control_traj: Calculate the trajectory of a discrete linear time invariant...
In netcontrol: Control Theory Methods for Networks

Description Usage Arguments Details Value References Examples

View source: R/control_traj.R

This function is designed to work with control_scheme objects generated by control_scheme_DLI_freestate In future versions of netcontrol this function will be used to simulate any control trajectory. For general details on control theory trajectories, see \insertCitelewisOptimalControl2012netcontrol.

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control_traj(t_max, x_0, A, B, theta = NA, gamma = NA, control_scheme,
  delta = NA, d_nosign = F, d_toggle = F, upper_bounds = NA,
  lower_bounds = NA, u_pos = F)

`t_max`	Required. An integer total number of time points to determine the trajectory over
`x_0`	Required. A p length numeric vector of starting values
`A`	Required. A p x p matrix of system coefficients
`B`	Required. A p x q matrix of control weights
`theta`	Optional. A p x p covariance matrix for state errors. If `NA`, state mechanics will be deterministic
`gamma`	Optional. A p x p covariance matrix for observation errors. If `NA`, no observation/measurement error will be modelled.
`control_scheme`	Required. 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 an appropriately constructed cost function
`delta`	Optional. A vector of length 2, where the first entry contains the point of saturation for control inputs, and the second entry contains the saturation value for control inputs.
`d_nosign`	Optional. Boolean. If `TRUE` and `delta` is not `NA`, control inputs are forced to be positive.
`d_toggle`	Optional. Boolean. If `TRUE` and `delta` is not `NA`, control inputs are either 0 or the saturation value.
`upper_bounds`	Optional. A p length vector of upper bounds on state values.
`lower_bounds`	Optional. A p length vector of lower bounds on state values.
`u_pos`	Optional. Boolean. If `TRUE` restricts control inputs to be positive,

CAUTION: Use of saturation parameters and/or bound parameters delta, d_nosign, d_toggle, upper.bound, lower.bound, u.pos leads to estimates of the optimal trajectory to be sub-optimal, as the Kalman gain calculations do not take any of those restrictions into account. This functionality will be added later, and this caution statement removed at that time.

A list containing 4 entries: a 't_max x p' state value matrix, a 't_max x p' observation matrix, a 't_max-1 x q' matrix of control inputs and a 't_max' length vector of cost function values.

\insertRef

lewisOptimalControl2012netcontrol.

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)

traj = control_traj(100, rep(100,3), A, B, control_scheme = CS)

#First 5 control inputs
print(head(traj[[3]]))