Property:Abstract
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H
Feedback regulation is pervasive in biology at both the organismal and cellular level. In this article, we explore the properties of a particular biomolecular feedback mechanism implemented using the sequestration binding of two molecules. Our work develops an analytic framework for understanding the hard limits, performance tradeoffs, and architectural properties of this simple model of biological feedback control. Using tools from control theory, we show that there are simple parametric relationships that determine both the stability and the performance of these systems in terms of speed, robustness, steady-state error, and leakiness. These findings yield a holistic understanding of the behavior of sequestration feedback and contribute to a more general theory of biological control systems. +
F
Flat systems, an important subclass of nonlinear control systems introduced
via differential-algebraic methods, are defined in a differential
geometric framework. We utilize the infinite dimensional geometry developed
by Vinogradov and coworkers: a control system is a diffiety, or more
precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold
equipped with a privileged vector field. After recalling the definition of
a Lie-Backlund mapping, we say that two systems are equivalent if they
are related by a Lie-Backlund isomorphism. Flat systems are those systems
which are equivalent to a controllable linear one. The interest of
such an abstract setting relies mainly on the fact that the above system
equivalence is interpreted in terms of endogenous dynamic feedback. The
presentation is as elementary as possible and illustrated by the VTOL
aircraft. +
T
For closed-loop control of thin film deposition, one would like to
directly control film properties such as roughness, stress, or
composition, rather than process parameters like
temperatures and flow rates. This requires a
model of the dynamic response of film properties to
changes in process conditions.
Direct atomistic simulation is far too slow to be used in this
capacity, but a promising approach we explore here is to derive
reduced-order dynamic models from atomistic simulations.
<p>
In this paper, we consider film growth on a vicinal surface
using a kinetic Monte
Carlo model. The temperature range spans the transition from
smooth step flow to rough island growth.
Proper Orthogonal Decomposition is used to extract
the dominant spatial modes from the KMC simulations. Only five spatial modes
adequately represent the roughness dynamics for all simulated times and
temperatures, indicating that a 5-state model may be
sufficient for real-time roughness control. +
S
For state estimation in networked control systems,
the impact of packet dropping and delay over network links is
an important problem. In this paper, we introduce multiple description
(MD) source coding scheme to improve the statistical
stability and performance of the estimation error covariance
of Kalman filtering with packet loss. We consider about two
cases: when the packet loss over network links occurs in an i.i.d.
fashion or in a bursty fashion. Compared with the traditional
single description source coding, MD coding scheme can greatly
improve the performance of Kalman filtering over a large set
of packet loss scenarios in both cases. +
For state estimation over a communication network, efficiency and reliability of the network are critical issues. The presence
of packet dropping and communication delay can greatly impair our ability to measure and predict states. In this paper,
multiple description (MD) codes, a type of network source codes, are used to compensate for this effect on Kalman filtering.
