2,376 research outputs found
Distributed Verification of Structural Controllability for Linear Time-Invariant Systems
Motivated by the development and deployment of large-scale dynamical systems,
often composed of geographically distributed smaller subsystems, we address the
problem of verifying their controllability in a distributed manner. In this
work we study controllability in the structural system theoretic sense,
structural controllability. In other words, instead of focusing on a specific
numerical system realization, we provide guarantees for equivalence classes of
linear time-invariant systems on the basis of their structural sparsity
patterns, i.e., location of zero/nonzero entries in the plant matrices. To this
end, we first propose several necessary and/or sufficient conditions to ensure
structural controllability of the overall system, on the basis of the
structural patterns of the subsystems and their interconnections. The proposed
verification criteria are shown to be efficiently implementable (i.e., with
polynomial time complexity in the number of the state variables and inputs) in
two important subclasses of interconnected dynamical systems: similar (i.e.,
every subsystem has the same structure), and serial (i.e., every subsystem
outputs to at most one other subsystem). Secondly, we provide a distributed
algorithm to verify structural controllability for interconnected dynamical
systems. The proposed distributed algorithm is efficient and implementable at
the subsystem level; the algorithm is iterative, based on communication among
(physically) interconnected subsystems, and requires only local model and
interconnection knowledge at each subsystem
Structural Controllability of a Networked Dynamic System with LFT Parameterized Subsystems
This paper studies structural controllability for a networked dynamic system
(NDS), in which each subsystem may have different dynamics, and unknown
parameters may exist both in subsystem dynamics and in subsystem
interconnections. In addition, subsystem parameters are parameterized by a
linear fractional transformation (LFT). It is proven that controllability keeps
to be a generic property for this kind of NDSs. Some necessary and sufficient
conditions are then established respectively for them to be structurally
controllable, to have a fixed uncontrollable mode, and to have a parameter
dependent uncontrollable mode, under the condition that each subsystem
interconnection link can take a weight independently. These conditions are
scalable, and in their verifications, all arithmetic calculations are performed
separately on each subsystem. In addition, these conditions also reveal
influences on NDS controllability from subsystem input-output relations,
subsystem uncontrollable modes and subsystem interconnection topology. Based on
these observations, the problem of selecting the minimal number of subsystem
interconnection links is studied under the requirement of constructing a
structurally controllable NDS. A heuristic method is derived with some provable
approximation bounds and a low computational complexity.Comment: Accepted by IEEE Transactions on Automatic Control as full paper,
scheduled to appear in Volume 64 (2019), Issue 12 (December
On the Controllability and Observability of Networked Dynamic Systems
Some necessary and sufficient conditions are obtained for the controllability
and observability of a networked system with linear time invariant (LTI)
dynamics. The topology of this system is fixed but arbitrary, and every
subsystem is permitted to have different dynamic input-output relations. These
conditions essentially depend only on transmission zeros of every subsystem and
the connection matrix among subsystems, which makes them attractive in the
analysis and synthesis of a large scale networked system. As an application,
these conditions are utilized to characterize systems whose steady state
estimation accuracy with the distributed predictor developed in (Zhou, 2013) is
equal to that of the lumped Kalman filter. Some necessary and sufficient
conditions on system matrices are derived for this equivalence. It has been
made clear that to guarantee this equivalence, the steady state update gain
matrix of the Kalman filter must be block diagonal.Comment: 30 pages, 1 figur
Verification and Design of Resilient Closed-Loop Structured System
This paper addresses the resilience of large-scale closed-loop structured
systems in the sense of arbitrary pole placement when subject to failure of
feedback links. Given a structured system with input, output, and feedback
matrices, we first aim to verify whether the closed-loop structured system is
resilient to simultaneous failure of any subset of feedback links of a
specified cardinality. Subsequently, we address the associated design problem
in which given a structured system with input and output matrices, we need to
design a sparsest feedback matrix that ensures the resilience of the resulting
closed-loop structured system to simultaneous failure of any subset of feedback
links of a specified cardinality. We first prove that the verification problem
is NP-complete even for irreducible systems and the design problem is NP-hard
even for so-called structurally cyclic systems. We also show that the design
problem is inapproximable to factor (1-o(1))log n, where n denotes the system
dimension. Then we propose algorithms to solve both the problems: a
pseudo-polynomial algorithm to address the verification problem of irreducible
systems and a polynomial-time O(log n)-optimal approximation algorithm to solve
the design problem for a special feedback structure, so-called back-edge
feedback structure.Comment: 14 Page
Controllability and data-driven identification of bipartite consensus on nonlinear signed networks
Nonlinear networked systems are of interest in several areas of research,
such as multi-agent systems and social networks. In this paper, we examine the
controllability of several classes of nonlinear networked dynamics on which the
underlying graph admits negative weights. Such signed networks exhibit
bipartite clustering when the underlying graph is structurally balanced. We
show that structural balance is the key ingredient inducing uncontrollability
when combined with a leader-node symmetry and a certain type of dynamical
symmetry. We then examine the problem of extracting the bipartite structure of
such graphs from data using Extended Dynamic Mode Decomposition to approximate
the corresponding Koopman operator.Comment: To be presented at the 56th IEEE Conference on Decision and Control
in Melbourne, Australi
Analysis and Design of Actuation-Sensing-Communication Interconnection Structures towards Secured/Resilient Closed-loop Systems
This paper considers the analysis and design of resilient/robust
decentralized control systems. Specifically, we aim to assess how the pairing
of sensors and actuators lead to architectures that are resilient to
attacks/hacks for industrial control systems and other complex cyber-physical
systems. We consider inherent structural properties such as internal fixed
modes of a dynamical system depending on actuation, sensing, and
interconnection/communication structure for linear discrete time-invariant
dynamical systems. We introduce the notion of resilient fixed-modes free system
that ensures the non-existence of fixed modes when the
actuation-sensing-communication structure is compromised due to attacks by a
malicious agent on actuators, sensors, or communication components and natural
failures. Also, we provide a graph-theoretical characterization for the
resilient structurally fixed modes that enables to capture the non-existence of
resilient fixed modes for almost all possible systems' realizations.
