Property:Abstract
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G
Global Dynamical Structure Reconstruction from Reconstructed Dynamical Structure Subnetworks: Applications to Biochemical Reaction Networks +
In this paper we consider the problem of network reconstruction, with applications to biochemical reaction networks. In particular, we consider the problem of global network reconstruction when there are a limited number of sensors that can be used to simultaneously measure state information. We introduce dynamical structure functions as a way to formulate the network reconstruction problem and motivate their usage with an example physical system from synthetic biology. In particular, we argue that in synthetic biology research, network verification is paramount to robust circuit operation and thus, network reconstruction is an invaluable tool. Nonetheless, we argue that existing approaches for reconstruction are hampered by limited numbers of biological sensors with high temporal resolution. In this way, we motivate the global network reconstruction problem using partial network information and prove that by performing a series of reconstruction experiments, where each experiment reconstructs a subnetwork dynamical structure function, the global dynamical structure function can be recovered in most cases. We illustrate these reconstruction techniques on a recently developed four gene biocircuit, an event detector, and show that it is capable of differentiating the temporal order of input events. +
M
In this paper we consider the problem of repre- senting a biological system and its environment using a stochas- tic modeling framework. We first introduce a decomposition of the global chemical reaction system into two systems: a system of interest and its environment. We then present and derive a decomposition of the chemical master equation to achieve a representation describing the dynamics of the system of inter- est, perturbed by an environmental disturbance. We use this decomposition to model examples of two types of environmental disturbances: the disturbance a system experiences through loading effects from limited resources and the disturbance a system experiences when perturbed by an antibiotic that modifies transcription or translation rates. +
K
In this paper we describe the response of a Kinetic Monte Carlo model to
time-varying growth conditions. We vary temperature and partial pressure
sinusoidally and identify behavior typical of low-dimensional nonlinear
systems. In particular, the frequency content of the roughness response is
sensitive to the presence of steps in the surface. +
A
In this paper we discuss a resilient, risk-aware software architecture for onboard, real-time autonomous operations that is intended to robustly handle uncertainty in space- craft behavior within hazardous and unconstrained environ- ments, without unnecessarily increasing complexity. This architecture, the Resilient Spacecraft Executive (RSE), serves three main functions: (1) adapting to component failures to allow graceful degradation, (2) accommodating environments, science observations, and spacecraft capabilities that are not fully known in advance, and (3) making risk-aware decisions without waiting for slow ground-based reactions. This RSE is made up of four main parts: deliberative, habitual, and reflexive layers, and a state estimator that interfaces with all three. We use a risk-aware goal-directed executive within the deliberative layer to perform risk-informed planning, to satisfy the mission goals (specified by mission control) within the specified priorities and constraints. Other state-of-the-art algorithms to be integrated into the RSE include correct-by-construction control synthesis and model-based estimation and diagnosis. We demonstrate the feasibility of the architecture in a simple implementation of the RSE for a simulated Mars rover scenario. +
In this paper we discuss the application of correct-by-construction techniques to a resilient, risk-aware software architecture for onboard, real-time autonomous operations. We mean to combat complexity and the accidental introduction of bugs through the use of verifiable auto-coding software and correct-by-construction techniques, and discuss the use of a toolbox for correct-by-construction Temporal Logic Planning (TuLiP) for such a purpose. We describe some of TuLiPâs current functionality, specifically its ability to model symbolic discrete systems and synthesize software controllers and control policies that are correct-by-construction. We then move on to discuss the use of these techniques to define a deliberative goal-directed executive capability that performs risk-informed action-planning â to satisfy the mission goals (specified by mission control) within the specified priorities and constraints. Finally, we discuss an application of the TuLiP process to a simple rover resilience scenario. +
E
In this paper we evaluate the actuator rate requirements for control of rotating stall
using a bleed valve and provide tools for predicting these requirements. Modification of
both the stable and unstable parts of the compressor characteristic via addition of
continuous air injection serves to reduce the requirement of a bleed valve used for the
purpose of rotating stall stabilization. Analytical tools based on low order models (2-3
states) and simulation tools based on a reduced order model (37 states) are described. A
bleed actuator rate limit study is presented to compare the actuator requirements
predicted by theory, simulation, and experiment. The comparisons show that the predictions
obtained from theory and simulations share the same trend as the experiments, with
increasing accuracy as the complexity of the underlying model increases. Some insights on
the design of a bleed-compressor pair are given. +
D
In this paper we explore the use of time-delayed differential equation as a means of obtaining a simplified description of very high order dynamics.This paper finds results for a particular type of system, a single-input single-output (SISO) linear system with a nonlinear feedback. We begin with a high dimensional system in state space and reduce the dimension by finding a delay based approximation which could be a smaller set of integro-differential equations or DDEs. We argue that approximations of high order linear subsystems whose distribution functions have relatively smaller variance such as delta functions, give a conservative approximation of a system's stable parameter space. Through examples inspired by biology, we show how these approximations can be used to verify stability. We analyze the system's stability and robustness dependence on statistical properties, mainly relative variance and expectation for a symmetric distribution function. +
In this paper we give a formulation of differential flatness---a concept originally
introduced by Fleiss, Levine, Martin, and Rouchon---in terms of absolute equivalence
between exterior differential systems. Systems which are differentially flat have several
useful properties which can be exploited to generate effective control strategies for
nonlinear systems. The original definition of flatness was given in the context of
differentiable algebra, and required that all mappings be meromorphic functions. Our
formulation of flatness does not require any algebraic structure and allows one to use
tools from exterior differential systems to help characterize differentially flat systems.
