Property:Abstract
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E
Motivated by robotic motion planning, we develop a framework for control policy synthesis for both non-deterministic transition systems and Markov decision processes that are subject to temporal logic task specifications. We introduce a fragment of linear temporal logic that can be used to specify common motion planning tasks such as safe navigation, response to the environment, surveillance, and persistent coverage. This fragment is computationally efficient; the complexity of control policy synthesis is a doubly-exponential improvement over standard linear temporal logic for both non-deterministic transition systems and Markov decision processes. This improvement is possible since we compute directly on the original system, as opposed to the automata-based approach commonly used for linear temporal logic. We give simulation results for representative motion planning tasks and compare to generalized reactivity(1). +
D
Motivated by the availability of different types of delays in embedded systems and biological circuits, the objective of this work is to study the benefits that delay can provide in simplifying the implementation of controllers for continuous-time systems. Given a continuous-time linear time-invariant (LTI) controller, we propose three methods to approximate this controller arbitrarily precisely by a simple controller composed of delay blocks, a few integrators and possibly a unity feedback. Different problems associated with the approximation procedures, such as finding the optimal number of delay blocks or studying the robustness of the designed controller with respect to delay values, are then investigated. We also study the design of an LTI continuous-time controller satisfying given control objectives whose delay-based implementation needs the least number of delay blocks. A direct application of this work is in the sampled-data control of a real-time embedded system, where the sampling frequency is relatively high and/or the output of the system is sampled irregularly. Based on our results on delay-based controller design, we propose a digital-control scheme that can implement every continuous-time stabilizing (LTI) controller. Unlike a typical sampled-data controller, the hybrid controller introduced here---consisting of an ideal sampler, a digital controller, a number of modified second-order holds and possibly a unity feedback---is robust to sampling jitter and can operate at arbitrarily high sampling frequencies without requiring expensive, high-precision computation. +
C
Motivated by the desire to analyze high dimen- sional control systems without explicitly forming computation- ally expensive linear matrix inequality (LMI) constraints, we seek to exploit special structure in the dynamics matrix. By using Jordan algebraic techniques we show how to analyze continuous time linear dynamical systems whose dynamics are exponentially invariant with respect to a symmetric cone. This allows us to characterize the families of Lyapunov functions that suffice to verify the stability of such systems. We highlight, from a computational viewpoint, a class of systems for which stability verification can be cast as a second order cone program (SOCP), and show how the same framework reduces to linear programming (LP) when the system is internally positive, and to semidefinite programming (SDP) when the system has no special structure. +
A
A geometric and structural approach to the analysis and design of biological circuit dynamics: a theory tailored for synthetic biology +
Much of the progress in developing our ability to successfully design genetic circuits with predictable dynamics has followed the strategy of molding biological systems to fit into conceptual frameworks used in other disciplines, most notably the engineering sciences. Because biological systems have fundamental differences from systems in these other disciplines, this approach is challenging and the insights obtained from such analyses are often not framed in a biologically-intuitive way. Here, we present a new theoretical framework for analyzing the dynamics of genetic circuits that is tailored towards the unique properties associated with biological systems and experiments. Our framework approximates a complex circuit as a set of simpler circuits, which the system can transition between by saturating its various internal components. These approximations are connected to the intrinsic structure of the system, so this representation allows the analysis of dynamics which emerge solely from the system’s structure. Using our framework, we analyze the presence of structural bistability in a leaky autoactivation motif and the presence of structural oscillations in the Repressilator. +
I
Neural networks in real-world applications have to satisfy critical properties such as safety and reliability. The analysis of such properties typically involves extracting informa- tion through computing pre-images of neural networks, but it is well-known that explicit computation of pre-images is intractable. We introduce new methods for computing compact symbolic abstractions of pre-images. Our approach relies on computing approximations that provably overapproximate and underapproximate the pre-images at all layers. The abstraction of pre-images enables formal analysis and knowl- edge extraction without modifying standard learning algo- rithms. We show how to use inverse abstractions to automatically extract simple control laws and compact representations for pre-images corresponding to unsafe outputs. We illustrate that the extracted abstractions are often interpretable and can be used for analyzing complex properties. +
R