We consider two packet dropping models: in one model, packet dropping occurs according to an independent and identically
distributed (i.i.d.) Bernoulli random process and in the other model, packet dropping is bursty and occurs according to a
Markov chain. We show that MD codes greatly improve the statistical stability and performance of Kalman filter over a large
set of packet loss scenarios in both cases. Our conclusions are verified by simulation results. +
P
For the synthesis of correct-by-construction control policies from temporal logic specifications the scalability of the synthesis algorithms is often a bottleneck. In this paper, we parallelize synthesis from specifications in the GR(1) fragment of linear temporal logic by introducing a hierarchical procedure that allows decoupling of the fixpoint computations. The state space is partitioned into equicontrollable sets using solutions to parameterized reachability games that arise from decomposing the original GR(1) game into smaller reachability games. Following the partitioning, another synthesis problem is formulated for composing the strategies from the decomposed reachability games. The formulation guarantees that composing the synthesized controllers ensures satisfaction of the given GR(1) property. Benchmarking experiments with robot planning problems demonstrate good scalability of the approach. +
A
Gene expression is often controlled by natural genetic regulatory networks that govern the rates at which genes
are transcribed. Recent work has shown that synthetic versions of genetic networks can be designed and built in living cells. Applications for these synthetic regulatory networks include intracellular decision-making and computation. In this study,
we propose a new synthetic genetic network that behaves as a digital clock, producing square waveform oscillations. We analyze two models of the network, a deterministic model based on Michaelis-Menten kinetics, as well as a stochastic model based on the Gillespie algorithm. Both models predict regions of oscillatory behavior; the deterministic model provides insight into the conditions required to produce the oscillating clock-like behavior, while the stochastic model is truer to natural
dynamics. Intracellular stochasticity is seen to contribute phase noise to the oscillator, and we propose improvements for the network and discuss the conceptual foundations of these improvements. +
R
Gene regulatory interactions are context dependent, active in some cellular states but not in others. Stochastic fluctuations, or 'noise', in gene expression propagate through active, but not inactive, regulatory links. Thus, correlations in gene expression noise could provide a noninvasive means to probe the activity states of regulatory links. However, global, 'extrinsic', noise sources generate correlations even without direct regulatory links. Here we show that single-cell time-lapse microscopy, by revealing time lags due to regulation, can discriminate between active regulatory connections and extrinsic noise. We demonstrate this principle mathematically, using stochastic modeling, and experimentally, using simple synthetic gene circuits. We then use this approach to analyze dynamic noise correlations in the galactose metabolism genes of Escherichia coli. We find that the CRP-GalS-GalE feed-forward loop is inactive in standard conditions but can become active in a GalR mutant. These results show how noise can help analyze the context dependence of regulatory interactions in endogenous gene circuits. +
D
Genetic regulatory networks are biochemical reaction systems, consisting of a network of interacting genes and associated proteins. The dynamics of genetic regulatory networks contain many complex facets that require careful consideration during the modeling process. The classical modeling approach involves studying systems of ordinary differential equations (ODEs) that model biochemical reactions in a deterministic, continuous, and instantaneous fashion. In reality, the dynamics of these systems are stochastic, discrete, and widely delayed. The first two complications are often successfully addressed by modeling regulatory networks using the Gillespie stochastic simulation algorithm (SSA), while the delayed behavior of biochemical events such as transcription and translation are often ignored due to their mathematically difficult nature. We develop techniques based on delay-differential equations (DDEs) and the delayed Gillespie SSA to study the effects of delays, in both continuous deterministic and discrete stochastic settings. Our analysis applies techniques from Floquet theory and advanced numerical analysis within the context of delay-differential equations, and we are able to derive stability sensitivities for biochemical switches and oscillators across the constituent pathways, showing which pathways in the regulatory networks improve or worsen the stability of the system attractors. These delay sensitivities can be far from trivial, and we offer a computational framework validated across multiple levels of modeling fidelity. This work suggests that delays may play an important and previously overlooked role in providing robust dynamical behavior for certain genetic regulatory networks, and perhaps more importantly, may offer an accessible tuning parameter for robust bioengineering. +
Given a differentially flat system of ODEs, flat outputs that depend only on original
variables but not on their derivatives are called zero-flat outputs and systems possessing
such outputs are called zero-flat. In this paper we present a theory of zero-flatness for
a system of two one-forms in arbitrary number of variables $(t,x^1,\dots,x^N)$. Our
approach splits the task of finding zero-flat outputs into two parts. First part involves
