average_control {netcontrol}

average_control - Average controllability as defined by the trace of the Gramian

Description

A commonly used measure (Pasqualetti et al. 2014) of the overall controllability of a system defined by x_(t+1) = Ax_(t) + Bu_(t).

Usage

average_control(A, B)

Arguments

A

A n x n matrix.

B

A n x m matrix.

Value

Trace of the infinite time Gramian.

References

Pasqualetti F, Zampieri S, Bullo F (2014). “Controllability Metrics, Limitations and Algorithms for Complex Networks.” In 2014 American Control Conference, 3287–3292. ISBN 978-1-4799-3274-0 978-1-4799-3272-6 978-1-4799-3271-9, doi: 10/ggkhs9.

Examples

A = matrix(c(0,-3,-2,2,-2,1,-1,2,-1), 3,3)
B = diag(3)

average_control(A, B)