2,352 research outputs found
Stabilization of Networked Control Systems with Sparse Observer-Controller Networks
In this paper we provide a set of stability conditions for linear
time-invariant networked control systems with arbitrary topology, using a
Lyapunov direct approach. We then use these stability conditions to provide a
novel low-complexity algorithm for the design of a sparse observer-based
control network. We employ distributed observers by employing the output of
other nodes to improve the stability of each observer dynamics. To avoid
unbounded growth of controller and observer gains, we impose bounds on their
norms. The effects of relaxation of these bounds is discussed when trying to
find the complete decentralization conditions
Limits on the Network Sensitivity Function for Multi-Agent Systems on a Graph
This report explores the tradeoffs and limits of performance in feedback control of interconnected multi-agent systems, focused on the network sensitivity functions. We consider the interaction topology described by a directed graph and we prove that the sensitivity transfer functions between every pair of agents, arbitrarily connected, can be derived using a version of the Mason's Direct Rule. Explicit forms for special types of graphs are presented. An analysis of the role of cycles points out that these structures influence and limit considerably the performance of the system. The more the cycles are equally distributed among the formation, the better performance the system can achieve, but they are always worse than the single agent case. We also prove the networked version of Bode's integral formula, showing that it still holds for multi-agent systems
Survivability of Deterministic Dynamical Systems
The notion of a part of phase space containing desired (or allowed) states of
a dynamical system is important in a wide range of complex systems research. It
has been called the safe operating space, the viability kernel or the sunny
region. In this paper we define the notion of survivability: Given a random
initial condition, what is the likelihood that the transient behaviour of a
deterministic system does not leave a region of desirable states. We
demonstrate the utility of this novel stability measure by considering models
from climate science, neuronal networks and power grids. We also show that a
semi-analytic lower bound for the survivability of linear systems allows a
numerically very efficient survivability analysis in realistic models of power
grids. Our numerical and semi-analytic work underlines that the type of
stability measured by survivability is not captured by common asymptotic
stability measures.Comment: 21 pages, 6 figure
Optimal LQG Control Across a Packet-Dropping Link
We examine optimal Linear Quadratic Gaussian control for a system in which communication between the sensor (output of the plant) and the controller occurs across a packet-dropping link. We extend the familiar LQG separation principle to this problem that allows us to solve this problem using a standard LQR state-feedback design, along with an optimal algorithm for propagating and using the information across the unreliable link. We present one such optimal algorithm, which consists of a Kalman Filter at the sensor side of the link, and a switched linear filter at the controller side. Our design does not assume any statistical model of the packet drop events, and is thus optimal for an arbitrary packet drop pattern. Further, the solution is appealing from a practical point of view because it can be implemented as a small modification of an existing LQG control design
Consensus-based control for a network of diffusion PDEs with boundary local interaction
In this paper the problem of driving the state of a network of identical
agents, modeled by boundary-controlled heat equations, towards a common
steady-state profile is addressed. Decentralized consensus protocols are
proposed to address two distinct problems. The first problem is that of
steering the states of all agents towards the same constant steady-state
profile which corresponds to the spatial average of the agents initial
condition. A linear local interaction rule addressing this requirement is
given. The second problem deals with the case where the controlled boundaries
of the agents dynamics are corrupted by additive persistent disturbances. To
achieve synchronization between agents, while completely rejecting the effect
of the boundary disturbances, a nonlinear sliding-mode based consensus protocol
is proposed. Performance of the proposed local interaction rules are analyzed
by applying a Lyapunov-based approach. Simulation results are presented to
support the effectiveness of the proposed algorithms
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