solving for distributions that satisfy a set of algebraic conditions. If the first part
has no solution then the system is not zero-flat. The second part involves finding an
integrable distribution from the solution set of the first part. Typically this part
involves solving PDEs. Our results are also applicable in determining if a control affine
system in $n$ states and $n-2$ controls has flat outputs that depend only on states. We
illustrate our method by examples. +
G
Grasping with flexible fingers presents an attractive approach for
certain robotic tasks. Its implementation requires simultaneous
position and force control of flexible manipulators, an area about
which there is little information in the literature. This paper
presents an initial effort at designing controllers for flexible link
robots to control both position and force. The analysis is done on a
two degree-of-freedom two-link manipulator with the last link
flexible. A control strategy is proposed and asymptotic stability is
proved. Results from using this control law in simulations and on an
experimental setup are presented. +
C
Convex optimal uncertainty quantification: Algorithms and a case study in energy storage placement for power grids +
How does one evaluate the performance of a stochastic system in the absence of a perfect model (i.e. probability distribution)? We address this question under the framework of optimal uncertainty quantification (OUQ), which is an information-based approach for worst-case analysis of stochastic systems. We are able to generalize previous results and show that the OUQ problem can be solved using convex optimization when the function under evaluation can be expressed in a polytopic canonical form (PCF). We also propose iterative methods for scaling the convex formulation to larger systems. As an application, we study the problem of storage placement in power grids with renewable generation. Numerical simulation results for simple artificial examples as well as an example using the IEEE 14-bus test case with real wind generation data are presented to demonstrate the usage of OUQ analysis. +
P
Protocols for Implementing an Escherichia coli Based TX-TL Cell-Free Expression System for Synthetic Biology +
Ideal cell-free expression systems can theoretically emulate an in vivo cellular environment in a controlled in vitro platform. This is useful for expressing proteins and genetic circuits in a controlled manner as well as for providing a prototyping environment for synthetic biology. To achieve the latter goal, cell-free expression systems that preserve endogenous Escherichia coli transcription-translation mechanisms are able to more accurately reflect in vivo cellular dynamics than those based on T7 RNA polymerase transcription. We describe the preparation and execution of an efficient endogenous E. coli based transcription-translation (TX-TL) cell-free expression system that can produce equivalent amounts of protein as T7-based systems at a 98% cost reduction to similar commercial systems. The preparation of buffers and crude cell extract are described, as well as the execution of a three tube TX-TL reaction. The entire protocol takes five days to prepare and yields enough material for up to 3000 single reactions in one preparation. Once prepared, each reaction takes under 8 hr from setup to data collection and analysis. Mechanisms of regulation and transcription exogenous to E. coli, such as lac/tet repressors and T7 RNA polymerase, can be supplemented.6 Endogenous properties, such as mRNA and DNA degradation rates, can also be adjusted.7 The TX-TL cell-free expression system has been demonstrated for large-scale circuit assembly, exploring biological phenomena, and expression of proteins under both T7- and endogenous promoters. Accompanying mathematical models are available. The resulting system has unique applications in synthetic biology as a prototyping environment, or "TX-TL biomolecular breadboard." +
R
In a complex real-time operating environment, external disturbances and uncertainties adversely affect the safety, stability, and performance of dynamical systems. This paper presents a robust stabilizing safety-critical controller synthesis framework with control Lyapunov functions (CLFs) and control barrier functions (CBFs) in the presence of disturbance. A high-gain input observer method is adapted to estimate the time-varying unmodelled dynamics of the CBF with an error bound using the first-order time derivative of the CBF. This approach leads to an easily tunable low order disturbance estimator structure with a design parameter as it utilizes only the CBF constraint. The estimated unknown input and associated error bound are used to ensure robust safety and exponential stability by formulating a CLF-CBF quadratic program. The proposed method is applicable to both relative degree one and higher relative degree CBF constraints. The efficacy of the proposed approach is demonstrated using a numerical simulations of an adaptive cruise control system and a Segway platform with an external disturbance. +
A
