3 research outputs found
Optimal Selection of Interconnections in Composite Systems for Structural Controllability
In this paper, we study structural controllability of a linear time invariant
(LTI) composite system consisting of several subsystems. We assume that the
neighbourhood of each subsystem is unconstrained, i.e., any subsystem can
interact with any other subsystem. The interaction links between subsystems are
referred as interconnections. We assume the composite system to be structurally
controllable if all possible interconnections are present, and our objective is
to identify the minimum set of interconnections required to keep the system
structurally controllable. We consider structurally identical subsystems, i.e.,
the zero/non-zero pattern of the state matrices of the subsystems are the same,
but dynamics can be different. We present a polynomial time optimal algorithm
to identify the minimum cardinality set of interconnections that subsystems
must establish to make the composite system structurally controllable
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
Thompson sampling for linear quadratic mean-field teams
We consider optimal control of an unknown multi-agent linear quadratic (LQ)
system where the dynamics and the cost are coupled across the agents through
the mean-field (i.e., empirical mean) of the states and controls. Directly
using single-agent LQ learning algorithms in such models results in regret
which increases polynomially with the number of agents. We propose a new
Thompson sampling based learning algorithm which exploits the structure of the
system model and show that the expected Bayesian regret of our proposed
algorithm for a system with agents of different types at time horizon
is irrespective of the
total number of agents, where the notation hides
logarithmic factors in . We present detailed numerical experiments to
illustrate the salient features of the proposed algorithm.Comment: Submitted to AISTATS 202