Property:Abstract
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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.
<p>
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. +
A
We introduce an algorithm for the optimal con- trol of stochastic nonlinear systems subject to temporal logic constraints on their behavior. We directly compute on the state space of the system, avoiding the expensive pre-computation of a discrete abstraction. An automaton that corresponds to the temporal logic specification guides the computation of a control policy that maximizes the probability that the system satisfies the specification. This reduces controller synthesis to solving a sequence of stochastic constrained reachability problems. The solution to each reachability problem corresponds to the solution to a corresponding Hamilton-Jacobi-Bellman (HJB) partial differential equation. To increase the efficiency of our approach, we exploit a class of systems where the HJB equation is linear due to structural assumptions on the noise. The linearity of the PDE allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to satisfy a complex temporal logic specification. +
We introduce an algorithm for the optimal control of stochastic nonlinear systems subject to temporal logic constraints on their behavior. We compute directly on the state space of the system, avoiding the expensive pre-computation of a discrete abstraction. An automaton that corresponds to the temporal logic specification guides the computation of a control policy that maximizes the probability that the system satisfies the specification. This reduces controller synthesis to solving a sequence of stochastic constrained reachability problems. Each individual reachability problem is solved via the Hamilton-Jacobi-Bellman (HJB) partial differential equation of stochastic optimal control theory. To increase the efficiency of our approach, we exploit a class of systems where the HJB equation is linear due to structural assumptions on the noise. The linearity of the partial differential equation allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to conservatively satisfy a complex temporal logic specification. +
D
We investigate nonlinear dynamical models for self- sustained
oscillations in the flow past a rectangular cavity. The models are
based on the method of Proper Orthogonal Decomposition (POD) and
Galerkin projection, and we introduce an inner product and formulation
of the equations of motion which enables one to use vector-valued POD
modes for compressible flows. We obtain models between 3 and 20
states, which accurately describe both the short-time and long-time
dynamics. This is a substantial improvement over previous models
based on scalar-valued POD modes,which capture the dynamics for short
time, but deviate for long time. +
M
We present a Python-based software package to automatically obtain phenomenological models of input-controlled synthetic biological circuits that guide the design using chemical reaction-level descriptive models. From the parts and mechanism description of a synthetic biological circuit, it is easy to obtain a chemical reaction model of the circuit under the assumptions of mass-action kinetics using various existing tools. However, using these models to guide design decisions during an experiment is difficult due to a large number of reaction rate parameters and species in the model. Hence, phenomenological models are often developed that describe the effective relationships among the circuit inputs, outputs, and only the key states and parameters. In this paper, we present an algorithm to obtain these phenomenological models in an automated manner using a Python package for circuits with inputs that control the desired outputs. This model reduction approach combines the common assumptions of time-scale separation, conservation laws, and species’ abundance to obtain the reduced models that can be used for design of synthetic biological circuits. We consider an example of a simple gene expression circuit and another example of a layered genetic feedback control circuit to demonstrate the use of the model reduction procedure. +
R
We present a counterexample-guided inductive synthesis approach to controller synthesis for cyber-physical systems subject to signal temporal logic (STL) specifications, operating in potentially adversarial nondeterministic environments. We encode STL specifications as mixed integer-linear constraints on the variables of a discrete-time model of the system and environment dynamics, and solve a series of optimization problems to yield a satisfying control sequence. We demonstrate how the scheme can be used in a receding horizon fashion to fulfill properties over unbounded horizons, and present experimental results for reactive controller synthesis for case studies in building climate control and autonomous driving. +
B
We present a detailed dynamical model of the behavior of
transcription-translation circuits in vitro that makes explicit the roles
played by essential molecular resources. A set of simple two-gene test
circuits operating in a cell-free biochemical âbreadboardâ validate this
