Property:Abstract
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E
Effective Sensor Scheduling Schemes in a Sensor Network by Employing Feedback in the Communication Loop +
In this paper, we consider a state estimation problem over a bandwidth limited network. A sensor network consisting of N sensors is used to observe the states of M plants, but only p les N sensors can transmit their measurements to a centralized esti..... +
D
In this paper, we consider the following problem. Suppose a sensor is taking measurements of a dynamic process.
It needs to communicate the information over a network of communication links that can drop packets stochastically. What
is the optimal processing at each node in the network? We provide a strategy that yields the optimal performance at the
cost of constant memory and processing at each node. We also provide conditions on the network for the estimate error
covariance to be stable under this algorithm. +
F
In this paper, we consider the optimal control of time-scalable systems.
The time-scaling property is shown to convert the PDE associated
with the Hamilton-Jacobi-Bellman (HJB) equation to a purely spatial PDE.
Solution of this PDE yields the value function at a fixed time, and that solutio
n can be
scaled to find the value function at any point in time. Furthermore, in certain
cases the
unscaled control law stabilizes the system, and the unscaled value function acts
as a
Lyapunov function for that system. For the example of the
nonholonomic integrator, this PDE is solved, and the
resulting optimal trajectories coincide with the known solution to that problem. +
O
In this paper, we consider the problem of active
sensing using mobile sensor nodes that are jointly estimating
the state of a dynamic target as a sensor network. We propose
a gradient search-based decentralized algorithm that demonstrates
the benefits of distributed sensing. We then examine the
task of tracking multiple targets. We use a greedy algorithm
for associating sensors with targets along with the gradientsearch
strategy for sensor vehicle motion planning. Simulation
results show that these simple decentralized strategies perform
quite well and the sensor nodes exhibit interesting cooperative
behavior. +
T
In this paper, we consider the problem of state estimation
using the standard Kalman filter recursions which takes
account of the available sensor health information. Given
a stochastic description of the sensor health, we are able
to show that the expected error covariance converges to a
unique value for all initial values, while the available
previous work only showed the upper bound of the expected
error covariance converges. Our approach provides both
theoretical value to the analysis as well as the potential
to get tighter upper bound. Our results provide a criterion
of evaluating the sensor measurement. In the multisensor
fusion problem, depending on the system error tolerance
levels, it can then be determined whether to fuse a
particular sensor measurement or not. Examples and
simulations are provided to assist the theory. +
A
In this paper, we consider the problem of synthesizing correct-by-construction controllers for discrete-time dynamical systems. A commonly adopted approach in the literature is to abstract the dynamical system into a finite transition system (FTS) and thus convert the problem into a two player game between the environment and the system on the FTS. The controller design problem can then be solved using synthesis tools for general linear temporal logic or generalized reactivity(1) (GR1) specifications. In this article, we propose a new abstraction algorithm. Instead of generating a single FTS to represent the system, we generate two FTSs, which are underand over-approximations of the original dynamical system. We further develop an iterative abstraction scheme by exploiting the concept of winning sets, i.e., the sets of states for which there exists a winning strategy for the system. Finally, the e�ciency of the new abstraction algorithm is illustrated by numerical examples. +
S
In this paper, we consider the scenario where many sensors
co-operate to estimate a process. Only one sensor can take
a measurement at any time step. We wish to come up with
optimal sensor scheduling algorithms. The problem is motivated
by the use of sonar range-finders used by the vehicles
on the Caltech Multi-Vehicle Wireless Testbed. We see that
this problem involves searching a tree in general and propose
and analyze two strategies for pruning the tree to keep
the computation limited. The first is a sliding window strategy
motivated by the Viterbi algorithm, and the second one
uses thresholding. We also study a technique that employs
choosing the sensors randomly from a probability distribution
which can then be optimized. The performance of the
algorithms are illustrated with the help of numerical examples. +
R
In this paper, we describe a receding horizon scheme that satisfies a class of linear temporal logic specifications sufficient to describe a wide range of properties including safety, stability, progress, obligation, response and guarantee. The resulting embedded control software consists of a goal generator, a tra jectory planner, and a continuous controller. The goal generator essentially reduces the tra jectory generation problem to a sequence of smaller problems of short horizon while preserving the desired system-level temporal properties. Subsequently, in each iteration, the tra jectory planner solves the corresponding short-horizon problem with the currently observed state as the initial state and generates a feasible tra jectory to be implemented by the continuous controller. Based on the simulation property, we show that the composition of the goal generator, tra jectory planner and continuous controller and the corresponding receding horizon scheme guarantee the correctness of the system. To handle failures that may occur due to a mismatch between the actual system and its model, we propose a response mechanism and illustrate, through an example, how the system is capable of responding to certain failures and continues to exhibit a correct behavior. +
