Property:Abstract
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S
It is infeasible to understand all dynamics in cell, but we can aim to understand the impact of design choices under our control. Here we consider a single gene oscillator as a case study to understand the influence of DNA copy number and repressor choice on the resulting dynamics. We first switch the repressor in the oscillator from the originally published lacI to treRL, a chimeric repressor with a lacI DNA binding domain that is inducible by trehalose. This slightly modified system produces faster and more regular oscillations than the original lacI oscillator. We then compare the treRL oscillator at three different DNA copy numbers. The period and amplitude of oscillations increases as the copy number is decreased. We cannot explain the change in period with differ- ential equation models without changing delays or degradation rates. The correlation and phase coherence between daughter cells after cell division also tend to fall off faster for the lower copy oscillator variants. These results suggest that lower copy number variants of our single gene oscillator produce more synchronized oscillations. +
T
It is the general assumption that in estimation and control over wireless links, the receiver should drop any erroneous packets. While this approach is appropriate for non real-time data-network applications, it can result in instability and loss of performance in networked control systems. In this technical note we consider estimation of a multiple-input multiple-output dynamical system over a mobile fading communication channel using a Kalman filter. We show that the communication protocols suitable for other already-existing applications like data networks may not be entirely applicable for estimation and control of a rapidly changing dynamical system. We then develop new design paradigms in terms of handling noisy packets for such delay-sensitive applications. We reformulate the estimation problem to include the impact of stochastic communication noise in the erroneous packets. We prove that, in the absence of a permanent cross-layer information path, packet drop should be designed to balance information loss and communication noise in order to optimize the performance. +
It is well known that synthetic gene expression is highly sensitive to how genetic elements (promoter structure, spacing regions between promoter and coding sequences, ribosome binding sites, etc.) are spatially configured. An important topic that has received far less attention is how the compositional context, or spatial arrangement, of entire genes within a synthetic gene network affects their individual expression levels. In this paper we show, both quantitatively and qualitatively, that compositional context significantly alters transcription levels in synthetic gene networks. We demonstrate that key characteristics of gene induction, such as ultra-sensitivity and dynamic range, strongly depend on compositional context. We postulate that supercoiling can be used to explain this interference and validate this hypothesis through modeling and a series of in vitro supercoiling relaxation experiments. This compositional interference enables a novel form of feedback in synthetic gene networks. We illustrate the use of this feedback by redesigning the toggle switch to incorporate compositional context. We show the context-optimized toggle switch has improved threshold detection and memory properties. +
C
Lagrangian control systems that are differentially flat with flat outputs that only
depend on configuration variables are said to be configuration flat. We provide a complete
characterisation of configuration flatness for systems with $n$ degrees of freedom and
$n-1$ controls whose range of control forces only depends on configuration but not on
velocity and whose Lagrangian has the form of kinetic energy minus potential. The method
presented allows us to determine if such a system is configuration flat and, if so
provides a constructive method for finding all possible configuration flat outputs. Our
characterisation relates configuration flatness to Riemannian geometry. We illustrate the
method by two examples. +
L
Layered feedback is an optimization strategy in feedback control designs widely used in electrical and mechanical engineering. Layered control theory suggests that the performance of controllers is bound by the universal robustness-efficiency tradeoff limit, which could be overcome by layering two or more feedbacks together. In natural biological networks, genes are often regulated with redundancy and layering to adapt to environmental perturbations. Control theory hypothesizes that this layering architecture is also adopted by nature to overcome this performance trade-off. In this work, we validated this property of layered control with a synthetic network in living E. coli cells. We performed system analysis on a node-based design to confirm the tradeoff properties before proceeding to simulations with an effective mechanistic model, which guided us to the best performing design to engineer in cells. Finally, we interrogated its system dynamics experimentally with eight sets of perturbations on chemical signals, nutrient abundance, and growth temperature. For all cases, we consistently observed that the layered control overcomes the robustness-efficiency trade-off limit. This work experimentally confirmed that layered control could be adopted in synthetic biomolecular networks as a performance optimization strategy. It also provided insights in understanding genetic feedback control architectures in nature. +
