspective on the use of doubly-infinite or semi-infinite time axes for signal spaces in control theory. We then focus on the implication of this time asymmetry in modeling uncertainty, regulation and robust control. We point out that modeling uncertainty and the ease of control depend critically on the direction of time. We finally discuss the relationship of this control-based time arrow with the well-known arrows of time in physics. © 2008 IEEE.

Ice storage characteristics of fresh and brined shark fillets

Ice storage characteristics of fresh and brined fillets from fresh shark (Carcharias melanopterus) were studied in and out of contact with ice for more than two weeks. Changes occurring in biochemical constituents, physical qualities and bacterial counts of the fillets are reported. Shelf life of brined fillets out of contact with ice was considerably longer than that of control samples tinder similar conditions. Icing of shark fillets is suggested as a method for the removal of urea on a commercial scale.

On control of drained weights in some fishery products

Canned and frozen prawns are subjected to compulsory pre-shipment inspection, during which compliance of the products with their declared drained weights is verified. The materials used in the processing of these products being biological in origin, the drained weights are susceptible to variation due to a number of factors. Since determination of the drained weights involves destructive and time consuming procedures, application of control chart for drained weights on the processing line is not possible. The present study has shown that gross weights of the products are significantly correlated with their drained weights and since the determination of the former does not have the disadvantages of determination of the latter, the drained weights can be controlled through the application of control chart for the gross weights.

Thickness control of Molecular Beam Epitaxy grown layers at the 0.01-0.1 monolayer level

Electron tunnelling through semiconductor tunnel barriers is exponentially sensitive to the thickness of the barrier layer, and in the most common system, the AlAs tunnel barrier in GaAs, a one monolayer variation in thickness results in a 300% variation in the tunnelling current for a fixed bias voltage. We use this degree of sensitivity to demonstrate that the level of control at 0.06 monolayer can be achieved in the growth by molecular beam epitaxy, and the geometrical variation of layer thickness across a wafer at the 0.01 monolayer level can be detected.

In vivo dynamics of the internal fibrous structure in smooth adhesive pads of insects.

Many insects with smooth adhesive pads can rapidly enlarge their contact area by centripetal pulls on the legs, allowing them to cope with sudden mechanical perturbations such as gusts of wind or raindrops. The short time scale of this reaction excludes any neuromuscular control; it is thus more likely to be caused by mechanical properties of the pad's specialized cuticle. This soft cuticle contains numerous branched fibrils oriented almost perpendicularly to the surface. Assuming a fixed volume of the water-filled cuticle, we hypothesized that pulls could decrease the fibril angle, thereby helping the contact area to expand laterally and longitudinally. Three-dimensional fluorescence microscopy on the cuticle of smooth stick insect pads confirmed that pulls significantly reduced the fibril angle. However, the fibril angle variation appeared insufficient to explain the observed increase in contact area. Direct strain measurements in the contact zone demonstrated that pulls not only expand the cuticle laterally, but also add new contact area at the pad's outer edge.