9,803 research outputs found
Minimal Actuator Placement with Optimal Control Constraints
We introduce the problem of minimal actuator placement in a linear control
system so that a bound on the minimum control effort for a given state transfer
is satisfied while controllability is ensured. We first show that this is an
NP-hard problem following the recent work of Olshevsky. Next, we prove that
this problem has a supermodular structure. Afterwards, we provide an efficient
algorithm that approximates up to a multiplicative factor of O(logn), where n
is the size of the multi-agent network, any optimal actuator set that meets the
specified energy criterion. Moreover, we show that this is the best
approximation factor one can achieve in polynomial-time for the worst case.
Finally, we test this algorithm over large Erdos-Renyi random networks to
further demonstrate its efficiency.Comment: This version includes all the omitted proofs from the one to appear
in the American Control Conference (ACC) 2015 proceeding
A Structured Systems Approach for Optimal Actuator-Sensor Placement in Linear Time-Invariant Systems
In this paper we address the actuator/sensor allocation problem for linear
time invariant (LTI) systems. Given the structure of an autonomous linear
dynamical system, the goal is to design the structure of the input matrix
(commonly denoted by ) such that the system is structurally controllable
with the restriction that each input be dedicated, i.e., it can only control
directly a single state variable. We provide a methodology that addresses this
design question: specifically, we determine the minimum number of dedicated
inputs required to ensure such structural controllability, and characterize,
and characterizes all (when not unique) possible configurations of the
\emph{minimal} input matrix . Furthermore, we show that the proposed
solution methodology incurs \emph{polynomial complexity} in the number of state
variables. By duality, the solution methodology may be readily extended to the
structural design of the corresponding minimal output matrix (commonly denoted
by ) that ensures structural observability.Comment: 8 pages, submitted for publicatio
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
Performance guarantees for greedy maximization of non-submodular controllability metrics
A key problem in emerging complex cyber-physical networks is the design of
information and control topologies, including sensor and actuator selection and
communication network design. These problems can be posed as combinatorial set
function optimization problems to maximize a dynamic performance metric for the
network. Some systems and control metrics feature a property called
submodularity, which allows simple greedy algorithms to obtain provably
near-optimal topology designs. However, many important metrics lack
submodularity and therefore lack provable guarantees for using a greedy
optimization approach. Here we show that performance guarantees can be obtained
for greedy maximization of certain non-submodular functions of the
controllability and observability Gramians. Our results are based on two key
quantities: the submodularity ratio, which quantifies how far a set function is
from being submodular, and the curvature, which quantifies how far a set
function is from being supermodular
Submodularity of Energy Related Controllability Metrics
The quantification of controllability and observability has recently received
new interest in the context of large, complex networks of dynamical systems. A
fundamental but computationally difficult problem is the placement or selection
of actuators and sensors that optimize real-valued controllability and
observability metrics of the network. We show that several classes of energy
related metrics associated with the controllability Gramian in linear dynamical
systems have a strong structural property, called submodularity. This property
allows for an approximation guarantee by using a simple greedy heuristic for
their maximization. The results are illustrated for randomly generated systems
and for placement of power electronic actuators in a model of the European
power grid.Comment: 7 pages, 2 figures; submitted to the 2014 IEEE Conference on Decision
and Contro
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