Property:Abstract
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D
The problem of estimating the discrete variables
in nondeterministic hybrid systems where the continuous
variables are available for measurement is considered. Using
partial order and lattice theory, we construct a discrete state
estimator, the LU estimator, which updates two variables at
each step. Namely, it updates the lower (L) and upper (U)
bounds of the set of all possible discrete variables values
compatible with the output sequence and with the systems'
dynamics. If the system is weakly observable, we show that
there always exist a lattice on which to construct the LU
estimator. For computational issues, some partial orders are to
be preferred to others.We thus show that nondeterminism may
be added to a system so as to obtain a new system that satisfies
the requirements for the construction of the LU estimator on
a chosen lattice. These ideas are applied to a nondeterministic
multi-robot system. +
N
The problem of finding a real time optimal
trajectory to minimize the probability of detection (to maximize
the probability of notbeingdetected, pnd, function) of
unmanned air vehicles by opponent radar detection systems
is investigated. This paper extends our preliminary results
on low observable trajectory generation in three ways. First,
trajectory planning in the presence of detection by multiple
radar systems, rather than single radar systems, is considered.
Second, an overall probability of detection function is
developed for the multiple radar case. In previous work, both
probability of detection by a single radar and signature were
developed in the theory section, but the examples used only
signature constraints. In this work, the use of the overall
probability of detection function is used, both because it
aids in the extension to multiple radar systems and because
it is a more direct measure of the desirable optimization
criteria. The third extension is the use of updated signature
and probability of detection models. The new models have a
greater number of sharp gradients than the previous models,
with low detectability regions for both a cone shaped areas
centered around the nose as in the previous paper, as well as a
cone-shaped area centered around rear of the air vehicle. The
Nonlinear Trajectory Generation method (NTG), developed
at Caltech, is used and motivated by the ability to provide
real time solutions for constrained nonlinear optimization
problems. Numerical simulations of multiple radar scenarios
illustrate UAV trajectories optimized for both detectability and
time. +
M
The problem of model reduction of linear systems with certain interconnection structure is considered
in this paper. To preserve the interconnection structure between subsystems in the reduction, special
care needs to be taken. This problem is important and timely because of the recent focus on complex
networked systems in control engineering. Two different model-reduction methods are introduced and
compared in the paper. Both methods are extensions to the well-known balanced truncation method.
Compared to earlier work in the area these methods use a more general linear fractional transformation
framework, and utilize linear matrix inequalities. Furthermore, new approximation error bounds that
reduce to classical bounds in special cases are derived. So-called structured Hankel singular values +
F
The prolific rise in autonomous systems has led to questions regarding their safe instantiation in real-world scenarios. Failures in safety-critical contexts such as human-robot interactions or even autonomous driving can ultimately lead to loss of life. In this context, this paper aims to provide a method by which one can algorithmically test and evaluate an autonomous system. Given a black-box autonomous system with some operational specifications, we construct a minimax problem based on control barrier functions to generate a family of test parameters designed to optimally evaluate whether the system can satisfy the specifications. To illustrate our results, we utilize the Robotarium as a case study for an autonomous system that claims to satisfy waypoint navigation and obstacle avoidance simultaneously. We demonstrate that the proposed test synthesis framework systematically finds those sequences of events (tests) that identify points of system failure. +
E
Engineering Transcriptional Regulator Effector Specificity Using Computational Design and In Vitro Rapid Prototyping: Developing a Vanillin Sensor +
