In this article, we consider the problem of stabilizing a class of degenerate stochastic processes, which are constrained to a bounded Euclidean domain or a compact smooth manifold, to a given target probability density. This stabilization problem arises in the field of swarm robotics, for example, in applications where a swarm of robots is required to cover an area according to a target probability density. Most existing works on modeling and control of robotic swarms that use partial differential equation (PDE) models assume that the robots' dynamics are holonomic and, hence, the associated stochastic processes have generators that are elliptic. We relax this assumption on the ellipticity of the generator of the stochastic processes, and consider the more practical case of the stabilization problem for a swarm of agents whose dynamics are given by a controllable driftless control-affine system. We construct state-feedback control laws that exponentially stabilize a swarm of nonholonomic agents to a target probability density that is sufficiently regular. State-feedback laws can stabilize a swarm only to target probability densities that are positive everywhere. To stabilize the swarm to probability densities that possibly have disconnected supports, we introduce a semilinear PDE model of a collection of interacting agents governed by a hybrid switching diffusion process. The interaction between the agents is modeled using a (mean-field) feedback law that is a function of the local density of the swarm, with the switching parameters as the control inputs. We show that under the action of this feedback law, the semilinear PDE system is globally asymptotically stable about the given target probability density. The stabilization strategies with and without agent interactions are verified numerically for agents that evolve according to the Brockett integrator; the strategy with interactions is additionally verified for agents that evolve according to an underactuated s...
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Scheduling Multiple Agents in a Persistent Monitoring Task Using Reachability Analysis
We consider the problem of controlling the dynamic
state of each of a finite collection of targets distributed in physical
space using a much smaller collection of mobile agents. Each
agent can attend to no more than one target at a given time,
thus agents must move between targets to control the collective
state, implying that the states of each of the individual targets
are only controlled intermittently. We assume that the state
dynamics of each of the targets are given by a linear, timeinvariant,
controllable system and develop conditions on the
visiting schedules of the agents to ensure that the property
of controllability is maintained in the face of the intermittent
control. We then introduce constraints on the magnitude of the
control input and a bounded disturbance into the target dynamics
and develop a method to evaluate system performance under
this scenario. Finally, we use this method to determine how the
amount of time the agents spend at a given target before switching
to the next in its sequence influences
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- PAR ID:
- 10122844
- Date Published:
- Journal Name:
- IEEE Transactions on Automatic Control
- ISSN:
- 0018-9286
- Page Range / eLocation ID:
- 1 to 1
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/TAC.2019.2922506
