netcontrol (version 0.1)

control_scheme_DLI_freestate: Discrete Linear Time-Invariant Free Final State Classic Control Scheme

Description

Given a system dynamics \(A\), control input matrix \(B\), final state weighting matrix \(S\), intermediate state weighting matrix sequence \(Q_seq\), and cost matrix sequence \(R_seq\), calculates the Kalman gain sequence to minimize the LQR by time \(t_max\). See section 2.2 of lewisOptimalControl2012netcontrol for details.

Usage

control_scheme_DLI_freestate(t_max, A, B, S, Q_seq, R_seq)

Arguments

t_max

Required. An integer total number of time points to determine the trajectory over

A

Required. A \(p x p\) matrix of system coefficients

B

Required. A \(p x q\) matrix of control weights

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

Value

A list containing an entry labeled gain_seq containing either 1 or t_max - 1 Kalman gain matrices and an entry labeled cost_func which contains a LQR function.

References

lewisOptimalControl2012netcontrol

Examples

# NOT RUN {
A = matrix(c(0,-3,-2,2,-2,1,-1,2,-1), 3,3)

#Normalize rows to sum to 1
A = solve(diag(rowSums(A))) %*% A

B = S = Q_seq = R_seq = diag(3)

CS = control_scheme_DLI_freestate(100, A, B, S, Q_seq, R_seq)

# }