The pursuit of circuits and metabolic pathways of increasing complexity and robustness in synthetic biology will require engineering new regulatory tools. Feedback control based on relevant molecules, including toxic intermediates and environmental signals, would enable genetic circuits to react appropriately to changing conditions. In this work, variants of qacR, a tetR family repressor, were generated by computational protein design and screened in a cell-free transcription-translation (TX-TL) system for responsiveness to a new targeted effector. The modified repressors target vanillin, a growth-inhibiting small molecule found in lignocellulosic hydrolysates and other industrial processes. Promising candidates from the in vitro screen were further characterized in vitro and in vivo in a gene circuit. The screen yielded two qacR mutants that respond to vanillin both in vitro and in vivo. While the mutants exhibit some toxicity to cells, presumably due to off-target effects, they are prime starting points for directed evolution toward vanillin sensors with the specifications required for use in a dynamic control loop. We believe this process, a combination of the generation of variants coupled with in vitro screening, can serve as a framework for designing new sensors for other target compounds. +
Engineering Transcriptional Regulator Effector Specificity using Computational Design and In Vitro Rapid Prototyping: Developing a Vanillin Sensor +
The pursuit of circuits and metabolic pathways of increasing complexity and robustness in synthetic biology will require engineering new regulatory tools. Feedback control based on relevant molecules, including toxic intermediates and environmental signals, would enable genetic circuits to react appropriately to changing conditions. In this work, variants of qacR, a tetR family repressor, were generated by compu- tational protein design and screened in a cell-free transcription-translation (TX-TL) system for responsiveness to a new targeted effector. The modified repressors target vanillin, a growth-inhibiting small molecule found in lignocellulosic hydrolysates and other industrial processes. Promising candidates from the in vitro screen were further characterized in vitro and in vivo in a gene circuit. The screen yielded two qacR mutants that respond to vanillin both in vitro and in vivo. We believe this process, a combination of the generation of variants coupled with in vitro screening, can serve as a framework for designing new sensors for other target compounds. +
Engineering Transcriptional Regulator Effector Specificity Through Rational Design and Rapid Prototyping +
The pursuit of circuits and metabolic pathways of increasing complexity and robustness in synthetic biology will require engineering new regulatory tools. Feedback control based on relevant molecules, including toxic intermediates and environmental signals, would enable genetic circuits to react appropriately to changing conditions. In this work, computational protein design was used to create functional variants of qacR, a tetR family repressor, responsive to a new targeted effector. The modified repressors target vanillin, a growth-inhibiting small molecule found in lignocellulosic hydrolysates and other industrial processes. A computatio ally designed library was screened using an in vitro transcription-translation (TX-TL) system. Leads from the in vitro screen were characterized in vivo. Preliminary results demonstrate dose-dependent regulation of a downstream fluorescent reporter by vanillin. These repressor designs provide a starting point for the evolution of improved variants. We believe this process can serve as a framework for designing new sensors for other target compounds. +
T
The realization of artificial biochemical reaction networks with unique functionality is one of the main challenges for the development of synthetic biology. Due to the reduced number of components, biochemical circuits constructed in vitro promise to be more amenable to systematic design and quantitative assessment than circuits embedded within living organisms. To make good on that promise, effective methods for composing subsystems into larger systems are needed. Here we used an artificial biochemical oscillator based on in vitro transcription and RNA degradation reactions to drive a variety of âloadâ processes such as the operation of a DNA-based nanomechanical device (âDNA tweezersâ) or the production of a functional RNA molecule (an aptamer for malachite green). We implemented several mechanisms for coupling the load processes to the oscillator circuit and compared them based on how much the load affected the frequency and amplitude of the core oscillator, and how much of the load was effectively driven. Based on heuristic insights and computational modeling, an âinsulator circuitâ was developed, which strongly reduced the detrimental influence of the load on the oscillator circuit. Understanding how to design effective insulation between biochemical subsystems will be critical for the synthesis of larger and more complex systems. +
Q
Quantitative Modeling of Integrase Dynamics Using a Novel Python Toolbox for Parameter Inference in Synthetic Biology +