A
An In Silico Modeling Toolbox for Rapid Prototyping of Circuits in a Biomolecular “Breadboard” System +
In this paper, we develop an experimentally val- idated MATLAB software toolbox as an accompaniment to an in vitro cell-free biomolecular “breadboard” system. The toolbox gives insight into the dynamics of unmeasured states in the cell-free system, accounting especially for the resource usage. Parameter lumping and the reduced order modeling are used to maintain computational tractability and to avoid ill-conditioning. The toolbox allows for most applications to be implemented with standard set of commands for ease of use. Due to the breadboarding nature of the underlying cell-free sys- tem, the toolbox provides a general framework for experiment planning and predictive modeling for synthetic biomolecular circuits cell-free systems, accelerating our capacity to rationally design circuits from well characterized parts. +
T
In this paper, we develop the machinery of exterior differential forms, more particularly the Goursat normal form for a Pfaffian system, for solving nonholonomic motion planning problems, i.e., motion planning for systems with nonintegrable velocity constraints. We use this technique to solve the problem of steering a mobile robot with n trailers, We present an algorithm for finding a family of transformations which will convert the system of rolling constraints on the wheels of the robot with n trailers into the Goursat canonical form. Two of these transformations are studied in detail. The Goursat normal form for exterior differential systems is dual to the so-called chained-form for vector fields that has been studied previously. Consequently, we are able to give the state feedback law and change of coordinates to convert the N-trailer system into chained form. Three methods for planning trajectories for chained-form systems using sinusoids, piecewise constants, and polynomials as inputs are presented.
The motion planning strategy is therefore to first convert the N-trailer system into Goursat form, use this to find the chained-form coordinates, plan a path for the corresponding chained-form system, and then transform the resulting trajectory back into the original coordinates. Simulations and frames of movie animations of the N-trailer system for parallel parking and backing into a loading dock using this strategy are included. +
C
In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no time-delays, ii) networks with fixed topology and communication time-delays, and iii) max-consensus problems (or leader determination) for groups of discrete-time agents. In each case, we introduce a linear/nonlinear consensus protocol and provide convergence analysis for the proposed distributed algorithm. Moreover, we establish a connection between the Fiedler eigenvalue of the information flow in a network (i.e. algebraic connectivity of the network) and the negotiation speed (or performance) of the corresponding agreement protocol. It turns out that balanced digraphs play an important role in addressing average-consensus problems. We introduce disagreement functions that play the role of Lyapunov functions in convergence analysis of consensus protocols. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results. +
R
Resource Competition as a Source of Non-Minimum Phase Behavior in Transcription-Translation Systems +
In this paper, we explore how resource limitations can lead to coupling interactions between orthogonal com- ponents in a transcription-translation system and the effect those interactions have on its dynamical behavior. To illustrate these ideas, we present a motivating example featuring a classical network motif: the signal cascade. We show that through coupling interactions arising from competition for limited resources, the system exhibits a non-minimum phase step response. These observations lead us to identify a key network motif with the potential to introduce right half plane zeros into the system transfer function. We characterize the parametric conditions under which the network motif produces a non-minimum phase transfer function and illustrate with two examples how resource limitations can 1) introduce the network motif through these coupling interactions, 2) satisfy the parametric conditions sufficient to produce a right half plane zero. +
F
In this paper, we generalize a recently proposed
method for model reduction of linear systems to the frequencyweighted
case. The method uses convex optimization and can be
used both with sample data and exact models. We also derive
simple a priori bounds on the frequency-weighted error. We
combine the method with a rank-minimization heuristic, to
approximate multi-inputÂmulti-output systems. We also present
two applications  environment compensation and simpli�cation
of interconnected models  where we argue the proposed
methods are useful. +
C
In this paper, we introduce a consensus protocol for a network of dynamic
agents that allows the agents to reach
a decision in a distributed and cooperative
fashion. We consider both linear and nonlinear protocols as well as
the characteristic function of the communication links in the network.
This includes links with delay and (possible) distortion/filtering effects.
