1,867 research outputs found
Minimum-Information LQG Control - Part I: Memoryless Controllers
With the increased demand for power efficiency in feedback-control systems,
communication is becoming a limiting factor, raising the need to trade off the
external cost that they incur with the capacity of the controller's
communication channels. With a proper design of the channels, this translates
into a sequential rate-distortion problem, where we minimize the rate of
information required for the controller's operation under a constraint on its
external cost. Memoryless controllers are of particular interest both for the
simplicity and frugality of their implementation and as a basis for studying
more complex controllers. In this paper we present the optimality principle for
memoryless linear controllers that utilize minimal information rates to achieve
a guaranteed external-cost level. We also study the interesting and useful
phenomenology of the optimal controller, such as the principled reduction of
its order
LQG Control and Sensing Co-Design
We investigate a Linear-Quadratic-Gaussian (LQG) control and sensing
co-design problem, where one jointly designs sensing and control policies. We
focus on the realistic case where the sensing design is selected among a finite
set of available sensors, where each sensor is associated with a different cost
(e.g., power consumption). We consider two dual problem instances:
sensing-constrained LQG control, where one maximizes control performance
subject to a sensor cost budget, and minimum-sensing LQG control, where one
minimizes sensor cost subject to performance constraints. We prove no
polynomial time algorithm guarantees across all problem instances a constant
approximation factor from the optimal. Nonetheless, we present the first
polynomial time algorithms with per-instance suboptimality guarantees. To this
end, we leverage a separation principle, that partially decouples the design of
sensing and control. Then, we frame LQG co-design as the optimization of
approximately supermodular set functions; we develop novel algorithms to solve
the problems; and we prove original results on the performance of the
algorithms, and establish connections between their suboptimality and
control-theoretic quantities. We conclude the paper by discussing two
applications, namely, sensing-constrained formation control and
resource-constrained robot navigation.Comment: Accepted to IEEE TAC. Includes contributions to submodular function
optimization literature, and extends conference paper arXiv:1709.0882
Optimal Control for LQG Systems on Graphs---Part I: Structural Results
In this two-part paper, we identify a broad class of decentralized
output-feedback LQG systems for which the optimal control strategies have a
simple intuitive estimation structure and can be computed efficiently. Roughly,
we consider the class of systems for which the coupling of dynamics among
subsystems and the inter-controller communication is characterized by the same
directed graph. Furthermore, this graph is assumed to be a multitree, that is,
its transitive reduction can have at most one directed path connecting each
pair of nodes. In this first part, we derive sufficient statistics that may be
used to aggregate each controller's growing available information. Each
controller must estimate the states of the subsystems that it affects (its
descendants) as well as the subsystems that it observes (its ancestors). The
optimal control action for a controller is a linear function of the estimate it
computes as well as the estimates computed by all of its ancestors. Moreover,
these state estimates may be updated recursively, much like a Kalman filter
Stabilization of Linear Systems Over Gaussian Networks
The problem of remotely stabilizing a noisy linear time invariant plant over
a Gaussian relay network is addressed. The network is comprised of a sensor
node, a group of relay nodes and a remote controller. The sensor and the relay
nodes operate subject to an average transmit power constraint and they can
cooperate to communicate the observations of the plant's state to the remote
controller. The communication links between all nodes are modeled as Gaussian
channels. Necessary as well as sufficient conditions for mean-square
stabilization over various network topologies are derived. The sufficient
conditions are in general obtained using delay-free linear policies and the
necessary conditions are obtained using information theoretic tools. Different
settings where linear policies are optimal, asymptotically optimal (in certain
parameters of the system) and suboptimal have been identified. For the case
with noisy multi-dimensional sources controlled over scalar channels, it is
shown that linear time varying policies lead to minimum capacity requirements,
meeting the fundamental lower bound. For the case with noiseless sources and
parallel channels, non-linear policies which meet the lower bound have been
identified
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