Anticipative LQG control. II. (English) Zbl 0753.93082
Applied stochastic analysis, Pap. Workshop, London/UK 1989, Stochastic Monogr. 5, 205-214 (1990).
Summary: [For the entire collection see Zbl 0728.00017.]
We continue the investigation, begun in the companion paper of the author [(*), IMA J. Math. Control Inf. 6, No. 3, 259-265 (1989; Zbl 0696.93072)], of a modification of the LQG problem of linear stochastic system theory in which the usual nonanticipativity condition on the controls is relaxed. It was shown in (*) that if the controller is allowed complete knowledge of the noise sample function before deciding on the control action then the cost is reduced on average by an amount \(\int\text{tr}\{U(t)\Theta\}dt\) below the standard LQG minimal cost.
Here we consider Lagrange multipliers. We show that the standard LQG control is globally optimal in the class of possibly anticipative controls if an appropriate linear functional is added to the usual LQG cost. This linear functional then gives a ‘price’ for anticipative perturbations away from the optimal nonanticipative control.
We continue the investigation, begun in the companion paper of the author [(*), IMA J. Math. Control Inf. 6, No. 3, 259-265 (1989; Zbl 0696.93072)], of a modification of the LQG problem of linear stochastic system theory in which the usual nonanticipativity condition on the controls is relaxed. It was shown in (*) that if the controller is allowed complete knowledge of the noise sample function before deciding on the control action then the cost is reduced on average by an amount \(\int\text{tr}\{U(t)\Theta\}dt\) below the standard LQG minimal cost.
Here we consider Lagrange multipliers. We show that the standard LQG control is globally optimal in the class of possibly anticipative controls if an appropriate linear functional is added to the usual LQG cost. This linear functional then gives a ‘price’ for anticipative perturbations away from the optimal nonanticipative control.
MSC:
| 93E20 | Optimal stochastic control |
