Property:Abstract
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D
We describe a method for discrete representation of continuous functions and show how
this may be used for typical computations in nonlinear control desi gn. The method
involves representing functions by their values and finitely many derivatives at discrete
set of points on the domain. We propose a grid structure based on a hierarchy of
rectangular boxes that provides flexibility in placing grid points densely in some regions
and sparsely in the other. The grids possess enough structure to facilitate easy
interpolation schemes based on piecewise polynomials. We illustrate the method using a
simple example where we compute the feedback linearizing output of a system. +
C
Coarse analysis of multiscale systems: diffuser flows, charged particle motion, and connections to averaging theory +
We describe a technique for the efficient computation of the dominant-scale dynamics of a fluid
system when only a high-fidelity simulation is available. Such a technique is desirable when governing equations for the dominant scales are unavailable, when model reduction is impractical, or
when the original high-fidelity computation is expensive. We adopt the coarse analysis framework
proposed by I. G. Kevrekidis (Comm. Math. Sci. 2003), where a computational superstructure is
designed to use short-time, high-fidelity simulations to extract the dominant features for a multi-
scale system. We apply this technique to compute the dominant features of the compressible flow
through a planar diffuser. We apply the proper orthogonal decomposition to classify the dominant
and subdominant scales of diffuser flows. We derive a suitable coarse pro jective Adams-Bashforth
time integration routine and apply it to compute averaged diffuser flows. The results include accu-
rate tracking of the dominant-scale dynamics for a range of parameter values for the computational
superstructure. These results demonstrate that coarse analysis methods are useful for solving fluid
flow problems of a multiscale nature.
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In order to elucidate the behavior of coarse analysis techniques, we make comparisons to averaging
theory. To this end, we derive governing equations for the average motion of charged particles in
a magnetic field in a number of different settings. First, we apply a novel procedure, inspired by WKB theory and Whitham averaging, to average the variational principle. The resulting equations
are equivalent to the guiding center equations for charged particle motion; this marks an instance
where averaging and variational principles commute. Secondly, we apply Lagrangian averaging
techniques, previously applied in fluid mechanics, to derive averaged equations. Making comparisons to the WKB/Whitham-style derivation allows for the necessary closure of the Lagrangian
averaging formulation. We also discuss the Hamiltonian setting and show that averaged Hamiltonian systems may be derivable using concepts from coarse analysis. Finally, we apply a prototypical
coarse analysis procedure to the system of charged particles and generate tra jectories that resemble
guiding center tra jectories. We make connections to perturbation theory to derive guidelines for the
design of coarse analysis techniques and comment on the prototypical coarse analysis application.
L
We describe the interaction of a rigid body and its incompressible fluid environment
with reduced Euler-Lagrange equations on the appropriate Cartesian product manifold. We
propose a modification to the planar form of these equations to accomodate control inputs
consistent with a model for carangiform swimming. Initial Lie algebraic analysis of the
resulting control system suggests its usefulness in predicting efficacious gaits for
piscimimetic robots. +
E
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph qualities for any arbitrary number of nodes and edges and analytically derive the form and properties of such networks. +
N
We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the smallest possible average distance. In contrast, there are many graphs with the same minimum average distance, ignoring their average clustering. The form of these graphs is shown with analytical arguments. Finally, we measure the sensitivity to rewiring of this architecture with respect to the clustering coefficient, and we devise a method to make these networks more robust with respect to vertex removal. +
S
We develop a framework for control protocol syn- thesis for a platoon of autonomous vehicles subject to temporal logic specifications. We describe the desired behavior of the platoon in a set of linear temporal logic formulas, such as collision avoidance, close spacing or comfortability. The problem of decomposing a global specification for the platoon into distributed specification for each pair of adjacent vehicles is hard to solve. We use the invariant specifications to tackle this problem and the decomposition is proved to be scalable.. Based on the specifications in Assumption/Guarantee form, we can construct a two-player game (between the vehicle and its closest leader) locally to automatically synthesize a controller protocol for each vehicle. Simulation example for a distributed vehicles control problem is also shown. +
O
Optimal Control of Non-deterministic Systems for a Computationally Efficient Fragment of Temporal Logic +
We develop a framework for optimal control policy synthesis for non-deterministic transition systems subject to temporal logic specifications. We use a fragment of temporal logic to specify tasks such as safe navigation, response to the environment, persistence, and surveillance. By restricting specifications to this fragment, we avoid a potentially doubly-exponential automaton construction. We compute feasible con- trol policies for non-deterministic transition systems in time polynomial in the size of the system and specification. We also compute optimal control policies for average, minimax (bottleneck), and average cost-per-task-cycle cost functions. We highlight several interesting cases when these can be computed in time polynomial in the size of the system and specification. Additionally, we make connections between computing optimal control policies for an average cost-per-task-cycle cost function and the generalized traveling salesman problem. We give simulation results for motion planning problems. +