In an aircraft electric power system, one or more supervisory control units actuate a set of electromechanical switches to dynamically distribute power from generators to loads, while satisfying safety, reliability, and real-time performance requirements. To reduce expensive redesign steps, this control problem is generally addressed by minor incremental changes on top of consolidated solutions. A more systematic approach is hindered by a lack of rigorous design methodologies that allow estimating the impact of earlier design decisions on the final implementation. To achieve an optimal implementation that satisfies a set of requirements, we propose a platform-based methodology for electric power system design, which enables independent implementation of system topology (i.e., interconnection among elements) and control protocol by using a compositional approach. In our flow, design space exploration is carried out as a sequence of refinement steps from the initial specification toward a final implementation by mapping higher level behavioral and performance models into a set of either existing or virtual library components at the lower level of abstraction. Specifications are first expressed using the formalisms of linear temporal logic, signal temporal logic, and arithmetic constraints on Boolean variables. To reason about different requirements, we use specialized analysis and synthesis frameworks and formulate assume guarantee contracts at the articulation points in the design flow. We show the effectiveness of our approach on a proof-of-concept electric power system design. +
L
Leveraging Classification Metrics for Quantitative System-Level Analysis with Temporal Logic Specifications +
In many autonomy applications, performance of perception algorithms is important for effective planning and control. In this paper, we introduce a framework for computing the probability of satisfaction of formal system specifications given a confusion matrix, a statistical average performance measure for multi-class classification. We define the probability of satisfaction of a linear temporal logic formula given a specific initial state of the agent and true state of the environment. Then, we present an algorithm to construct a Markov chain that represents the system behavior under the composition of the perception and control components such that the probability of the temporal logic formula computed over the Markov chain is consistent with the probability that the temporal logic formula is satisfied by our system. We illustrate this approach on a simple example of a car with pedestrian on the sidewalk environment, and compute the probability of satisfaction of safety requirements for varying parameters of the vehicle. We also illustrate how satisfaction probability changes with varied precision and recall derived from the confusion matrix. Based on our results, we identify several opportunities for future work in developing quantitative system-level analysis that incorporates perception models. +
E
In mobile sensor networks, sensor measurements
as well as control commands are transmitted over
wireless time-varying links. It then becomes considerably
important to address the impact of imperfect communication
on the overall performance. In this paper, we
study the effect of time-varying communication links on
the control performance of a mobile sensor node. In
particular, we investigate the impact of fading. We derive
key performance measure parameters to evaluate the
overall feedback control performance over narrowband
channels. We show that fading can result in considerable
delay and/or poor performance of the mobile sensor
depending on the system requirements. To improve the
performance, we then show how the application layer can
use the channel status information of the physical layer
to adapt control commands accordingly. We show that
sharing information across layers can improve the overall
performance considerably. We verify our analytical
results by simulating a wireless speed control problem. +
S
In multicellular organisms, cells actively sense, respond to, and control their own population density. Synthetic mammalian quorum sensing circuits could provide insight into principles of population control and improve cell therapies. However, a key challenge is avoiding their inherent sensitivity to “cheater” mutations that evade control. Here, we repurposed the plant hormone auxin to enable orthogonal mammalian cell-cell communication and quorum sensing. Further, we show that a “paradoxical” circuit design, in which auxin stimulates and inhibits net cell growth at different concentrations, achieves population control that is robust to cheater mutations, controlling growth for 43 days of continuous culture. By contrast, a non-paradoxical control circuit limited growth but was susceptible to mutations. These results establish a foundation for future cell therapies that can respond to and control their own population sizes. +
W
In recent years, numerous distributed algorithms
have been proposed which, when executed by a team of
dynamic agents, result in the completion of a joint task.
However, for any such algorithm to be practical, one should be
able to guarantee that the task is still satisfactorily executed
even when agents fail to communicate with others or to
perform their designated actions correctly. In this paper,
we present a concept of robustness which is well-suited for
general distributed algorithms for teams of dynamic agents.
Our definition extends a similar notion introduced in the
distributed computation literature for consensus problems. We
illustrate the definition by considering a variety of algorithms. +
T
In robotic finger gaiting, fingers continuously manipulate an object until joint limitations or mechanical limitations periodically force a switch of grasp. Current approaches to gait planning and control are slow, lack formal guarantees on correctness, and are generally not reactive to changes in object geometry. To address these issues, we apply advances in formal methods to model a gait subject to external perturbations as a two-player game between a finger controller and its adversarial environment. High-level specifications are expressed in linear temporal logic (LTL) and low-level control primitives are designed for continuous kinematics. Simulations of planar manipulation with our synthesized correct-by-construction gait controller demonstrate the benefits of this approach. +
