Property:Abstract
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D
Differentially flat systems are underdetermined systems of (nonlinear) ordinary differential equations
(ODEs) whose solution curves are in smooth one-one correspondence with arbitrary curves in a space
whose dimension equals the number of equations by which the system is underdetermined. For control
systems this is the same as the number of inputs. The components of the map from the system space to
the smaller dimensional space are referred to as the flat outputs. Flatness allows one to systematically
generate feasible trajectories in a relatively simple way. Typically the flat outputs may depend on the
original independent and dependent variables in terms of which the ODEs are written as well as finitely
many derivatives of the dependent variables. Flatness of systems underdetermined by one equation is
completely characterised by Elie Cartan's work. But for general underdetermined systems no complete
characterisation of flatness exists.
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In this dissertation we describe two different geometric frameworks for studying flatness and provide
constructive methods for deciding the flatness of certain classes of nonlinear systems and for finding
these flat outputs if they exist. We first introduce the concept of ``absolute equivalence'' due to Cartan
and define flatness in this frame work. We provide a method of testing for the flatness of systems, which
involves making a guess for all but one of the flat outputs after which the problem is reduced to the case
solved by Cartan. Secondly we present an alternative geometric approach to flatness which uses ``jet
bundles'' and present a theorem which partially characterises flat outputs that depend only on the
original variables but not on their derivatives, for the case of systems described by two independent
one-forms in arbitrary number of variables. Finally, for the class of Lagrangian mechanical systems whose
number of control inputs is one less than the number of degrees of freedom, we provide a
characterisation of flat outputs that depend only on the configuration variables, but not on their
derivatives. This characterisation makes use of the Riemannian metric provided by the kinetic energy of
the system.
A
Distributed algorithms for averaging have attracted interest in the control and sensing literature. However, previous works have not addressed some practical concerns that will arise in actual implementations on packet-switched communication networks..... +
D
Distributed algorithms for averaging have at-
tracted interest in the control and sensing literature. However,
previous works have not addressed some practical concerns
that will arise in actual implementations on packet-switched
communication networks such as the Internet. In this paper,
we present several implementable algorithms that are robust to
asynchronism and dynamic topology changes. The algorithms
do not require global coordination and can be proven to
converge under very general asynchronous timing assumptions.
Our results are verified by both simulation and experiments on
a real-world TCP/IP network. +
A
Due to the increasing complexity of space missions and distance to exploration targets, future robotic systems used for space exploration call for more resilience and autonomy. Instead of minimizing the failure risk, we are focusing on missions that will inevitably encounter significant failures and are developing an algorithm that will autonomously reconfigure the system controller to continue to make progress towards the mission goal despite being in a reduced capacity state - we call this extreme resilience. In this paper, we develop a model-free framework to autonomously react to locomotion failures of robotic systems. This is done by the use of a neural network for path planning using the neuroevolution of aug- menting topologies (NEAT) algorithm and a dynamic database of possible moves and their effect on the system’s position and orientation. Two modes of failure detection and resolution are being introduced: (a) relative position failure detection, which is triggered by large, unexpected moves and results in a complete update of the database before a retraining of the neural network, and (b) absolute position failure detection, which triggers from large build-ups of position error from small failures and will induce a retraining of the neural network without an explicit database reset. We implement and validate this framework on a high-fidelity planetary rover simulation using Unreal Engine and on a hardware setup of a TurtleBot2 with a PhantomX Pincher robot arm. +
Engineered bacterial sensors have potential applications in human health monitoring, environmental chemical detection, and materials biosynthesis. While such bacterial devices have long been engineered to differentiate between combinations of inputs, their potential to process signal timing and duration has been overlooked. In this work, we present a two-input temporal logic gate that can sense and record the order of the inputs, the timing between inputs, and the duration of input pulses. Our temporal logic gate design relies on unidirectional DNA recombination mediated by bacteriophage integrases to detect and encode sequences of input events. For an E. coli strain engineered to contain our temporal logic gate, we compare predictions of Markov model simulations with laboratory measurements of final population distributions for both step and pulse inputs. Although single cells were engineered to have digital outputs, stochastic noise created heterogeneous single-cell responses that translated into analog population responses. Furthermore, when single-cell genetic states were aggregated into population-level distributions, these distributions contained unique information not encoded in individual cells. Thus, final differentiated sub-populations could be used to deduce order, timing, and duration of transient chemical events. +