A
We develop a method for the control of discrete-time nonlinear systems
subject to temporal logic specifications. Our approach uses a coarse
abstraction of the system and an automaton representing the temporal logic
specification to guide the search for a feasible trajectory. This decomposes
the search for a feasible trajectory into a series of constrained
reachability problems. Thus, one can create controllers for any system for
which techniques exist to compute (approximate) solutions to constrained
reachability problems. Representative techniques include sampling-based
methods for motion planning, reachable set computations for linear systems,
and graph search for finite discrete systems. Our approach avoids the
expensive computation of a discrete abstraction, and its implementation is
amenable to parallel computing. We demonstrate our approach with numerical
experiments on temporal logic motion planning problems with high-dimensional
(10+ states) continuous systems. +
We develop a system for implementing “packet-based” intercellular communication in an engineered bacterial population via conjugation. Our system uses gRNA-based identification markers that allow messages to be addressed to specific strains via Cas9-mediated cleavage of messages sent to the wrong recipient, which we show reduces plasmid transfer by four orders of magnitude. Integrase-mediated editing of the address on the message plasmid allows cells to dynamically update the message’s recipients in vivo. As a proof-of-concept demonstration of our system, we propose a linear path scheme that would propagate a message sequentially through the strains of a population in a defined order. +
C
We develop the study of primitives of human motion, which we
refer to as movemes. The idea is to understand human motion by
decomposing it into a sequence of elementary building blocks that belong
to a known alphabet of dynamical systems. Where do these dynamic
primitives come from in practice? How can we construct an alphabet of
movemes from human data? In this paper we address these issues. We define
conditions under which collections of signals are well-posed according to
a dynamical model class M and thus can generate movemes. Using examples
from human drawing data, we show that the definition of well-posedness
can be applied in practice so to establish if sets of actions, reviewed as
signals in time, can define movemes. +
R
We establish a framework to reason about test campaigns described formally. First, we introduce the notion of a test structure — an object that carries i) the formal specifications of the system under test, and ii) the test objective, which is specified by a test engineer. We build on test structures to define test campaigns and specifications for the tester. Secondly, we use the algebra of assume-guarantee contracts to reason about constructing tester specifications, comparing test struc- tures and test campaigns, and combining and splitting test structures. Using the composition operator, we characterize the conditions on the constituent tester specifications and test objectives for feasibly combin- ing test structures. We illustrate the different applications of the quotient operator to split the test objective, the system into subsystems, or both. Finally, we illustrate test executions corresponding to the combined and split test structures in a discrete autonomous driving example and an aircraft formation-flying example. We anticipate that reasoning over test specifications would aid in generating optimal test campaigns. +
O
We examine optimal Linear Quadratic Gaussian control for a system in which communication between
the sensor (output of the plant) and the controller occurs across a packet-dropping link. We extend the
familiar LQG separation principle to this problem that allows us to solve this problem using a standard
LQR state-feedback design, along with an optimal algorithm for propagating and using the information
across the unreliable link. We present one such optimal algorithm, which consists of a Kalman Filter at
the sensor side of the link, and a switched linear filter at the controller side. Our design does not assume
any statistical model of the packet drop events, and is thus optimal for an arbitrary packet drop pattern.
Further, the solution is appealing from a practical point of view because it can be implemented as a
small modification of an existing LQG control design. +
We examine two special cases of the problem of optimal linear quadratic Gaussian control of a system whose state is being measured by sensors that communicate with the controller over packet-dropping links. We pose the problem as an +
P
We explored the possibility of supplementing an in vitro S30-based Escherichia coli expression system (or âTX-TLâ) with ClpXP, an AAA+ protease pair that selectively degrades tagged proteins, to provide finely-tuned degradation. The mechanism of ClpXP degradation has been extensively studied both in vitro and in vivo. However, it has not been characterized for use in synthetic circuits -- metrics such as toxicity, ATP usage, degradation variation over time, and cellular loading need to be determined. In particular, TX-TL in batch mode is known to be resource limited, and ClpXP is known to require significant amounts of ATP to unfold different protein targets. We find that ClpXPâs protein degradation dynamics is dependent on protein identity, but can be determined experimentally. Degradation follows Michaels- Menten kinetics, and can be fine tuned by ClpX or ClpP concentration. Added purified ClpX is also not toxic to TX-TL reactions. Therefore, ClpXP provides a controllable way to introduce protein degradation and dynamics into synthetic circuits in TX-TL.