Additionally, we address the minimum actuation-sensing-communication co-design
ensuring the non-existence of resiliently structurally fixed modes, which we
show to be NP-hard. Notwithstanding, we identify conditions that are often
satisfied in engineering settings and under which the co-design problem is
solvable in polynomial-time complexity. Furthermore, we leverage the structural
insights and properties to provide a convex optimization method to design the
gain for a parametrized system and satisfying the sparsity of a given
information pattern. Thus, exploring the interplay between structural and
non-structural systems to ensure their resilience. Finally, the efficacy of the
proposed approach is demonstrated on a power grid example
Affine Dependence of Network Controllability/Observability on Its Subsystem Parameters and Connections
This paper investigates observability/controllability of a networked dynamic
system (NDS) in which system matrices of its subsystems are expressed through
linear fractional transformations (LFT). Some relations have been obtained
between this NDS and descriptor systems about their
observability/controllability. A necessary and sufficient condition is
established with the associated matrices depending affinely on subsystem
parameters/connections. An attractive property of this condition is that all
the required calculations are performed independently on each individual
subsystem. Except well-posedness, not any other conditions are asked for
subsystem parameters/connections. This is in sharp contrast to recent results
on structural observability/controllability which is proven to be NP hard. Some
characteristics are established for a subsystem which are helpful in
constructing an observable/controllable NDS. It has been made clear that
subsystems with an input matrix of full column rank are helpful in constructing
an observable NDS, while subsystems with an output matrix of full row rank are
helpful in constructing a controllable NDS. These results are extended to an
NDS with descriptor form subsystems. As a byproduct, the full normal rank
condition of previous works on network observability/controllability has been
completely removed. On the other hand, satisfaction of this condition is shown
to be appreciative in building an observable/controllability NDS.Comment: 15 pages, 1 figure. Results without proof of Section III in this
paper have been presented in the 58th IEEE Conference on Decision and
Control, Nice, France, 2019. This work has been submitted to the IEEE for
possible publication. Copyright may be transferred without notice, after
which this version may no longer be accessibl
Optimal Network Topology Design in Composite Systems with Constrained Neighbors for Structural Controllability
Composite systems are large complex systems con- sisting of interconnected
agents (subsystems). Agents in a com- posite system interact with each other
towards performing an in- tended goal. Controllability is essential to achieve
desired system performance in linear time-invariant composite systems. Agents
in a composite system are often uncontrollable individually, further, only a
few agents receive input. In such a case, the agents share/communicate their
private state information with pre-specified neighboring agents so as to
achieve controllability. Our objective in this paper is to identify an optimal
network topology, optimal in the sense of minimum cardinality information
transfer between agents to guarantee the controllability of the composite
system when the possible neighbor set of each agent is pre-specified. We focus
on graph-theoretic analysis referred to as structural controllability as
numerical entries of system matrices in complex systems are mostly unknown. We
first prove that given a set of agents and the possible set of neighbors,
finding a minimum cardinality set of information (interconnections) that must
be shared to accomplish structural controllability of the composite system is
NP-hard. Subsequently, we present a polynomial-time algorithm that finds a
2-optimal solution to this NP-hard problem. Our algorithm combines a minimum
weight bipartite matching algorithm and a minimum spanning tree algorithm and
gives a subset of interconnections which when established guarantees structural
controllability, such that the worst-case performance is 2-optimal. Finally, we
show that our approach directly extends to weighted constrained optimal net-
work topology design problem and constrained optimal network topology design
problem in switched linear systems
A unified framework for modeling and implementation of hybrid systems with synchronous controllers
This paper presents a novel approach to including non-instantaneous discrete
control transitions in the linear hybrid automaton approach to simulation and
verification of hybrid control systems. In this paper we study the control of a
continuously evolving analog plant using a controller programmed in a
synchronous programming language. We provide extensions to the synchronous
subset of the SystemJ programming language for modeling, implementation, and
verification of such hybrid systems. We provide a sound rewrite semantics that
approximate the evolution of the continuous variables in the discrete domain
inspired from the classical supervisory control theory. The resultant discrete
time model can be verified using classical model-checking tools. Finally, we
show that systems designed using our approach have a higher fidelity than the
ones designed using the hybrid automaton approach.Comment: 16 page
A Graphical Characterization of Structurally Controllable Linear Systems with Dependent Parameters
One version of the concept of structural controllability defined for
single-input systems by Lin and subsequently generalized to multi-input systems
by others, states that a parameterized matrix pair whose nonzero
entries are distinct parameters, is structurally controllable if values can be
assigned to the parameters which cause the resulting matrix pair to be
controllable. In this paper the concept of structural controllability is
broadened to allow for the possibility that a parameter may appear in more than
one location in the pair . Subject to a certain condition on the
parameterization called the "binary assumption", an explicit graph-theoretic
characterization of such matrix pairs is derived
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