In particular, we shown that in the case of single input control systems (i.e.,
codimension 2 Pfaffian systems), a system is differentially flat if and only if it is
feedback linearizable via static state feedback. However, in higher codimensions feedback
linearizability and flatness are *not* equivalent: one must be careful with the role of
time as well the use of prolongations which may not be realizable as dynamic feedbacks in
a control setting. Applications of differential flatness to nonlinear control systems and
open questions will be discussed. +
T
In this paper we introduce the Caltech
Multi-Vehicle Wireless Testbed (MVWT), a platform for testing
decentralized control methodologies for multiple vehicle
coordination and formation stabilization. The testbed consists of
eight mobile vehicles, an overhead vision system providing
GPS-like position information and wireless Ethernet for
communications. Each vehicle rests on omni-direction casters and
is powered by two high-performance ducted fans. Thus, a unique
feature of our testbed is that the vehicles have second order
dynamics, requiring real-time feedback algorithms to stabilize the
system while performing cooperative tasks. The testbed will be
used by various research groups at Caltech and elsewhere as a
means to validate theoretical advances in multiple-vehicle
coordination and control, networked control systems, real time
networking and high confidence distributed computation. +
N
In this paper we investigate methods for steering systems with nonholonomic
constraints between arbitrary configurations. Early work by Brockett derives the optimal
controls for a set of canonical systems in which the tangent space to the configuration
manifold is spanned by the input vector fields and their first order Lie brackets. Using
Brockett's result as motivation, we derive suboptimal trajectories for systems which are
not in canonical form and consider systems in which it takes more than one level of
bracketing to achieve controllability. These trajectories use sinusoids at integrally
related frequencies to achieve motion at a given bracketing level. We define a class of
systems which can be steered using sinusoids (chained systems) and give conditions under
which a class of two-input systems can be converted into this form. +
O
In this paper we investigate the optimal control of affine connection
control systems. The formalism of the affine connection can be used to
describe geometrically the dynamics of me chanical systems, including those
with nonholonomic constraints. In the standard variational approach to such
problems, one converts an n dimensional second order system into a 2n
dimensional first order system, and uses these equations as constraints on
the optimization. An alternative approach, which we develop in this paper,
is to include the system dynamics as second order constraints of the
optimization, and optimize relative to variations in the configuration
space. Using the affine connection, its associated tensors, and the notion
of covariant differentiation, we show how variations in the configuration
space induce variations in the tangent space. In this setting, we derive
second order equations have a geometric formulation parallel to that of the
system dynamics. They also specialize to results found in the literature. +
In this paper we look at the problem of multi-sensor data fusion when data is being communicated over
channels that drop packets randomly. We are motivated by
the use of wireless links for communication among nodes in
upcoming sensor networks. We wish to identify the information that should be communicated by each node to others given
that some of the information it had transmitted earlier might
have been lost. We solve the problem exactly for the case
of two sensors and study the performance of the algorithm
when more sensors are present. For the two-sensor case, the
performance of our algorithm is optimal in the sense that if
a packet is received from the other sensor, it is equivalent to
receiving all previous measurements, irrespective of the packet
drop pattern. +
N
In this paper we present a control law for globally asymptotically stabilizing a class
of controllable nonlinear systems without drift. The control law converts into closed loop
feedback earlier strategies for open loop steering of nonholonomic systems using sinusoids
at integrally related frequencies. The global result is obtained by introducing saturation
functions. Simulation results for stabilizing a simple kinematic model of an automobile
are included. +
C
In this paper we present a definition of "configuration controllability" for
mechanical systems whose Lagrangian is kinetic energy with respect to a Riemannian metric
minus potential energy. A computable test for this new version of controllability is also
derived. This condition involves a new object which we call the symmetric product. Of
