3 research outputs found
Optimal Infinite Horizon Decentralized Networked Controllers with Unreliable Communication
We consider a decentralized networked control system (DNCS) consisting of a
remote controller and a collection of linear plants, each associated with a
local controller. Each local controller directly observes the state of its
co-located plant and can inform the remote controller of the plant's state
through an unreliable uplink channel. The downlink channels from the remote
controller to local controllers were assumed to be perfect. The objective of
the local controllers and the remote controller is to cooperatively minimize
the infinite horizon time average of expected quadratic cost. The finite
horizon version of this problem was solved in our prior work [2]. The optimal
strategies in the finite horizon case were shown to be characterized by coupled
Riccati recursions. In this paper, we show that if the link failure
probabilities are below certain critical thresholds, then the coupled Riccati
recursions of the finite horizon solution reach a steady state and the
corresponding decentralized strategies are optimal. Above these thresholds, we
show that no strategy can achieve finite cost. We exploit a connection between
our DNCS Riccati recursions and the coupled Riccati recursions of an auxiliary
Markov jump linear system to obtain our results. Our main results in Theorems 1
and 2 explicitly identify the critical thresholds for the link failure
probabilities and the optimal decentralized control strategies when all link
failure probabilities are below their thresholds.Comment: 52 pages, Submitted to IEEE Transactions on Automatic Contro
Input Perturbations for Adaptive Control and Learning
This paper studies adaptive algorithms for simultaneous regulation (i.e.,
control) and estimation (i.e., learning) of Multiple Input Multiple Output
(MIMO) linear dynamical systems. It proposes practical, easy to implement
control policies based on perturbations of input signals. Such policies are
shown to achieve a worst-case regret that scales as the square-root of the time
horizon, and holds uniformly over time. Further, it discusses specific settings
where such greedy policies attain the information theoretic lower bound of
logarithmic regret. To establish the results, recent advances on
self-normalized martingales together with a novel method of policy
decomposition are leveraged
Optimal Local and Remote Controls of Multiple Systems with Multiplicative Noises and Unreliable Uplink Channels
In this paper, the optimal local and remote linear quadratic (LQ) control
problem is studied for a networked control system (NCS) which consists of
multiple subsystems and each of which is described by a general multiplicative
noise stochastic system with one local controller and one remote controller.
Due to the unreliable uplink channels, the remote controller can only access
unreliable state information of all subsystems, while the downlink channels
from the remote controller to the local controllers are perfect. The
difficulties of the LQ control problem for such a system arise from the
different information structures of the local controllers and the remote
controller. By developing the Pontyagin maximum principle, the necessary and
sufficient solvability conditions are derived, which are based on the solution
to a group of forward and backward difference equations (G-FBSDEs).
Furthermore, by proposing a new method to decouple the G-FBSDEs and introducing
new coupled Riccati equations (CREs), the optimal control strategies are
derived where we verify that the separation principle holds for the
multiplicative noise NCSs with packet dropouts. This paper can be seen as an
important contribution to the optimal control problem with asymmetric
information structures