LQR: Linear Quadratic Regulator

In netcontrol: Control Theory Methods for Networks

Description

Creates a function that can be used to calculate the cumulative value of the LQR for any set of states and control inputs. By setting eval to True, the LQR is immediately calculated. See \insertCitelewisOptimalControl2012netcontrol

NOTE: LQR functions, as they are calculated forward in time, go to 0 by the maximum time regardless of input. This is expected behavior, but that does make using the LQR value to evaluate control efficacy somewhat difficult.

Usage

LQR(X, U, S, Q_seq, R_seq, eval = TRUE)

Arguments

X	A t x p matrix of state values
U	A t-1 x q matrix of control inputs'
S	A p x p final state weighting matrix
Q_seq	A list of t p x p intermediate state weighting matrices or a single p x p intermediate state weighting matrix
R_seq	A list of t q x q intermediate cost matrices or a single q x q cost matrix
eval	Boolean, if FALSE returns a function, if TRUE calculates the LQR series

Value

A function or a t length numeric vector

References

\insertRef

lewisOptimalControl2012netcontrol

Examples

X = matrix(1, 100, 3)
U = matrix(-1, 99, 3)
S = Q_seq = R_seq = diag(3)

print(LQR(X,U, S, Q_seq, R_seq)[1:5])

netcontrol documentation built on March 26, 2020, 7:25 p.m.