Set Membership Algorithms¶

Distributed Set Membership¶

class disropt.algorithms.setmembership.SetMembership(agent, initial_condition, enable_log=False)[source]¶

Bases: disropt.algorithms.consensus.Consensus

Distributed Set Membership Algorithm [FaGa18]

From the perspective of agent \(i\) the algorithm works as follows. For \(k=0,1,\dots\)

\[ \begin{align}\begin{aligned}X_i^{k+1} &= X_i^k \cap M_i^{k+1}\\z_i^{k} &= \sum_{j=1}^N w_{ij} x_j^k\\x_i^{k+1} &= \Pi_{X_i^{k+1}}[z_i^k]\end{aligned}\end{align} \]

where \(x_i,z_i\in\mathbb{R}^n\), \(M_i^{k+1},X_i^{k+1}\subseteq\mathbb{R}^n\) are the current feasible (measurement) set and the feasible (parameter) set respectively, and \(\Pi_X[]\) denotes the projection operator over the set \(X\).

Parameters

agent (Agent) – agent to execute the algorithm (must be a Agent)
initial_condition (numpy.ndarray) – initial condition
enable_log (bool) – True for enabling log

agent¶

agent to execute the algorithm

Type: Agent

x0¶

initial condition

Type: numpy.ndarray

x¶

current value of the local solution

Type: numpy.ndarray

shape¶

shape of the variable

Type: tuple

x_neigh¶

dictionary containing the local solution of the (in-)neighbors

Type: dict

enable_log¶

True for enabling log

Type: bool

measure()[source]¶: Takes a new measurement and updates parameter_set

set_measure_generator(generator)[source]¶

set the measure generator

Parameters: generator (Callable) – measure generator

Asynchronous Distributed Set Membership¶

class disropt.algorithms.setmembership.AsynchronousSetMembership(agent, initial_condition, **kwargs)[source]¶

Bases: disropt.algorithms.consensus.AsynchronousConsensus

Asynchronous Distributed Set Membership Algorithm [FaGa19]