Property:Abstract
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F
In systems and synthetic biology, it is common to build chemical reaction network (CRN) models of biochemical circuits and networks. Although automation and other high-throughput techniques have led to an abundance of data enabling data-driven quantitative modeling and parameter estimation, the intense amount of simulation needed for these methods still frequently results in a computational bottleneck. Here we present bioscrape (Bio-circuit Stochastic Single-cell Reaction Analysis and Parameter Estimation) - a Python package for fast and flexible modeling and simulation of highly customizable chemical reaction networks. Specifically, bioscrape supports deterministic and stochastic simulations, which can incorporate delay, cell growth, and cell division. All functionalities - reaction models, simulation algorithms, cell growth models, partitioning models, and Bayesian inference - are implemented as interfaces in an easily extensible and modular object-oriented framework. Models can be constructed via Systems Biology Markup Language (SBML) or specified programmatically via a Python API. 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 show the package’s simulation capabilities on a variety of example simulations of stochastic gene expression. We also demonstrate the package by using it to do parameter inference on a model of integrase enzyme-mediated DNA recombination dynamics with experimental data. The bioscrape package is publicly available online (Pandey, Poole, et al., 2023) along with more detailed documentation and examples. +
A
In the geometric theory of nonlinear control systems, the notion of a distribution and
the dual notion of codistribution play a central role. Many results in nonlinear control
theory require certain distributions to be integrable. Distributions (and codistributions)
are not generically integrable and, moreover, the integrability property is not likely to
persist under small perturbations of the system. Therefore, it is natural to consider the
problem of approximating a given codistribution by an integrable codistribution, and to
determine to what extent such an approximation may be used for obtaining approximate
solutions to various problems in control theory. In this note, we concentrate on the
purely mathematical problem of approximating a given codistribution by an integrable
codistribution. We present an algorithm for approximating an m-dimensional nonintegrable
codistribution by an integrable one using a homotopy approach. The method yields an
approximating codistribution that agrees with the original codistribution on an
m-dimensional submanifold E_0 of R^n. +
U
Uncertain semantics, representation nuisances, and necessary invariance properties of bootstrapping agents +
In the problem of bootstrapping, an agent must learn to use an unknown body, in an unknown world, starting from zero information about the world, its sensors, and its actuators. So far, this fascinating problem has not been given a proper formalization. In this paepr, we provide a possible rigorous definition of one of the key aspects of bootstrapping, namely the fact that an agent must be able to use âuninterpretedâ observations and commands. We show that this can be formalized by positing the existence of representation nuisances that act on the data, and which must be tolerated by an agent. The classes of nuisances tolerated indirectly encode the assumptions needed about the world, and therefore the agent's ability to solve smaller or larger classes of bootstrapping instances. Moreover, we argue that the behavior of an agent that claims optimality must actually be invariant to the representation nuisances, and we discuss several design principles to obtain such invariance. +
C
In this article is presented a dynamical systems framework for analysing multi-agent rendezvous problems and characterize the dynamical behaviour 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 the 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 modelled as linear first-order systems. These algorithms have also been applied to non-linear first-order systems.
The rendezvous problem in the framework of cooperative and competitive dynamical systems is analysed that has had some remarkable applications to biological sciences. Cooperative and competitive dynamical systems are shown to generate monotone flows by the classical Muller--Kamke theorem, which is analysed using the set invariance theory. In this article, equivalence between the rendezvous problem and invariance of an appropriately defined cone is established. The problem of rendezvous is cast as a stabilization problem, with a the set of constraints on the trajectories of the agents defined on the phase plane. The n-agent rendezvous problem is formulated as an ellipsoidal cone invariance problem in the n-dimensional phase space. Theoretical results based on set invariance theory and monotone dynamical systems are developed. The necessary and sufficient conditions for rendezvous of linear systems are presented in the form of linear matrix inequalities. These conditions are also interpreted in the Lyapunov framework using multiple Lyapunov functions. Numerical examples that demonstrate application are also presented. +
O
In this chapter, we present a framework for online control customization that
makes use of finite-horizon, optimal control combined with real-time
trajectory generation and optimization. The results are based on a novel
formulation of receding-horizon optimal control that replaces the traditional
terminal constraints with a control Lyapunov function-based terminal cost.