B
Learning and adaptivity will play a large role in robotics in the future, as robots move from structured to unstructured environments that cannot be fully predicted or understood by the designer. Two questions that are open: 1) in principle, how much it is possible to learn; and, 2) in practice, how much we should learn. The bootstrapping scenario describes the extremum case where agents need to learn âeverythingâ from scratch, including a torque-to-pixels models for its robotic body. Systems with such capabilities will be advantaged in terms of being resilient to unforeseen changes and deviations from prior assumptions. This paper considers the bootstrapping problem for a subset of the set of all robots: the Vehicles, inspired by Braitenbergâs work, are idealization of mobile robots equipped with a set of âcanonicalâ exteroceptive sensors (camera; range- finder; field-sampler). Their sensel-level dynamics are derived and shown to be surprising close. We define the class of BDS models, which assume an instantaneous bilinear dynamics between observations and commands, and derive streaming-based bilinear strategies for them. We show in what sense the BDS dynamics approximates the set of Vehicles to guarantee success in the task of generalized servoing: driving the observations to a given goal snapshot. Simulations and experiments substantiate the theoretical results. This is the first instance of a bootstrapping agent that can learn the dynamics of a relatively large universe of systems, and use the models to solve well-defined tasks, with no parameter tuning or hand-designed features. +
D
Locomotion of microorganisms and tiny artificial swimmers is governed by low- Reynolds-number hydrodynamics, where viscous effects dominate and inertial effects are negligible. While the theory of low-Reynolds-number locomotion is well studied for unbounded fluid domains, the presence of a boundary has a significant influence on the swimmer's trajectories, and poses problems of dynamic stability of its motion. In this paper we consider a simple theoretical model of a micro-swimmer near a wall, study its dynamics, and analyze the stability of its motion. We highlight the underlying geometric structure of the dynamics, and establish a relation between the reversing symmetry of the system and existence and stability of periodic and steady solutions of motion near the wall. The results are demonstrated by numerical simulations and validated by motion experiments with robotic swimmer prototypes. +
E
Lux-type quorum sensing systems enable communication in bacteria with only two protein components: a signal synthase and an inducible transcription activator. The simplicity of these systems makes them a popular choice for engineering collaborative behaviors in synthetic bacterial consortia, such as photographic edge detection and synchronized oscillation. To add to this body of work, we propose a pulsatile communication circuit that enables dynamic patterning and long-distance communication analogous to action potentials traveling through nerve tissue. We employed a model-driven design paradigm involving incremental characterization of in vivo design candidates with increasing circuit complexity. Beginning with a simple inducible reporter system, we screened a small number of circuits varying in their promoter and ribosomal binding site strengths. From this candidate pool, we selected a candidate to be the seed network for the subsequent round of more complex circuit variants, likewise variable in promoter and RBS strengths. The selection criteria at each level of complexity is tailored to optimize a different desirable performance characteristic. By this approach we individually optimized reporter signal-to-background ratio, pulsatile response to induction, and quiescent basal transcription, avoiding large library screens while ensuring robust performance of the composite circuit. +
G
Manipulation of particles suspended in fluids is crucial for many applications, such as precision machining, chemical processes, bio-engineering, and self-feeding of microorganisms. In this paper, we study the problem of particle manipulation by cyclic fluid boundary excitations from a geometric-control viewpoint. We focus on the simplified problem of manipulating a single particle by generating controlled cyclic motion of a circular rigid body in a two-dimensional perfect fluid. We show that the drift in the particle location after one cyclic motion of the body can be interpreted as the geometric phase of a connection induced by the system's hydrodynamics. We then formulate the problem as a control system, and derive a geometric criterion for its nonlinear controllability. Moreover, by exploiting the geometric structure of the system, we explicitly construct a feedback-based gait that results in attraction of the particle towards the rigid body. We argue that our gait is robust and model-independent, and demonstrate it in both perfect fluid and Stokes fluid. +
E
Many algorithms have been proposed in the literature for control of
multi-fingered robot hands. This paper compares the performance of
several of these algorithms, as well as some extensions of more
conventional manipulator control laws, in the case of planar grasping.
