21 research outputs found
Optimal Control of Two-Player Systems with Output Feedback
In this article, we consider a fundamental decentralized optimal control
problem, which we call the two-player problem. Two subsystems are
interconnected in a nested information pattern, and output feedback controllers
must be designed for each subsystem. Several special cases of this architecture
have previously been solved, such as the state-feedback case or the case where
the dynamics of both systems are decoupled. In this paper, we present a
detailed solution to the general case. The structure of the optimal
decentralized controller is reminiscent of that of the optimal centralized
controller; each player must estimate the state of the system given their
available information and apply static control policies to these estimates to
compute the optimal controller. The previously solved cases benefit from a
separation between estimation and control which allows one to compute the
control and estimation gains separately. This feature is not present in
general, and some of the gains must be solved for simultaneously. We show that
computing the required coupled estimation and control gains amounts to solving
a small system of linear equations
Information Structure Design in Team Decision Problems
We consider a problem of information structure design in team decision
problems and team games. We propose simple, scalable greedy algorithms for
adding a set of extra information links to optimize team performance and
resilience to non-cooperative and adversarial agents. We show via a simple
counterexample that the set function mapping additional information links to
team performance is in general not supermodular. Although this implies that the
greedy algorithm is not accompanied by worst-case performance guarantees, we
illustrate through numerical experiments that it can produce effective and
often optimal or near optimal information structure modifications
H2 Optimal Coordination of Homogeneous Agents Subject to Limited Information Exchange
Controllers with a diagonal-plus-low-rank structure constitute a scalable
class of controllers for multi-agent systems. Previous research has shown that
diagonal-plus-low-rank control laws appear as the optimal solution to a class
of multi-agent H2 coordination problems, which arise in the control of wind
farms. In this paper we show that this result extends to the case where the
information exchange between agents is subject to limitations. We also show
that the computational effort required to obtain the optimal controller is
independent of the number of agents and provide analytical expressions that
quantify the usefulness of information exchange
Optimal Local and Remote Controllers with Unreliable Communication
We consider a decentralized optimal control problem for a linear plant
controlled by two controllers, a local controller and a remote controller. The
local controller directly observes the state of the plant and can inform the
remote controller of the plant state through a packet-drop channel. We assume
that the remote controller is able to send acknowledgments to the local
controller to signal the successful receipt of transmitted packets. The
objective of the two controllers is to cooperatively minimize a quadratic
performance cost. We provide a dynamic program for this decentralized control
problem using the common information approach. Although our problem is not a
partially nested LQG problem, we obtain explicit optimal strategies for the two
controllers. In the optimal strategies, both controllers compute a common
estimate of the plant state based on the common information. The remote
controller's action is linear in the common estimated state, and the local
controller's action is linear in both the actual state and the common estimated
state
Optimal Output Feedback Architecture for Triangular LQG Problems
Distributed control problems under some specific information constraints can
be formulated as (possibly infinite dimensional) convex optimization problems.
The underlying motivation of this work is to develop an understanding of the
optimal decision making architecture for such problems. In this paper, we
particularly focus on the N-player triangular LQG problems and show that the
optimal output feedback controllers have attractive state space realizations.
The optimal controller can be synthesized using a set of stabilizing solutions
to 2N linearly coupled algebraic Riccati equations, which turn out to be easily
solvable under reasonable assumptions.Comment: To be presented at 2014 American Control Conferenc
Optimal Decentralized State-Feedback Control with Sparsity and Delays
This work presents the solution to a class of decentralized linear quadratic
state-feedback control problems, in which the plant and controller must satisfy
the same combination of delay and sparsity constraints. Using a novel
decomposition of the noise history, the control problem is split into
independent subproblems that are solved using dynamic programming. The approach
presented herein both unifies and generalizes many existing results