This formulation leads to reduced computational requirements and allows proof
of stability under a variety of realistic assumptions on computation. By
combining these theoretical advances with advances in computational power for
real-time, embedded systems, we demonstrate the efficacy of online control
customization via optimization-based control. The results are demonstrated
using a nonlinear, flight control experiment at Caltech. +
D
In this letter we present a decomposition for control systems whose drift vector field
is the geodesic spray associated with an affine connection. With the geometric insight
gained with this decomposition, we are able to easily prove some special results for this
class of control systems. Examples illustrate the theory. +
O
On a Stochastic Sensor Selection Algorithm with Applications in Sensor Scheduling and Sensor Coverage +
In this note we consider the following problem. Suppose a set of sensors is jointly trying to estimate a process. One sensor takes a measurement at every time step and the measurements are then exchanged among all the sensors. What is the sensor schedule that results in the mininmum error covariance? We describe a stoachastic sensor selection strategy that is easy to implement and is computationally tractable. The problem described above comes up in many domains out of which we discuss two. In the sensor selection problem, there are multiple sensors that cannot operate simultaneously (eg, sonars in the same frequency band). Thus measurements need to be scheduled. In the sensor coverage problem, a geographical area needs to be covered by mobile sensors each with limited range. Thus from every position, the sensors obtain a different viewpoint of the area and the sensors need to optimize their positions. The algorithm is applied to these problems and illustrated through simple examples. +
A
In this paper analysis of interconnected dynamical systems
is considered. A framework for the analysis of the stability
of interconnection is given. The results from Fax and
Murray that studies the SISO-case for a constant interconnection
matrix are genralized to the MIMO-case where
arbitrary interconnection is allowed. The analysis show existness
of a separation principle that is very useful in the
sense of the simplicity for stability analysis. Stability could
be checked graphically using a Nyquist-like criterion. The
problem with time-delays and interconnection variation and
robustness appear to be natural special cases of the general
framework, and hence, simple stability criteria are derived
easly. +
E
In this paper various design techniques are applied to the trajectory tracking problem for a mobile
robot with trailers. Using simulations and experiments, we evaluate linear and nonlinear designs
on the basis of implementation issues, stability and performance. After a careful design of their
gains, the various feedback controllers have very close performance measures. In both the
simulations and the experiments, all the controllers show a strong dependence on the knowledge
of the reference trajectory. The flatness of the system is exploited in precomputing this quantity. +
In this paper we analyze the effects of fluid noise, actuator bandwidth,
magnitude saturation and rate limits on rotating stall control by
studying a two dimensional system which is the approximation
of the dynamics on the attracting saddle-sink connections of the three
state low $B$ parameter Moore Greitzer model together with the
dynamics of the bleed valve controller. We show that the region of
attraction to the stabilized rotating stall
equilibria is seriously restrained by the fluid noise level, the
actuator bandwidth, magnitude saturation and rate limits. The
bandwidth and rate requirement for a fixed extension of stable region
is estimated by calculating the stable manifold of the saddle fixed
point of the two dimensional system. +
In this paper we apply some recently developed control laws for
stabilization of mechanical systems with nonholonomic constraints to
an experimental system consisting of a mobile robot towing a trailer.
We verify the applicability of various control laws which have
appeared in the recent literature, and compare the performance of
these controllers in an experimental setting. In particular, we show
that time-periodic, non-smooth controllers can be used to achieve
exponential stability of a desired equilibrium configuration, and that
these controllers outperform smooth, time-varying control laws. We
also point out several practical considerations which must be taken
into account when implementing these controllers. +
A
A hovercraft robot that uses insect-inspired visual autocorrelation for motion control in a corridor +
In this paper we are concerned with the challenge of flight control of computationally-constrained micro-aerial vehicles that must rely primarily on vision to navigate confined spaces. We turn to insects for inspiration. We demonstrate that it is possible to control a robot with inertial, flight-like dynamics in the plane using insect-inspired visual autocorrelators or âelementary motion detectorsâ (EMDs) to detect patterns of visual optic flow. The controller, which requires minimal computation, receives visual information from a small omnidirectional array of visual sensors and computes thrust outputs for a fan pair to stabilize motion along the centerline of a corridor. To design the controller, we provide a frequency- domain analysis of the response of an array of correlators to a flat moving wall. The model incorporates the effects of motion parallax and perspective and provides a means for computing appropriate inter-sensor angular spacing and visual blurring. The controller estimates the state of robot motion by decomposing the correlator response into harmonics, an analogous operation to that performed by tangential cells in the fly. This work constitutes the first-known demonstration of control of non-kinematic inertial dynamics using purely correlators. +
C
Communication and Sensing Trade-Offs in Decentralized Mobile Sensor Networks: A Cross-Layer Design Approach +
In this paper we characterize the impact of imperfect communication
on the performance of a decentralized mobile sensor network.