The recent abundance of high-throughput data for biological circuits enables data-driven quantitative modeling and parameter estimation. Common modeling issues include long computational times during parameter estimation, and the need for many iterations of this cycle to match data. Here, we present BioSCRAPE (Bio-circuit Stochastic Single-cell Reaction Analysis and Parameter Estimation) - a Python package for fast and flexible modeling and simulation for biological circuits. The BioSCRAPE package can be used for deterministic or stochastic simulations and can incorporate delayed reactions, cell growth, and cell division. Simulation run times obtained with the package are comparable to those obtained using C code - this is particularly advantageous for computationally expensive applications such as Bayesian inference or simulation of cell lineages. We first show the package's simulation capabilities on a variety of example simulations of stochastic gene expression. We then further demonstrate the package by using it to do parameter inference for a model of integrase dynamics using experimental data. The BioSCRAPE package is publicly available online along with more detailed documentation and examples. +
I
The rules that govern decision making in systems
controlled by humans are often simple to describe. However,
deriving these rules from the actions of a group can be very
difficult, making human behavior hard to predict. We develop
an algorithm to determine the rules implemented by drivers
at a traffic intersection by observing the trajectories of their
cars. We applied such algorithm to a traffic intersection scenario
reproduced in the Caltech multi-vehicle lab, with human subjects
remotely driving kinematic robots. The results obtained on these
data suggest that this kind of human behavior is to some extent
predictable on our data set, and different subjects implement
similar rules. +
N
Nonlinear Control of Rotating Stall and Surge with Axisymmetric Bleed and Air Injection on Axial Flow Compressors +
The study of compressor instabilities in gas turbine engines has received
much attention in recent years. In particular, rotating stall and surge
are major causes of problems ranging from component stress and lifespan
reduction to engine explosion. In this thesis, modeling and control of
rotating stall and surge using bleed valve and air injection is studied and
validated on a low speed, single stage, axial compressor at Caltech.
<p>
Bleed valve control of stall is achieved only when the compressor
characteristic is actuated, due to the fast growth rate of the stall cell
compared to the rate limit of the valve. Furthermore, experimental results
show that the actuator rate requirement for stall control is reduced by a
factor of fourteen via compressor characteristic actuation. Analytical
expressions based on low order models (2--3 states) and a high fidelity
simulation (37 states) tool are developed to estimate the minimum rate
requirement of a bleed valve for control of stall. A comparison of the
tools to experiments show a good qualitative agreement, with increasing
quantitative accuracy as the complexity of the underlying model increases.
<p>
Air injection control of stall and surge is also investigated.
Simultaneous control of stall and surge is achieved using axisymmetric air
injection. Three cases with different injector back pressure are studied.
Surge control via binary air injection is achieved in all three cases.
Simultaneous stall and surge control is achieved for two of the cases, but
is not achieved for the lowest authority case. This is consistent with
previous results for control of stall with axisymmetric air injection
without a plenum attached.
<p>
Non--axisymmetric air injection control of stall and surge is also studied.
Three existing control algorithms found in literature are modeled and
analyzed. A three--state model is obtained for each algorithm. For two
cases, conditions for linear stability and bifurcation criticality on
control of rotating stall are derived and expressed in terms of
implementation--oriented variables such as number of injectors. For the
third case, bifurcation criticality conditions are not obtained due to
complexity, though linear stability property is derived. A theoretical
comparison between the three algorithms is made, via the use of low--order
models, to investigate pros and cons of the algorithms in the context of
operability.
<p>
The effects of static distortion on the compressor facility at Caltech is
characterized experimentally. Results consistent with literature are
obtained. Simulations via a high fidelity model (34 states) are also
performed and show good qualitative as well as quantitative agreement to
experiments. A non--axisymmetric pulsed air injection controller for stall
is shown to be robust to static distortion.