A brief introduction to the subject of robot hands and the notation
used in this paper is included. +
O
Many problems in nonlinear control theory (like, for instance, feedback
linearization problem) lead to examination of integrability of a Pfaffian
system. In a generic case a Pfaffian system is not integrable. Therefore,
how to approximate nonintegrable Pfaffian systems by integrable ones and how
this approximation can be applied in practice appears to be a natural and
important problem. In the present paper we establish some measures of
non-integrability of Pfaffian system of arbitrary dimension and discuss
their relation to approxiations of non-integrable Pfaffian systems by
integrable ones. Our work is motivated by expected applications to
approximate feedback linearization of multi-input nonlinear systems. +
D
Many systems comprised of interconnected sub-units exhibit coordinated behaviors; social groups,
networked computers, financial markets, and numerous biological systems come to mind. There
has been long-standing interest in developing a scientific understanding of coordination, both for ex-
planatory power in the natural and economic sciences, and also for constructive power in engineering
and applied sciences. This thesis is an abstract study of coordination, focused on developing a sys-
tematic âdesign theoryâ for producing interconnected systems with specifiable coordinated behavior;
this is in contrast to the bulk of previous work on this sub ject, in which any design component has
been primarily ad-hoc.
<p>The main theoretical contribution of this work is a geometric formalism in which to cast dis-
tributed systems. This has numerous advantages and ânaturallyâ parametrizes a wide class of
distributed interaction mechanisms in a uniform way. We make use of this framework to present
a model for distributed optimization, and we introduce the distributed gradient as a general design
tool for synthesizing dynamics for distributed systems. The distributed optimization model is a
useful abstraction in its own right and motivates a definition for a distributed extremum. As one
might expect, the distributed gradient is zero at a distributed extremum, and the dynamics of a
distributed gradient flow must converge to a distributed extremum. This forms the basis for a wide
variety of designs, and we are in fact able to recover a widely studied distributed averaging algorithm
as a very special case.
<p>We also make use of our geometric model to introduce the notion of coordination capacity;
intuitively, this is an upper bound on the âcomplexityâ of coordination that is feasible given a
particular distributed interaction structure. This gives intuitive results for local, distributed, and
global control architectures, and allows formal statements to be made regarding the possibility of
âsolvingâ certain optimization problems under a particular distributed interaction model.
<p>Finally, we present a number of applications to illustrate the theoretical approach presented;
these range from âstandardâ distributed systems tasks (leader election and clock synchronization)
to more exotic tasks like graph coloring, distributed account balancing, and distributed statistical
computations.
E
Engineering the soil bacterium Pseudomonas synxantha 2-79 into a ratiometric bioreporter for phosphorus limitation +
Microbial bioreporters hold promise for addressing challenges in medical and environmental applications. However, the difficulty of ensuring their stable persistence and function within the target environment remains a challenge. One strategy is to integrate information about the host strain and target environment into the design-build-test cycle of the bioreporter itself. Here, we present a case study for such an environmentally-motivated design process by engineering the wheat commensal bacterium Pseudomonas synxantha 2-79 into a ratiometric bioreporter for phosphorus limitation. Comparative analysis showed that an exogenous P-responsive promoter outperformed its native counterparts. This reporter can selectively sense and report phosphorus limitation at plant-relevant concentrations of 25-100 µM without cross-activation from carbon or nitrogen limitation or high cell densities. Its performance is robust over a field-relevant pH range (5.8-8), and it responds only to inorganic phosphorus, even in the presence of common soil organic P. Finally, we used fluorescein-calibrated flow cytometry to assess whether the reporter’s performance in shaken liquid culture predict its performance in soil, finding that although the reporter is still functional at the bulk level, its variability in performance increases when grown in a soil slurry as compared to planktonic culture, with a fraction of the population not expressing the reporter proteins. Together, our environmentally-aware design process provides an example of how laboratory bioengineering efforts can generate microbes with greater promise to function reliably in their applied contexts. +
P
Mistuning or blade to blade variation in jet-engine bladed-disks can
lead to large changes in engine performance. Even the small random
mistuning associated with manufacturing tolerances can significantly
change both stability boundaries and forced response. This thesis
addresses two questions. Analysis: given any mistuning (random or intentional),
what is the resulting change in performance? And passive control: can intentiona
l
mistuning be used to improve stability and forced response in a robust
manner?
<p>
A general framework based on symmetry arguments and eigenvalue/vector
perturbations is presented to answer both questions.
Symmetry constrains all facets of mistuning behaviour and provides
simplifications for both the analysis and control problems. This is combined
with the eigenvalue/vector perturbation which captures the nonlinear
mistuning dependence and solves the analysis problem. It is shown that
intentional mistuning can provide robust damping and so guarantee
improved stability and forced response under fixed manufacturing
tolerances. Results are demonstrated on a high-fidelity low-order
model derived from computational-fluid-dynamic data.