New control paradigms are needed for large networks of wireless sensors and actuators in order to efficiently utilise system resources. In this study, the authors consider the problem of discrete-tie state estimation over a wireless sensor network. Given a tree that represents the sensor communications with the fusion centre, the authors derive the optimal estimation algorithm at the fusion centre, and provide a closed-form expression for the steady-state error covariance matrix. They then present a tree reconfiguration algorithm that produces a sensor tree that has low overall energy consumption and guarantees a desired level of estimation quality at the fusion centre. The authors further propose a sensor tree construction and scheduling algorithm that leads to a longer network lifetime than the tree reconfiguration algorithm. Examples are provided throughout the paper to demonstrate the algorithms and theory developed. +
F
Finding stationary solutions to the chemical master equation by gluing state spaces at one or two states recursively +
Noise is indispensible to key cellular activities, including gene expression coordination and probabilistic differentiation. Stochastic models, such as the chemical master equation (CME), are essential to model noise in the levels of cellular components. In the CME framework, each state is associated with the molecular counts of all component species, and specifies the probability for the system to have that set of molecular counts. Analytic solutions to the CME are rarely known but can bring exciting benefits. For instance, simulations of biochemical reaction networks that are multiscale in time can be sped up tremendously by incorporating analytic solutions of the slow time-scale dynamics. Ana- lytic solutions also enable the design of stationary distributions with properties such as the modality of the distribution, the mean expression level, and the level of noise. One way to derive the analytic steady state response of a biochemical reaction network was re- cently proposed by (Mélykúti et al. 2014). The paper recursively glues simple state spaces together, for which we have analytic solutions, at one or two states.
<p>
In this work, we explore the benefits and limitations of the gluing technique proposed by Mélykúti et al., and introduce recursive algorithms that use the technique to solve for the analytic steady state response of stochastic biochemical reaction networks. We give formal characterizations of the set of reaction networks whose state spaces can be obtained by carrying out single-point gluing of paths, cycles or both sequentially. We find that the dimension of the state space of a reaction network equals the maximum number of linearly independent reactions in the system. We then characterize the complete set of stochastic biochemical reaction networks that have elementary reactions and two-dimensional state spaces. As an example, we propose a recursive algorithm that uses the gluing technique to solve for the steady state response of a mass-conserving system with two connected monomolecular reversible reactions. Even though the gluing technique can only construct finite state spaces, we find that, by taking the size of a finite state space to infinity, the steady state response can converge to the analytic solution on the resulting infinite state space. Finally, we illustrate the aforementioned ideas with the example of two interconnected transcriptional components, which was first studied by (Ghaemi and Del Vecchio 2012).
R
Recursively constructing analytic expressions for equilibrium distributions of stochastic biochemical reaction networks +
Noise is often indispensable to key cellular activities, such as gene expression, necessitating the use of stochastic models to capture its dynamics. The chemical master equation (CME) is a commonly used stochastic model of Kolmogorov forward equations that describe how the probability distribution of a chemically reacting system varies with time. Finding analytic solutions to the CME can have benefits, such as expediting simulations of multiscale biochemical reaction networks and aiding the design of distributional responses. However, analytic solutions are rarely known. A recent method of computing analytic stationary solutions relies on gluing simple state spaces together recursively at one or two states. We explore the capabilities of this method and introduce algorithms to derive analytic stationary solutions to the CME. We first formally characterize state spaces that can be constructed by performing single-state gluing of paths, cycles or both sequentially. We then study stochastic biochemical reaction networks that consist of reversible, elementary reactions with two-dimensional state spaces. We also discuss extending the method to infinite state spaces and designing the stationary behaviour of stochastic biochemical reaction networks. Finally, we illustrate the aforementioned ideas using examples that include two interconnected transcriptional components and biochemical reactions with two-dimensional state spaces. +
N
Nonlinear control of mechanical systems is a challenging discipline that lies at the
intersection between control theory and geometric mechanics. This thesis sheds new light
on this interplay while investigating motion control problems for Lagrangian systems. Both
stability and motion planning aspects are treated within a unified framework that accounts
for a large class of devices such as robotic manipulators, autonomous vehicles and
locomotion systems.</p>
<p>One distinguishing feature of mechanical systems is the number of control forces. For
systems with as many input forces as degrees of freedom, many control problems are
tractable. One contribution of this thesis is a set of trajectory tracking controllers
designed via the notions of configuration and velocity error. The proposed approach
includes as special cases a variety of results on joint and workspace control of
manipulators as well as on attitude and position control of vehicles.</p>