T
The synthesis of controllers guaranteeing linear temporal logic specifications on partially observable Markov decision processes (POMDP) via their belief models causes computational issues due to the continuous spaces. In this work, we construct a finite-state abstraction on which a control policy is synthesized and refined back to the original belief model. We introduce a new notion of label- based approximate stochastic simulation to quantify the deviation between belief models. We develop a robust synthesis methodology that yields a lower bound on the satisfaction probability, by compensating for deviations a priori, and that utilizes a less conservative control refinement. +
R
Real-time trajectory generation for constrained nonlinear dynamical systems using non-uniform rational B-spline basis functions +
The thesis describes a new method for obtaining minimizers for optimal control problems whose minima serve as control policies for guiding nonlinear dynamical systems to achieve prescribed goals under imposed trajectory and actuator constraints. One of the major contributions of the present work resides in the approximation of such minimizers by piecewise polynomial functions expressed in terms of a linear combination of non-uniform rational B-spline (NURBS) basis functions and the judicious exploitation of the properties of the resulting NURBS curves to improve the computational effort often associated with solving optimal control problems for constrained dynamical systems. In particular, by exploiting the two structures combined in a NURBS curve, NURBS basis functions and an associated union of overlapping polytopes constructed from the coefficients of the linear combination, we are able to separate an optimal control problem into two subproblems +
C
There is a growing interest in building autonomous systems that interact with complex environments. The difficulty associated with obtaining an accurate model for such environments poses a challenge to the task of assessing and guaranteeing the system’s performance. We present a data-driven solution that allows for a system to be evaluated for specification conformance without an accurate model of the environment. Our approach involves learning a conservative reactive bound of the environment’s behavior using data and specification of the system’s desired behavior. First, the approach begins by learning a conservative reactive bound on the environment’s actions that captures its possible behaviors with high probability. This bound is then used to assist verification, and if the verification fails under this bound, the algorithm returns counter-examples to show how failure occurs and then uses these to refine the bound. We demonstrate the applicability of the approach through two case-studies: i) verifying controllers for a toy multi-robot system, and ii) verifying an instance of human-robot interaction during a lane-change maneuver given real-world human driving data. +
M
Thin film deposition is a manufacturing process in which tolerances may approach
the size of individual atoms. The final film is highly sensitive to the processing
conditions, which can be intentionally manipulated to control film properties. A
lattice model of surface evolution during thin film growth captures many important
features, including the nucleation and growth of clusters of atoms and the
propagation of atomic-height steps. The dimension of this probabilistic master
equation is too large to directly simulate for any physically realistic domain, and
instead stochastic realizations of the lattice model are obtained with kinetic Monte
Carlo simulations.
<p>
In this thesis simpler representations of the master equation are developed for
use in analysis and control. The static map between macroscopic process conditions
and microscopic transition rates is first analyzed. In the limit of fast periodic
process parameters, the surface responds only to the mean transition rates, and,
since the map between process parameters and transition rates is nonlinear, new
effective combinations of transition rates may be generated. These effective rates
are the convex hull of the set of instantaneous rates.
<p>
The map between transition rates and expected film properties is also studied.
The dimension of a master equation can be reduced by eliminating or grouping
configurations, yielding a reduced-order master equation that approximates the
original one. A linear method for identifying the coefficients in a master equation
is then developed, using only simulation data. These concepts are extended to
generate low-order master equations that approximate the dynamic behavior seen
in large Monte Carlo simulations. The models are then used to compute optimal
time-varying process parameters.
<p>
The thesis concludes with an experimental and modeling study of germanium
film growth, using molecular beam epitaxy and reflection high-energy electron
diffraction. Growth under continuous and pulsed flux is compared in experiment,
and physical parameters for the lattice model are extracted. The pulsing accessible
in the experiment does not trigger a change in growth mode, which is consistent
with the Monte Carlo simulations. The simulations are then used to suggest other
growth strategies to produce rougher or smoother surfaces.
R
Thin film deposition encompasses a variety of physical processes,
which occur over a wide range of length and time scales. A major challenge in modeling and simulating thin film deposition is this disparity
in scales. In this study we focus on an atomic-scale lattice model of
surface processes. Kinetic Monte Carlo simulations provide stochastic
realizations of the surface evolution, which may then inform a reacting flow or heat transfer model. Unfortunately, these simulations are
extremely computationally intensive, particularly for design and optimization studies in which many cases are considered.