We first examine and demonstrate the trade-offs between communication
and sensing objectives, by determining the optimal sensor configurations
when introducing imperfect communication. We further illustrate the
performance degradation caused by non-ideal communication links in
a decentralized mobile sensor network. To address this, we propose a
decentralized motion-planning algorithm that considers communication
effects. The algorithm is a cross-layer design based on the proper interface
of physical and application layers. Simulation results will show the
performance improvement attained by utilizing this algorithm. +
E
Estimation Over Wireless Sensor Networks: Tradeoff between Communication, Computation and Estimation Qualities +
In this paper we consider a state estimation problem over a wireless sensor network. A fusion center dynamically forms a local multi-hop tree of sensors and fuses the data into a state estimate. It is shown that the optimal estimator over a sensor tree is given by a Kalman filter of certain structure. Using estimation quality as a metric, two communication schemes are studied and compared. In scheme one, sensor nodes communicate measurement data to their parent nodes, while in scheme two, sensor nodes communicate their local state estimates to their parent nodes. We show that under perfect communication links, the two schemes produce the same estimate at the fusion center with unlimited computation at each sensor node; scheme one is always better than scheme two with limited computation. When data packet drops occur on the communication links, we show that scheme two always outperforms scheme one with unlimited computation; with limited computation, we show that there exists a critical packet arrival rate, above which, scheme one outperforms scheme two. Simulations are provided to demonstrate the two schemes under various circumstances. +
F
In this paper we consider nonlinear systems with steady-state or Hopf bifurcations for
which the bifurcated modes are linearly uncontrollable. The goal is to find state
feedbacks such that the bifurcation for the closed loop system is supercritical, and at
the same time, the linearly controllable subsystem is asymptotically stable. Necessary and
sufficient conditions for the non-existence of sufficiently smooth state feedbacks have
been obtained under certain nondegeneracy conditions. For the cases when those conditions
are not satisfied, we give explicit constructions of the feedbacks. The construction has
the following separation property: for any linear state feedback such that the
controllable subsystem is asymptotically stable, we could construct gains in the nonlinear
state feedbacks such that the closed loop system is asymptotically stable at the
bifurcation point. +
O
Optimal Sensor Hop Selection: Sensor Energy Minimization and Network Lifetime Maximization with Guaranteed System Performance +
In this paper we consider state estimation carried over a sensor network. A fusion center forms a local multi-hop tree of sensors and gateways and fuses the data into a state estimate. It is shown that the optimal estimator over a sensor tree is given by a Kalman filter of certain structure. The number of hops that the sensors use to communicate data with the fusion center is optimized such that either the overall transmission energy is minimized or the network lifetime is maximized. In both cases the fusion center provides a specified level of estimation accuracy. Some heuristic algorithms are proposed which lead to suboptimal solutions in the energy minimization problem, while an algorithm that leads to the global optimal solution is proposed in the lifetime maximization problem. In both cases, the algorithms are shown to have low computational complexity. Examples are provided to demonstrateand algorithms. +
In this paper we consider task scheduling when
sensing and controlling over a network with packet dropping
links. We find optimum ways of allocating limited computing
resources for estimation and control of a number
of linear dynamical systems with different characteristics
over communication links with different qualities. We find
theoretical expressions relating the optimum sampling rates to
the characteristics of the communication links and dynamics of
the plants.When considering resource allocation for estimation
of the plants, we derive optimum ways of task scheduling for
two performance metrics: decay rate and the asymptotic value
of the estimation error variance. When scheduling the control
tasks, we consider rate of convergence of the state and the
overall control cost as performance measures. The work lays
the theoretical foundations for considering the impact of both
limited computing and communication resources on estimation
and control. +
C
In this paper we consider the impact of communication noise on distributed sensing and estimation in mobile networks. We characterize when a node should rely on getting information from others and when it should rely on self exploration. In doing so, we explore the trade-offs between sensing and communication by finding the optimum network configuration under communication constraints. We also show how to achieve the optimum configuration in a distributed manner. While our main results are presented in one dimension (1D), we provide insight into the two dimension (2D) setup and extend a number of key results to 2D. +
T
In this paper we consider the problem of generating feasible motions
for a towed cable, flight control system that has been proposed for
use in remote sensor applications. Using the fact that the system is
differentially flat, we illustrate how to construct feasible
trajectories for the system and demonstrate the strengths and
limitations of this approach. Simulations of the full dynamics are
included to illustrate the proposed techniques. A significant
limitation of the current approach is the numerical instability of the
algorithm, resulting in the need for careful tuning of parameters to
achieve convergence. +
O
In this paper we consider the problem of estimating discrete
variables in a class of hybrid systems where we assume that the continuous
variables are available for measurement. Using lattice and order
theory we develop a framework for constructing an observer on an enlarged
space of variables with lattice structure, which updates only two
variables at each step. We apply our ideas to a multi-robot system example,
the RoboFlag Drill. +