<p>Whenever fewer input forces are available than degrees of freedom, various control
questions arise. The main contribution of this thesis is the design of motion algorithms
for vehicles, i.e., rigid bodies moving in Euclidean space. First, an algebraic
controllability analysis characterizes the set of reachable configurations and velocities
for a system starting at rest. Then, provided a certain controllability condition is
satisfied, various motion algorithms are proposed to perform tasks such as short range
reconfiguration and hovering. </p>
<p>Finally, stabilization techniques for underactuated systems are investigated. The
emphasis is on relative equilibria, i.e., steady motions for systems that have a conserved
momentum. Local exponential stabilization is achieved via an appropriate splitting of the
control authority. +
B
Nonlinear qualitative analysis is performed on the Moore-Greitzer
model to evaluate the tradeoff of fluid noise, actuator magnitude saturation,
bandwidth, rate limits, and the shape of compressor characteristics in active
control of rotating stall in axial compressors with bleed valve actuators. Model
order reduction is achieved by approximating the dynamics on the invariant manifold
that captures the bifurcations and instabilities. Bifurcations and qualitative
dynamics are obtained by analyzing the reduced system. The operability enhancement
is defined as the extension of operating range for which fully developed rotating
stall is avoided. Analytic formulas are derived for the operability enhancement
as a function of noise level, actuator saturation limits, and the shape of the
compressor characteristic, which is the major nonlinearity in the model. The
shape of the compressor characteristic, especially the unstable part, is critical
to the rate required for robust operability near the peak for the closed loop
system. Experiments are carried out on a single-stage low-speed axial compressor
using different level of steady air injections to generate different compressor
characteristics. The theoretical formulas give good qualitative estimates to
experimental data and simulations using a high fidelity model (37 states). +
F
One of the challenges in designing the next genera- tion of robots operating in non-engineered environments is that there seems to be an infinite amount of causes that make the sensor data unreliable or actuators ineffective. In this paper, we discuss what faults are possible to detect using zero modeling effort: we start from uninterpreted streams of observations and commands, and without a prior knowledge of a model of the world. We show that in sensorimotor cascades it is possible to define static faults independently of a nominal model. We define an information-theoretic usefulness of a sensor reading and we show that it captures several kind of sensorimotor faults frequently encountered in practice. We particularize these ideas to the case of BDS/BGDS models, proposed in previous work as suitable candidates for describing generic sensorimotor cascades. We show several examples with camera and range-finder data, and we discuss a possible way to integrate these techniques in an existing robot software architecture. +
M
Modeling the Effects of Compositional Context on Promoter Activity in an E. Coli Extract based Transcription-Translation System +
One of the fundamental challenges in synthesizing complex biocircuits from existing biocircuit components is understanding how the spatial arrangement of biocircuit components impacts component behavior. In this paper we develop a set of synthetic biology parts for systematically probing the effects of spatial arrangement on transcriptional expression. Our initial experimental assays prove that even the rearrangement of two biocircuit parts (comprised of a promoter, coding sequence, and terminator) into three spatially distinct orientations (convergent, divergent, and tandem orientation) can exhibit significantly different levels of transcriptions. These findings motivate the need for mathematical models to describe these spatial context effects. We pose a novel nonlinear mass-action kinetics based model that enables the integration of knowledge about spatial or compositional context and canonical descriptions of transcriptional dynamics. Our findings suggest that compositional context is a key factor in determining bio- circuit part performance and thus represent another important piece in biocircuit interconnection theory. +
E
Operability enhancement is one of the major goals for active control of rotating stall
and surge in aeroengines. The model developed by Moore and Greitzer exhibits the
qualitative behavior of rotating stall and surge dynamics and thus can be used for
controller designs. Based on this model, we derive a normal form from which explicit
relations between the stall and surge inception process and the shape of compressor
characteristics are obtained via bifurcation analysis. Analysis for the normal form with
bleed valve actuator dynamics shows that under certain circumstances the optimal control
is the "bang-on" control law that drives the bleed valve to open against its
rate limit once the disturbances grow out of the noise level. +
C
Optimal uncertainty quantification (OUQ) is a framework for nu- merical extreme-case analysis of stochastic systems with imperfect knowl- edge of the underlying probability distribution and functions/events. This paper presents sufficient conditions (when underlying functions are known) under which an OUQ problem can be reformulated as a finite-dimensional convex optimization problem. +
S
Synthesizing Combination Therapies for Evolutionary Dynamics of Disease for Nonlinear Pharmacodynamics +