<p>
We develop reduced-order models of thin film growth using two techniques: balanced truncation and eigensystem realization. After identifying the underlying structure of the lattice model as a linear differential
equation, we apply the reduction techniques to obtain reduced-order
models of root-mean-square roughness and step edge density. Three
modes are needed for a very small model system, while only five modes
capture the evolution of a 200x200-site system over a range of growth
modes, from stochastic roughening to island nucleation and coalescence. +
E
Thin film deposition is an industrially-important process that is highly dependent on the process
conditions. Most films are grown under constant conditions, but a few studies show that modified
properties may be obtained with periodic inputs. However, assessing the effects of modulation
experimentally becomes impractical with increasing material complexity. Here we consider periodic
conditions in which the period is short relative to the time-scales of growth. We analyze a stochastic
model of thin film growth, computing effective transition rates associated with rapid periodic
process parameters. Combinations of effective rates may exist which are not attainable under
steady conditions, potentially enabling new film properties. An algorithm is presented to construct
the periodic input for a desired set of effective transition rates. These ideas are first illustrated
by two simple examples using kinetic Monte Carlo simulations and are then compared to existing
deposition techniques. +
M
Modeling and Control of Thin Film Morphology Using Unsteady Processing Parameters: Problem Formulation and Initial Results +
Thin film deposition is an industrially-important process to which control theory has not historically been applied. The need for control is growing as the size of integrated
circuits shrinks, requiring increasingly tighter tolerances in the manufacture of thin films. Our contributions in this study are two-fold: we formulate a model of thin film
growth as a control system and we examine the effects of fast periodic forcing.
<p>
We choose a lattice formulation of crystal growth as our physical model, which captures atomic length scale effects at a time scale compatible with film growth. We focus on the control of film morphology, or surface height profile. Although the system
dimension is high, the structure is simple: the dynamics and the output are linear in the state. We consider the process conditions as inputs, which alter the transition rate
functions. In the evolution equation, each of these nonlinear functions is multiplied by a linear vector field, yielding a system with a structure similar to a bilinear system.
<p>
The process conditions in some deposition methods are inherently unsteady, which
produces films with altered morphology. We use the model developed in this study to analyze the effects of fast periodic forcing on thin film evolution. With the method of
averaging we develop new effective transition rates which may produce film properties
unattainable with constant inputs. We show that these effective rates are the convex
hull of the set of rates associated with constant inputs. We present conditions on
the convex hull for which the finite-time and infinite-time reachability sets cannot be
expanded with fast periodic forcing. An example in which this forcing increases the
reachability set and produces more desirable morphology is also presented. +
F
This paper deals with fault-tolerant controller design for linear time-invariant (LTI) systems with multiple actuators. Given some critical subsets of the actuators, it is assumed that every combination of actuators can fail as long as the set of the remaining actuators includes one of these subsets. Motivated by electric power systems and biological systems, the goal is to design a controller so that the closed-loop system satisfies two properties: (i) stability under all permissible sets of faults and (ii) better performance after clearing every subset of the existing faults in the system. It is shown that a state-feedback controller satisfying these properties exists if and only if a linear matrix inequality (LMI) problem is feasible. This LMI condition is then transformed into an optimal-control condition, which has a useful interpretation. The results are also generalized to output-feedback and decentralized control cases. The efficacy of this work is demonstrated by designing fault-tolerant speed governors for a power system. The results developed here can be extended to more general types of faults, where each fault can possibly affect all state-space matrices of the system. +
C
This article focuses on extending, disseminating and interpreting the findings of an IEEE Control Systems Society working group looking at the role of control theory and engineering in solving some of the many current and future societal challenges. The findings are interpreted in a manner designed to give focus and direction to both future education and research work in the general control theory and engineering arena, interpreted in the broadest sense. The paper is intended to promote discussion in the community and also provide a useful starting point for colleagues wishing to re-imagine the design and delivery of control-related topics in our education systems, especially at the tertiary level and beyond. +