Engineered consortia are a major research focus for synthetic biologists because they can implement sophisticated behaviors inaccessible to single-strain systems. However, this functional capacity is constrained by their constituent strains’ ability to engage in complex communication. DNA messaging, by enabling information-rich channel-decoupled communication, is a promising candidate architecture for implementing complex communication. But its major advantage, its messages’ dynamic mutability, is still unexplored. We develop a framework for addressable and adaptable DNA messaging that leverages all three of these advantages and implement it using plasmid conjugation in E. coli. Our system can bias the transfer of messages to targeted receiver strains by 100- to 1000-fold, and their recipient lists can be dynamically updated in situ to control the flow of information through the population. This work lays the foundation for future developments that further utilize the unique advantages of DNA messaging to engineer previously-inaccessible levels of complexity into biological systems. +
R
Engineering microbial consortia is an important new frontier for synthetic biology given its efficiency in performing complex tasks and endurance to environmental uncertainty. Most synthetic circuits regulate population level behaviors via cell-to-cell communications, which are affected by spatially heterogeneous environments. Therefore, it is important to understand the limits on controlling system dynamics that are determined by interconnections among cell agents and provide a control strategy for engineering consortia. Here, we build a network model for a fractional population control circuit in two-strain consortia, and characterize the cell-to-cell communication network by topological properties, such as symmetry, locality and connectivity. Using linear network control theory, we relate the network topology to system output tracking performance. We analytically and numerically demonstrate that the minimum network control energy for accurate tracking depends on locality difference between two cell populations and how strongly the controller node contributes to communication strength. To realize robust consortia, we can manipulate the communication network topology and construct strongly connected consortia by altering chemicals in environments. Our results ground the expected cell population dynamics in its spatially organized communication network, and inspire directions in cooperative control in microbial consortia. +
I
Ensuring safety through set invariance has proven a useful method in a variety of applications in robotics and control. However, finding analytical expressions for maximal invariant sets, so as to maximize the operational freedom of the system without compromising safety, is notoriously difficult for high-dimensional systems with input constraints. Here we present a generic method for characterizing invariant sets of nth-order integrator systems, based on analyzing roots of univariate polynomials. Additionally, we obtain analytical expressions for the orders n <= 4. Using differential flatness we subsequently leverage the results for the n = 4 case to the problem of obstacle avoidance for quadrotor UAVs. The resulting controller has a light computational footprint that showcases the power of finding analytical expressions for control-invariant sets. +
C
Construction of an inducible amyloid expression circuit in Bacillus megaterium: A case study with CsgA and TasA +
Environmental applications of synthetic biology such as water remediation require engineered strains to function robustly in a fluctuating and potentially hostile environment. The construction of synthetic biofilm formation circuits could potentially alleviate this issue by promoting cell survival. Towards this end, we construct a xylose-inducible system for the expression of the functional amyloids CsgA and TasA in the soil bacterium Bacillus megaterium. We find that although both amyloids are expressed, only TasA is successfully exported from the cells. Furthermore, expression of CsgA results in a significant growth penalty for the cells while expression of TasA does not. Finally, we show that TasA expression conveys a small but detectable increase in cells’ adhesion to nickel beads. These results suggest that TasA is a promising candidate for future work on synthetic biofilm formation in B. megaterium. +
P
Establishing performance metrics is a key part of a systematic design process. In particular, specifying metrics useful for quantifying performance in the ongoing efforts towards biomolecular circuit design is an important problem. Here we address this issue for the design of a fast biomolec- ular step response that is uniform across different cells and widely different environmental conditions using a combination of simple mathematical models and experimental measure- ments using single-cell time-lapse microscopy. We evaluate two metrics, the difference of the step response from an ideal step and the relative difference between multiple realizations of the step response, that can provide a single number to measure performance. We use a model of protein production- degradation to show that these performance metrics correlate with response features of speed and noise. Finally, we work through an experimental methodology to estimate these metrics for step responses that have been acquired for inducible protein expression circuits in E. coli. These metrics will be useful to evaluate biomolecular step responses, as well as for setting similar performance measures for other design goals. +
A
Experimental comparisons between four different control design
methodologies are applied to a small vectored thrust engine.
Each controller is applied to three trajectories of varying
aggressiveness. The control strategies considered are LQR,
H_infty, gain scheduling, and feedback linearization. The
experiments show that gain scheduling
is essential to achieving good performance. The
strengths and weaknesses of each methodology are also examined. +
M
Experiments using active control to reduce oscillations
in the flow past a rectangular cavity have uncovered
surprising phenomena: in the controlled system,
often new frequencies of oscillation appear, and
often the main frequency of oscillation is split into
two sideband frequencies. The goal of this paper is
to explain these effects using physics-based models,
and to use these ideas to guide control design.