Our previous results proposed an iterative scalable algorithm for the systematic design of sparse, small gain feedback strategies that stabilize the evolutionary dynamics of a generic disease model with linear pharmacodynamics. Here we use piecewise linear approximations to model the nonlinear drug effects and leverage results from optimal controller synthesis for positive systems to formulate the feedback synthesis problem as an optimization problem that sequentially explores piecewise linear subsystems corresponding to higher and higher treatment dosages. +
R
Rapid prototyping of biomolecular circuits through module characterization in cell-free expression systems +
Over the past years, the field of synthetic biology has gained a significant array of tools and parts, making way for increasingly complex bio-molecular circuits to be constructed. The development of biocircuits can be facilitated by assembling parts in a less complex, cell-free, environment which contains only the machinery for gene transcription (TX) and translation (TL), which have been extracted from bacteria. In this project, a part library was collected and used to assemble DNA constructs for a newly designed biocircuit. An in vitro TX-TL extract was used to test the circuit modules using linear DNA, and in parallel with predictive modeling of the biomolecular reactions, the overall circuit design was evaluated. The results have given valuable insight into the performance of the circuit modules in a much shorter time than conventional in vivo cloning and testing would have achieved. +
M
Model of Paradoxical Signaling Regulated T-Cell Population Control for Design of Synthetic Circuits +
Paradoxical signaling occurs when the same sig- naling molecule can trigger antagonistic cell functions. For example, T-Cells secret cytokine IL-2 which promotes T-Cell proliferation and also affects cell death. It has been shown that cells with this signaling capability have bi-stable population dynamics and can achieve identical levels of population homeostasis independent of initial cell concentrations. These capabilities are desirable in the context of synthetic population control circuits designed for application in therapeutic treatment of various diseases. It thus becomes important to understand the dependence of the cell system on the intracellular paradoxical components and to develop accurate models to provide insight into optimal design characteristics. Here, we create a model that integrates three IL-2 driven intracellular mechanisms that trigger 1) T-cell proliferation 2) T-cell apoptosis and 3) IL-2 production. Using this model, we are able to explore the internal mechanisms necessary for paradoxical signaling in T-Cells. It was shown that the intracellular mechanisms considered were sufficient to produce population dynamic characteristics of paradoxical signaling consistent with published systems level models and data. Furthermore, analysis of parameters revealed dependency of population homeostatic stability on the production and activation of the specific intracellular proteins considered. +
R
Performance analysis of a large class of nonlinear
systems is proven to be equivalent to performance
analysis of a constrained uncertain linear system,
for which computable analysis methods have already been
developed. +
Q
Performance of biomolecular circuits is affected by changes in temperature, due to its influence on underlying reaction rate parameters. While these performance variations have been estimated using Monte Carlo simulations, how to analytically bound them is generally unclear. To address this, we apply control-theoretic representations of uncertainty to examples of different biomolecular circuits, developing a framework to represent uncertainty due to temperature. We estimate bounds on the steady-state performance of these circuits due to temperature uncertainty. Through an analysis of the linearised dynamics, we represent this uncertainty as a feedback uncer- tainty and bound the variation in the magnitude of the input- output transfer function, providing a estimate of the variation in frequency-domain properties. Finally, we bound the variation in the time trajectories, providing an estimate of variation in time-domain properties. These results should enable a framework for analytical characterisation of uncertainty in biomolecular circuit performance due to temperature variation and may help in estimating relative performance of different controllers. +
T
Phage integrase-based circuits are an alternative approach to relying on transcriptional and translational repression for biomolecular circuits. Previous research has shown that circuits based on integrases can perform a variety of functions, including counters, Boolean logic operators, memory modules and temporal event detectors. It is therefore essential to develop a principled theoretical and experimental framework for the design, implementation and study of such circuits. One of the fundamental questions that such a framework should address concerns the functionality limitations and temporal dynamics of the integrases as regulatory elements. We have tested the functionality of several large serine type integrases from a recently published library in a cell-free transcription-translation (TX-TL) platform. In addition, we have explored experimentally and through mathematical modelling and simulations how integrase dynamics depends on the concentration of integrase and that of its binding sites.
We report that sequestration of integrase molecules, either in the form of monomers or dimers, by the integrase's own binding sites dominates integrase dynamics, and that the delay in the activation of the reporter is negatively correlated with integrase plasmid concentration. We have validated our sequestration hypothesis by building a model with MATLAB’s SimBiology toolbox, and running simulations with various integrase and binding sites concentrations. The simulation results qualitatively match the experimental results, and offer further insights into the system. +