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NOTE: This is a technical report for future inclusion in work pending submission, review, and publication. Therefore, this work has not been peer-reviewed and is presented as-is. +
F
We have approached the problem of reverse engineering the flight control mechanism of the fruit fly by studying the dynamics of the responses to a visual stimulus during takeoff. Building upon a prior framework we seek to understand the strategies employed by the animal to stabilize attitude and orientation during these evasive, highly dynamical maneuvers. As a first step, we consider the dynamics from a gray-box perspective: examining lumped forces produced by the insect's legs and wings. The reconstruction of the flight initiation dynamics, based on the unconstrained motion formulation for a rigid body, allows us to assess the fly's responses to a variety of initial conditions induced by its jump. Such assessment permits refinement by using a visual tracking algorithm to extract the kinematic envelope of the wings in order to estimate lift and drag forces, and recording actual leg-joint kinematics and using them to estimate jump forces. In this paper we present the details of our approach in a comprehensive manner including the salient results. +
T
We have developed a mathematical framework to analyze the cooperative control of cell population homeostasis via paradoxical signaling in synthetic contexts. Paradoxical signaling functions through quorum sensing (where cells produce and release a chemical signal as a function of cell density). Precisely, the same quorum sensing signal provides both positive (proliferation) and negative (death) feedback in different signal concentration regimes. As a consequence, the relationship between intercellular quorum sensing signal concentration and net growth rate (cell proliferation minus death rates) can be non-monotonic. This relationship is a condition for robustness to certain cell mutational overgrowths and allows for increased stability in the presence of environmental perturbations. Here, we explore stability and robustness of a conceptualized synthetic circuit. Furthermore, we asses possible design principles that could exist among a subset of paradoxical circuit implementations. This analysis sparks the development a bio-molecular control theory to identify ideal underlying characteristics for paradoxical signaling control systems. +
A
We have developed a new course as well as an undergraduate minor in
Control and Dynamical Systems for teaching design and analysis of
feedback systems to students from diverse fields such as biology,
computer science, and economics as well as all traditional engineering
%disciplines. +
We introduce a MATLAB-based simulation toolbox, called txtlsim, for an Escherichia coli-based Transcription–Translation (TX–TL) system. This toolbox accounts for several cell-free-related phenomena, such as resource loading, consumption and degradation, and in doing so, models the dynamics of TX–TL reactions for the entire duration of solution phase batch-mode experiments. We use a Bayesian parameter inference approach to characterize the reaction rate parameters associated with the core transcription, translation and mRNA degradation mechanics of the toolbox, allowing it to reproduce constitutive mRNA and protein-expression trajectories. We demonstrate the use of this characterized toolbox in a circuit behavior prediction case study for an incoherent feed-forward loop. +
C
We introduce a class of triangulated graphs for algebraic representation
of formations that allows us to specify a mission cost for a group of vehicles.
This representation plus the navigational information allows us to formally
specify and solve tracking problems for groups of vehicles in formations using
an optimization-based approach. The approach is illustrated using a collection
of six underactuated vehicles that track a desired trajectory in formation.<br> +
T
We introduce a theoretical framework for the dynamic sensor coverage
problem for a simple case with multiple discrete time linear dynamical systems
located in different spacial locations. The objective is to keep an appreciable
estimate of the states of the systems at all times by deploying a few mobile sensors.
The sensors are assumed to have a limited range and they implement a Kalman
filter to estimate the states of all the systems. The motion of the sensor is modeled
as a discrete time discrete state Markov chain. Based on some recent results on
the Kalman filtering problem with intermittent observations by Sinopoli et. al., we
derive conditions under which a single sensor fails to solve the coverage problem.
We also give conditions under which we can guarantee that a single sensor is
enough to solve the dynamic coverage problem. +