It turns out that for a number of protocols, the convergence properties
and the decision-value obtained via this protocol is strongly related
to connectivity and algebraic graph theoretic properties of the information
flow in the network of decision-making agents. Standard
tools from multivariable control and linear control theory such as Nyquist
plots appear naturally for convergence analysis of the obtained linear
protocols. For the analysis of the nonlinear protocols, certain
disagreement costs are constructed that are minimized by the consensus
protocols in a distributed way. Simulation results are provided for attitude
alignment of a group of 20 dynamic agents. +
S
In this paper, we investigate formal test-case generation for high-level mission objectives, specifically reachability, of autonomous systems. We use Kripke structures to represent the high-level decision-making of the agent under test and the abstraction of the test environment. First, we define the notion of a test specification, focusing on a fragment of linear temporal logic represented by sequence temporal logic formulas. Second, we formulate the problem of test graph synthesis to find a test configuration for which the agent must satisfy the test specification to satisfy its mission objectives. We an algorithm, based on network flows, for synthesizing a test graph by restricting transitions, represented by edge deletions, on the original graph induced by the Kripke structures. The algorithm synthesizes the test graph iteratively using an integer linear program. We prove completeness for our algorithm, and we show that the edge deletions in each iteration maintain feasibility of the integer linear program in the subsequent iteration. We formalize the notion of a minimally constrained test graph in terms of maximum flow, and prove the synthesized test graph to be minimally constrained. We demonstrate our algorithm on a simple graph and on gridworlds. +
P
In this paper, we investigate pre-orders for reasoning about input-to-state stability properties of hybrid systems. We define the notions of uniformly continuous input simulations and bisimulations, which extend the notions in previous work to include inputs. We show that uniformly con- tinuous input bisimulations preserve incremental input-to-state stability of hybrid systems, and thus provide a basis for constructing abstractions for verification. We show that Lyapunov function based input-to-state stability analysis can be cast in our framework as constructing a simpler one-dimensional system, using a uniformly continuous input simulation, which is input-to-state stable, and thus, inferring the input-to-state stability of the original system. +
B
In this paper, we investigate pre-orders for reason- ing about input-to-state stability properties of hybrid systems. We define the notions of uniformly continuous input simulations and bisimulations, which extend the notions in previous work to include inputs. We show that uniformly continuous input bisimulations preserve incremental input-to-state stability of hybrid systems, and thus provide a basis for constructing abstractions for verification. We show that Lyapunov function based input-to-state stability analysis can be cast in our frame- work as constructing a simpler one-dimensional system, using a uniformly continuous input simulation, which is input-to-state stable, and thus, inferring the input-to-state stability of the original system. +
P
In this paper, we pose the N-scalar agent rendezvous
as a polyhedral cone invariance problem in the N
dimensional phase space. The underlying dynamics of the
agents are assumed to be linear. We derive a condition
for positive invariance for polyhedral cones. Based on this
condition, we demonstrate that the problem of determining a
certificate for rendezvous can be stated as a convex feasibility
problem. Under certain rendezvous requirements, we show
that there are no robust closed-loop linear solutions that satisfy
the invariance conditions. We show that the treatment of the
rendezvous problem on the phase plane can be extended to
the case where agent dynamics are non-scalar. +
D
Distributed Cooperative Control of Multiple Vehicle Formations Using Structural Potential Functions +
In this paper, we propose a framework for formation stabilization of
multiple autonomous vehicles in a distributed fashion. Each vehicle is assumed to
have simple dynamics, i.e. a double-integrator, with a directed (or an undirected)
information ow over the formation graph of the vehicles. Our goal is to find
a distributed control law (with an efficient computational cost) for each vehicle
that makes use of limited information regarding the state of other vehicles. Here,
the key idea in formation stabilization is the use of natural potential functions
obtained from structural constraints of a desired formation in a way that leads to
a collision-free, distributed, and bounded state feedback law for each vehicle. +
V
In this paper, we propose reactive control impro- visation to synthesize voluntary lane-change policy that meets human preferences under given traffic environments. We first train Markov models to describe traffic patterns and the motion of vehicles responding to such patterns using traffic data. The trained parameters are calibrated using control improvisation to ensure the traffic scenario assumptions are satisfied. Based on the traffic pattern, vehicle response models, and Bayesian switching rules, the lane-change environment for an automated vehicle is modeled as a Markov decision process. Based on human lane-change behaviors, we train a voluntary lane- change policy using explicit-duration Markov decision process. Parameters in the lane-change policy are calibrated through reactive control improvisation to allow an automated car to pursue faster speed while maintaining desired frequency of lane-change maneuvers in various traffic environments. +