We present a linear model for the cavity flow,
based on the physical mechanisms of the familiar
Rossiter model. Experimental data indicates
that under many operating conditions, the oscillations
are not self-sustained, but in fact are caused
by amplification of external disturbances. We
present some experimental results demonstrating
the peak-splitting phenomena mentioned above, use
the physics-based model to study the phenomena,
and discuss fundamental performance limitations
which limit the achievable performance of any control
scheme. +
P
Planning and Optimization for Multi-Robot Planetary Cave Exploration under Intermittent Connectivity Constraints +
Exploring subsurface structures with autonomous robots is of growing interest in the context of planetary caves studies. Communication between robots in these environments is severely degraded which complicates coordination and information distribution. In this paper we focus on planning for mobility and communication in a cave exploration scenario where the situational awareness of a static base station is critical. We propose a notion of information-consistency where a plan itself is part of the information to be shared between robots, and propose a method for generating informationconsistent plans. We discuss in detail how the resulting plan can be robustly implemented with minimal communication through local mission executives that run on individual robots. We describe preliminary results on the performance of the planning algorithm and integration of the local mission executives in a high-fidelity simulation environment. +
F
Fault tolerance and safety verification of control systems that have state estimation uncertainty are essential for the success of autonomous robotic systems. A software control architecture called Mission Data System, developed at the Jet Propulsion Laboratory, uses goal networks as the control program for autonomous systems. Certain types of goal networks can be converted into linear hybrid systems and verified for safety using existing symbolic model checking software. A process for calculating the probability of failure of some verifiable goal networks due to state estimation uncertainty is presented. Extensions of this procedure to include other types of uncertainties are discussed, and example problems are presented to illustrate these procedures. +
C
Fault tolerance and safety verification of control systems are essential for the success of autonomous robotic systems. A control architecture called Mission Data System (MDS), developed at the Jet Propulsion Laboratory, takes a goal-based control approach. A software algorithm for converting goal network control programs into linear hybrid systems exists and is a bisimulation; the resulting linear hybrid system can be verified for safety in the presence of failures using existing symbolic model checkers, and thus the original goal network is verified. A substantial example control program based on a proposed mission to Titan, a moon of Saturn, is converted using the procedures discussed. +
A
Fault tolerance and safety verification of control systems are essential for the success of autonomous robotic systems. A control architecture called Mission Data System (MDS), developed at the Jet Propulsion Laboratory, takes a goal-based control approach. In this paper, a software algorithm for converting goal network control programs into linear hybrid systems is described. The conversion process is a bisimulation; the resulting linear hybrid system can be verified for safety in the presence of failures using existing symbolic model checkers, and thus the original goal network is verified. A moderately complex goal network control program is converted to a linear hybrid system using the automatic conversion software and then verified. +
C
Fault tolerance and safety verification of control systems are essential for the success of autonomous robotic systems. A control architecture called Mission Data System, developed at the Jet Propulsion Laboratory, takes a goal-based control approach. In this paper, a method for converting goal network control programs into linear hybrid systems is developed. The linear hybrid system can then be verified for safety in the presence of failures using existing symbolic model checkers. An example task is developed and successfully verified using HyTech, a symbolic model checking software for linear hybrid systems. +
S
Fault tolerance and safety verification of control systems that have state variable estimation uncertainty are essential for the success of autonomous robotic systems. A software control architecture called Mission Data System, developed at the Jet Propulsion Laboratory, uses goal networks as the control program for autonomous systems. Certain types of goal networks can be converted into linear hybrid systems and verified for safety using existing symbolic model checking software. A process for calculating the probability of failure of certain classes of verifiable goal networks due to state estimation uncertainty is presented. A verifiable example task is presented and the failure probability of the control program based on
estimation uncertainty is found. +
D
Feedback control is the key to achieve robust performances for many engineered systems. However, its application in biological contexts is still largely unexplored. In this work, we designed, analyzed and simulated a layered controller functioning at both molecular and populational levels. First, we used a minimal model of three states to represent a system where state A activates state B; state R is a by-product of state B that acts as a negative feedback regulating both state A, B, and sequentially R. We call the feedback applied to state B a cis feedback and the one applied to state A a trans feedback. Through stability analysis via linearization at equilibrium and sensitivity analysis at transient state, we found that the cis feedback attenuates disturbances better but recovers slower; the trans feedback recovers faster but has more dramatic responses to fluctuations; the layered feedback demonstrates both advantageous traits of the two single layers. Then we designed two versions of synthetic genetic circuits to implement the layered controller in living cells. One version with an sRNA as regulator R, the other with a transcription factor protein as the regulator R. The analysis and dynamical simulation of the models confirmed the analytical results from the minimal model. At the same time, we found that the protein regulated feedback controls have faster recovery speed but the RNA version has a stronger disturbance attenuation effect. +
S
Synergistic dual positive feedback loops established by molecular sequestration generate robust bimodal response +
Feedback loops are ubiquitous features of biological networks and can produce significant phenotypic heterogeneity, including a bimodal distribution of gene expression across an isogenic cell population. In this work, a combination of experiments and computational modeling was used to explore the roles of multiple feedback loops in the bimodal, switch-like response of the Saccharomyces cerevisiae galactose regulatory network. Here, we show that bistability underlies the observed bimodality, as opposed to stochastic effects, and that two unique positive feedback loops established by Gal1p and Gal3p, which both regulate network activity by molecular sequestration of Gal80p, induce this bimodality. Indeed, systematically scanning through different single and multiple feedback loop knockouts, we demonstrate that there is always a concentration regime that preserves the systemâs bimodality, except for the double deletion of GAL1 and the GAL3 feedback loop, which exhibits a graded response for all conditions tested. The constitutive production rates of Gal1p and Gal3p operate as bifurcation parameters because variations in these rates can also abolish the systemâs bimodal response. Our model indicates that this second loss of bistability ensues from the inactivation of the remaining feedback loop by the overexpressed regulatory component. More broadly, we show that the sequestration binding affinity is a critical parameter that can tune the range of conditions for bistability in a circuit with positive feedback established by molecular sequestration. In this system, two positive feedback loops can significantly enhance the region of bistability and the dynamic response time. +