model and highlight the consequences of limited resource availability. In
particular, we are able to confirm the existence of biomolecular âcrosstalkâ
and isolate its individual sources. The implications of crosstalk for
biomolecular circuit design and function are discussed. +
M
We present a framework for applying the method of Proper Orthogonal Decomposition
(POD) and Galerkin projection to compressible fluids. For incompressible flows,
only the kinematic variables are important, and the techniques are well known. In
a compressible flow, both the kinematic and thermodynamic variables are dynamically
important, and must be included in the configuration space. We introduce
an energy-based inner product which may be used to obtain POD modes for this
configuration space. We then obtain an approximate version of the Navier-Stokes
equations, valid for cold flows at moderate Mach number, and project these equations
onto a POD basis. The resulting equations of motion are quadratic, and are
much simpler than projections of the full compressible Navier-Stokes equations. +
T
We present a framework for merging unit tests for autonomous systems. Typically, it is intractable to test an autonomous system for every scenario in its operating environment. The question of whether it is possible to design a single test for multiple requirements of the system motivates this work. First, we formally define three attributes of a test: a test specification that characterizes behaviors observed in a test execution, a test environment, and a test policy. Using the merge operator from contract-based design theory, we provide a formalism to construct a merged test specification from two unit test specifications. Temporal constraints on the merged test specification guarantee that non-trivial satisfaction of both unit test specifications is necessary for a successful merged test execution. We assume that the test environment remains the same across the unit tests and the merged test. Given a test specification and a test environment, we synthesize a test policy filter using a receding horizon approach, and use the test policy filter to guide a search procedure (e.g. Monte-Carlo Tree Search) to find a test policy that is guaranteed to satisfy the test specification. This search procedure finds a test policy that maximizes a pre-defined robustness metric for the test while the filter guarantees a test policy for satisfying the test specification. We prove that our algorithm is sound. Furthermore, the receding horizon approach to synthesizing the filter ensures that our algorithm is scalable. Finally, we show that merging unit tests is impactful for designing efficient test campaigns to achieve similar levels of coverage in fewer test executions. We illustrate our framework on two self-driving examples in a discrete-state setting. +
C
Characterization of Integrase and Excisionase Activity in Cell-free Protein Expression System Using a Modeling and Analysis Pipeline +
We present a full-stack modeling, analysis, and parameter identification pipeline to guide the modeling and design of biological systems starting from specifications to circuit implementations and parameterizations. We demonstrate this pipeline by characterizing the integrase and excisionase activity in cell-free protein expression system. We build on existing Python tools — BioCRNpyler, AutoReduce, and Bioscrape — to create this pipeline. For enzyme-mediated DNA recombination in cell-free system, we create detailed chemical reaction network models from simple high-level descriptions of the biological circuits and their context using BioCRNpyler. We use Bioscrape to show that the output of the detailed model is sensitive to many parameters. However, parameter identification is infeasible for this high-dimensional model, hence, we use AutoReduce to automatically obtain reduced models that have fewer parameters. This results in a hierarchy of reduced models under different assumptions to finally arrive at a minimal ODE model for each circuit. Then, we run sensitivity analysis-guided Bayesian inference using Bioscrape for each circuit to identify the model parameters. This process allows us to quantify integrase and excisionase activity in cell extracts enabling complex-circuit designs that depend on accurate control over protein expression levels through DNA recombination. The automated pipeline presented in this paper opens up a new approach to complex circuit design, modeling, reduction, and parameterization. +
T
We present a general framework for the control of Lagrangian systems with as many
inputs as degrees of freedom. Relying on the geometry of mechanical systems on manifolds,
we propose a design algorithm for the tracking problem. The notion of error function and
transport map lead to a proper definition of configuration and velocity error. These are
the crucial ingredients in designing a proportional derivative feedback and feedforward
controller. The proposed approach includes as special cases a variety of results on
control of manipulators, pointing devices and autonomous vehicles. Our design provides
particular insight into both aerospace and underwater applications where the configuration
manifold is a Lie group. +
