38 research outputs found
A Dynamic Boundary Guarding Problem with Translating Targets
We introduce a problem in which a service vehicle seeks to guard a deadline
(boundary) from dynamically arriving mobile targets. The environment is a
rectangle and the deadline is one of its edges. Targets arrive continuously
over time on the edge opposite the deadline, and move towards the deadline at a
fixed speed. The goal for the vehicle is to maximize the fraction of targets
that are captured before reaching the deadline. We consider two cases; when the
service vehicle is faster than the targets, and; when the service vehicle is
slower than the targets. In the first case we develop a novel vehicle policy
based on computing longest paths in a directed acyclic graph. We give a lower
bound on the capture fraction of the policy and show that the policy is optimal
when the distance between the target arrival edge and deadline becomes very
large. We present numerical results which suggest near optimal performance away
from this limiting regime. In the second case, when the targets are slower than
the vehicle, we propose a policy based on servicing fractions of the
translational minimum Hamiltonian path. In the limit of low target speed and
high arrival rate, the capture fraction of this policy is within a small
constant factor of the optimal.Comment: Extended version of paper for the joint 48th IEEE Conference on
Decision and Control and 28th Chinese Control Conferenc
FlipDyn with Control: Resource Takeover Games with Dynamics
We present the FlipDyn, a dynamic game in which two opponents (a defender and
an adversary) choose strategies to optimally takeover a resource that involves
a dynamical system. At any time instant, each player can take over the resource
and thereby control the dynamical system after incurring a state-dependent and
a control-dependent costs. The resulting model becomes a hybrid dynamical
system where the discrete state (FlipDyn state) determines which player is in
control of the resource. Our objective is to compute the Nash equilibria of
this dynamic zero-sum game. Our contributions are four-fold. First, for any
non-negative costs, we present analytical expressions for the saddle-point
value of the FlipDyn game, along with the corresponding Nash equilibrium (NE)
takeover strategies. Second, for continuous state, linear dynamical systems
with quadratic costs, we establish sufficient conditions under which the game
admits a NE in the space of linear state-feedback policies. Third, for scalar
dynamical systems with quadratic costs, we derive the NE takeover strategies
and saddle-point values independent of the continuous state of the dynamical
system. Fourth and finally, for higher dimensional linear dynamical systems
with quadratic costs, we derive approximate NE takeover strategies and control
policies which enable the computation of bounds on the value functions of the
game in each takeover state. We illustrate our findings through a numerical
study involving the control of a linear dynamical system in the presence of an
adversary.Comment: 17 Pages, 2 figures. Under review at IEEE TA
A Concentration-Based Approach for Optimizing the Estimation Performance in Stochastic Sensor Selection
In this work, we consider a sensor selection drawn at random by a sampling
with replacement policy for a linear time-invariant dynamical system subject to
process and measurement noise. We employ the Kalman filter to estimate the
state of the system. However, the statistical properties of the filter are not
deterministic due to the stochastic selection of sensors. As a consequence, we
derive concentration inequalities to bound the estimation error covariance of
the Kalman filter in the semi-definite sense. Concentration inequalities
provide a framework for deriving semi-definite bounds that hold in a
probabilistic sense. Our main contributions are three-fold. First, we develop
algorithmic tools to aid in the implementation of a matrix concentration
inequality. Second, we derive concentration-based bounds for three types of
stochastic selections. Third, we propose a polynomial-time procedure for
finding a sampling distribution that indirectly minimizes the maximum
eigenvalue of the estimation error covariance. Our proposed sampling policy is
also shown to empirically outperform three other sampling policies: uniform,
deterministic greedy, and randomized greedy
Incentivizing Collaboration in Heterogeneous Teams via Common-Pool Resource Games
We consider a team of heterogeneous agents that is collectively responsible
for servicing, and subsequently reviewing, a stream of homogeneous tasks. Each
agent has an associated mean service time and a mean review time for servicing
and reviewing the tasks, respectively. Agents receive a reward based on their
service and review admission rates. The team objective is to collaboratively
maximize the number of "serviced and reviewed" tasks. We formulate a
Common-Pool Resource (CPR) game and design utility functions to incentivize
collaboration among heterogeneous agents in a decentralized manner. We show the
existence of a unique Pure Nash Equilibrium (PNE), and establish convergence of
best response dynamics to this unique PNE. Finally, we establish an analytic
upper bound on three measures of inefficiency of the PNE, namely the price of
anarchy, the ratio of the total review admission rate, and the ratio of
latency, along with an empirical study