<p> +
T
Mixed observable Markov decision processes (MOMDPs) are a modeling framework for autonomous systems described by both fully and partially observable states. In this work, we study the problem of synthesizing a control policy for MOMDPs that minimizes the expected time to complete the control task while satisfying syntactically co-safe Linear Temporal Logic (scLTL) specifications. First, we present an exact dynamic programming update to compute the value function. Afterwards, we propose a point-based approximation, which allows us to compute a lower bound of the closed-loop probability of satisfying the specifications. The effectiveness of the proposed approach and comparisons with standard strategies are shown on high-fidelity navigation tasks with partially observable static obstacles. +
F
Model checking is a widely used technique for formal verification of distributed systems. It works by effectively examining the complete reachable state space of a model in order to determine whether the system satisfies its requirements or desired properties. The complexity of an autonomous vehicle system, however, renders model checking of the entire system infeasible due to the state explosion problem. In this paper, we illustrate how to exploit the structure of the system to systematically decompose the overall system-level requirements into a set of component-level requirements. Each of the components can then be model checked separately. A case study is presented where we formally verify the state consistency between different software modules of Alice, an autonomous vehicle developed by the California Institute of Technology for the 2007 DARPA Urban Challenge. +
M
Model predictive control (MPC) is applied to the Caltech ducted fan, a
thrust-vectored flight experiment. A real-time trajectory generation software based
on spline theory and sequential quadratic programming is used to implement the
MPC controllers. Timing issues related to the computation and implementation of
repeatedly updated optimal trajectories are discussed. Results show computational
speeds greater than 10 Hz, 2.5 times that of the actuator dynamics. The MPC
controllers successfully stabilize a step disturbance applied to the ducted fan and
compare favorably to LQR methods. +
R
Robustness guarantees for structured model reduction of dynamical systems with applications to biomolecular models +
Model reduction methods usually focus on the error performance analysis; however, in presence of uncertainties, it is important to analyze the robustness properties of the error in model reduction as well. This problem is particularly relevant for engineered biological systems that need to function in a largely unknown and uncertain environment. We give robustness guarantees for structured model reduction of linear and nonlinear dynamical systems under parametric uncertainties. We consider a model reduction problem where the states in the reduced model are a strict subset of the states of the full model, and the dynamics for all of the other states are collapsed to zero (similar to quasi-steady-state approximation). We show two approaches to compute a robustness guarantee metric for any such model reduction—a direct linear analysis method for linear dynamics and a sensitivity analysis based approach that also works for nonlinear dynamics. Using the robustness guarantees with an error metric and an input-output mapping metric, we propose an automated model reduction method to determine the best possible reduced model for a given detailed system model. We apply our method for the (1) design space exploration of a gene expression system that leads to a new mathematical model that accounts for the limited resources in the system and (2) model reduction of a population control circuit in bacterial cells. +
Model reduction methods usually focus on the error performance analysis; however, in presence of uncertainties, it is important to analyze the robustness properties of the error in model reduction as well. In this paper, we give robustness guarantees for structured model reduction of linear and nonlinear dynamical systems under parametric uncertainties. In particular, we consider a model reduction where the states in the reduced model are a strict subset of the states of the full model, and the dynamics for all other states are collapsed to zero (similar to quasi-steady state approximation). We show two approaches to compute a robustness metric for any such model reduction — a direct linear analysis method for linear dynamics and a sensitivity analysis based approach that also works for nonlinear dynamics. We also prove that for linear systems, both methods give equivalent results. +
L
Models for understanding and controlling oscillations in the flow past a rectangular cavity are developed. These models may be used to guide control designs, to understand performance limits of feedback, and to interpret experimental results. Traditionally, cavity oscillations are assumed to be self-sustained: no external disturbances are necessary to maintain the oscillations, and amplitudes are limited by nonlinearities. We present experimental data which suggests that in some regimes, the oscillations may not be self-sustained, but lightly damped: oscillations are sustained by external forcing, such as boundary-layer turbulence. In these regimes, linear models suffice to describe the behaviour, and the final amplitude of oscillations depends on the characteristics of the external disturbances. These linear models are particularly appropriate for describing cavities in which feedback has been used for noise suppression, as the oscillations are small and nonlinearities are less likely to be important. It is shown that increasing the gain too much in such feedback control experiments can lead to a peak-splitting phenomenon, which is explained by the linear models. Fundamental performance limits indicate that peak splitting is likely to occur for narrow-bandwidth actuators and controllers. +