particular interest is a definition of "equilibrium controllability" for which
we are able to derive computable sufficient conditions. Examples illustrate the theory. +
In this paper we present a dynamical systems framework for analyzing multi-agent rendezvous problems
and characterize the dynamical behavior of the collective system. Recently, the problem of rendezvous has been
addressed considerably in the graph theoretic framework, which is strongly based on the communication aspects of
the problem. The proposed approach is based on set invariance theory and focusses on how to generate feedback
between the vehicles, a key part of the rendezvous problem. The rendezvous problem is defined on the positions
of the agents and the dynamics is modeled as linear first order systems. The proposed framework however is not
fundamentally limited to linear first order dynamics and can be extended to analyze rendezvous of higher order agents. +
A
In this paper we present a dynamical systems representation for multi-agent rendezvous on
the phase plane. We restrict our attention to two agents, each with scalar dynamics. The problem of rendezvous is cast as a stabilization problem, with a set of constraints on the trajectories
of the agents, defined on the phase plane. We also describe a method to generate control Lyapunov functions that when used in conjunction with a stabilizing control law, such as Sontag's
formula, make sure that the two-agent system attains rendezvous. The main result of this paper
is a Lyapunov-like certificate theorem that describes a set of constraints, which when satisfied
are su±cient to guarantee rendezvous. +
V
In this paper we present two methods, the nonholonomic method and the vakonomic
method, for deriving equations of motion for a mechanical system with constraints. The
resulting equations are compared. Results are also presented from an experiment for a
model system: a ball rolling without sliding on a rotating table. Both sets of equations
of motion for the model system are compared with the experimental results. The effects of
various forms of friction are considered in the nonholonomic equations. With appropriate
friction terms, the nonholonomic equations of motion for the model system give reasonable
agreement with the experimental observations. +
N
In this paper we provide new design principles
for estimation over wireless fading channels in mobile sensor
networks. We show how to optimize receiver and transmitter
designs to improve estimation performance in the application
layer. On the receiver side, we show that the optimum packet
drop mechanism is the one that provides a balance between
information loss and communication noise. On the transmitter
side, we show how to optimize and adapt the transmission
rate for performance improvement in the application layer.
We further provide stability conditions for different design
strategies. The work confirms that delay-sensitive mobile
sensor applications require new design paradigms and applying
the same design principles of data networks can lead
to performance degradation. The work also highlights the
importance of cross-layer feedback and provides alternative
designs if such feedbacks are not available. +
S
In this paper we study the problem of synthesizing correct-by-construction Behavior Trees (BTs) controlling agents in adversarial environments. The proposed approach combines the modularity and reactivity of BTs with the formal guarantees of Linear Temporal Logic (LTL) methods. Given a set of admissible environment specifications, an agent model in form of a Finite Transition System and the desired task in form of an LTL formula, we synthesize a BT in polynomial time, that is guaranteed to correctly execute the desired task. To illustrate the approach, we present three examples of increasing complexity. +
P
In this paper we study the stabilization problem for control systems
defined on SE(3), the Euclidean group of rigid--body motions.
Assuming one actuator is available for each degree of freedom, we
exploit geometric properties of Lie groups (and corresponding Lie
algebras) to generalize the classical PD control in a coordinate--free
way. For the SO(3) case, the compactness of the group gives rise to a
natural metric structure and to a natural choice of preferred control
direction: an optimal (in the sense of geodesic) solution is given to
the attitude control problem. In the SE(3) case, no natural metric is
uniquely defined, so that more freedom is left in the control design.
Different formulations of PD feedback can be adopted by extending the
SO(3) approach to the whole of SE(3) or by breaking the problem into a
control problem on SO(3) x R^3. For the simple SE(2) case,
simulations are reported to illustrate the behavior of the different
choices. Finally, we discuss the trajectory tracking problem and show
how to reduce it to a stabilization problem, mimicking the usual
approach in R^n. +
