Property:Abstract
From Murray Wiki
Jump to navigationJump to search
This is a property of type Text.
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. +
S
Modern aircraft increasing rely on electric power, resulting in high safety-criticality and complexity in their electric power generation and distribution systems. Moti- vated by the resulting rapid increase in the costs and duration of the design cycles for such systems, we investigate the use of formal specification and automated, correct-by-construction control protocols synthesis for primary distribution in vehicular electric power networks. We discuss a design workflow that aims to transition from the traditional âdesign+verifyâ approach to a âspecify+synthesizeâ approach. We give an overview of a subset of the recent advances in the synthesis of reactive control proto- cols. We apply these techniques in the context of reconfiguration of the networks in reaction to the changes in their operating environment. We also validate these automatically synthesized control protocols on high-fidelity simulation models and on an academic-scale hardware testbed. +
A
An Aircraft Electric Power Testbed for Validating Automatically Synthesized Reactive Control Protocols +
Modern aircraft increasingly rely on electric power for sub- systems that have traditionally run on mechanical power. The complexity and safety-criticality of aircraft electric power systems have therefore increased, rendering the design of these systems more challenging. This work is mot vated by the potential that correct-by-construction reactive controller synthesis tools may have in increasing the effectiveness of the electric power system design cycle. In particular, we have built an experimental hardware platform that captures some key elements of aircraft electric power systems within a simplified setting. We intend to use this plat- form for validating the applicability of theoretical advances in correct-by-construction control synthesis and for study- ing implementation-related challenges. We demonstrate a simple design workflow from formal specifications to auto- generated code that can run on software models and be used in hardware implementation. We show some preliminary results with different control architectures on the developed hardware testbed. +
F
Modern safety-critical systems are difficult to formally verify, largely due to their large scale. In particular, the widespread use of lookup tables in embedded systems across diverse industries, such as aeronautics and automotive systems, create a critical obstacle to the scala- bility of formal verification. This paper presents a novel approach for the formal verification of large-scale systems with lookup tables. We use a learning-based technique to automatically learn abstractions of the lookup tables and use the abstractions to then prove the desired property. If the verification fails, we propose a falsification heuristic to search for a violation of the specification. In contrast with previous work on lookup table verification, our technique is completely automatic, making it ideal for deployment in a production environment. To our knowledge, our approach is the only technique that can automatically verify large-scale systems lookup with tables.
We illustrate the effectiveness of our technique on a benchmark which cannot be handled by the commer- cial tool SLDV, and we demonstrate the performance improvement provided by our technique. +
B
Bistable State Switch Enables Ultrasensitive Feedback Control in Heterogeneous Microbial Populations +
Molecular feedback control circuits can improve robustness of gene expression at the single cell-level. This achievement can be offset by requirements of rapid protein expression, that may induce cellular stress, known as burden, that reduces colony growth. To begin to address this challenge we take inspiration by ‘division-of-labor’ in heterogeneous cell populations: we propose to combine bistable switches and quorum sensing systems to coordinate gene expression at the population-level. We show that bistable switches in individual cells operating in parallel yield an ultrasensitive response, while cells maintain heterogeneous levels of gene expression to avoid burden across all cells. Within a feedback loop, these switches can achieve robust reference tracking and adaptation to disturbances at the population-level. We also demonstrate that molecular sequestration enables tunable hysteresis in individual switches, making it possible to obtain a wide range of stable population-level expressions. +
R
Most automated systems operate in uncertain or adversarial conditions, and have to be capable of reliably reacting to changes in the environment. The focus of this paper is on automatically synthesizing reactive controllers for cyber-physical systems subject to signal temporal logic (STL) specifications. We build on recent work that encodes STL specifications as mixed integer linear constraints on the variables of a discrete-time model of the system and environment dynamics. To obtain a reactive controller, we present solutions to the worst-case model predictive control (MPC) problem using a suite of mixed integer linear programming techniques. We demonstrate the comparative effectiveness of several existing worst-case MPC techniques, when applied to the problem of control subject to temporal logic specifications; our empirical results emphasize the need to develop specialized solutions for this domain. +
Motion planning in environments with multiple agents is critical to many important autonomous applications such as autonomous vehicles and assistive robots. This paper considers the problem of motion planning, where the controlled agent shares the environment with multiple uncontrolled agents. First, a predictive model of the uncontrolled agents is trained to predict all possible trajectories within a short horizon based on the scenario. The prediction is then fed to a motion planning module based on model predictive control. We proved generalization bound for the predictive model using three different methods, post-bloating, support vector machine (SVM), and conformal analysis, all capable of generating stochastic guarantees of the correctness of the predictor. The proposed approach is demonstrated in simulation in a scenario emulating autonomous highway driving. +
S
Motivated by current technological advances in the design of real-time embedded systems, this work deals with the digital control of a continuous-time linear time-invariant (LTI) system whose output can be sampled at a high frequency. Since a typical sampled-data controller operating at a high sampling frequency needs heavy (high-precision) computation to alleviate its sensitivity to measurement and computational errors, the objective is to design a robust hybrid controller for high- frequency applications with limited computational power. To this end, we exploit our recent results on delay-based controller design and propose a digital-control scheme that can implement every continuous-time stabilizing (LTI) controller. This robust hybrid controller, which consists of an ideal sampler, a digital controller, a number of modified second-order holds and possibly a unity feedback, can operate at arbitrarily high sampling frequencies without requiring expensive, high-precision computation. Later on, it is discussed how to find a continuous-time LTI controller satisfying prescribed design specifications so that its correspond- ing digital controller requires the least processing time. +
I
Motivated by exploration of communication- constrained underground environments using robot teams, we study the problem of planning for intermittent connectivity in multi-agent systems. We propose a novel concept of information-consistency to handle situations where the plan is not initially known by all agents, and suggest an integer linear program for synthesizing information-consistent plans that also achieve auxiliary goals. Furthermore, inspired by network flow problems we propose a novel way to pose connectivity constraints that scales much better than previous methods. In the second part of the paper we apply these results in an exploration setting, and propose a clustering method that separates a large exploration problem into smaller problems that can be solved independently. We demonstrate how the resulting exploration algorithm is able to coordinate a team of ten agents to explore a large environment. +
S
Motivated by problems in flight control, we present a technique for
stabilizing a chain
of integrators in the presence of rate limitations on the input. Our
technique improves on several existing techniques in the literature
and has a number of interesting features. The controller is
evaluated experimentally on a pitch axis flight control experiment at
Caltech. The experimental results show that even in the presence of
rate limits that cause a linear controller to go unstable, the
time-varying controller stabilizes the system with minimal loss in performance. +
E
Motivated by problems such as active control of rotating stall in compression systems,
an analysis of the effects of controller magnitude saturation in feedback stabilization of
steady-state bifurcations is performed. In particular the region of attraction to the
stabilized bifurcated equilibria is solved for feedback controllers with magnitude
saturation limits using the technique of center manifold reduction and bifurcation
analysis. It has been shown that the stability boundary is the saturation envelope formed
by the unstable (or stable) equilibria for the closed loop system when the controllers
saturate. The framework allows the design of feedback control laws to achieve desirable
size of region of attraction when the noise is modeled as a closed set of initial
conditions in the phase space. It is also possible to extend the techniques and results to
Hopf bifurcations. +
