A stochastic linear quadratic optimal control problem is considered in which some of the plant states may be measured without a measurement noise component. This set of states are assumed to be associated with the plant inputs and force transducers. The optimal controller is shown to include state feedback from this part of the system. The states which cannot be measured are assumed to be combined in noisy output signal. The optimal controller corresponding to this second subsystem is shown to include a Kalman filter and state-estimate feedback.
The combination of state and state-estimate feedback has the advantage that the dimension of the Kalman filter is equal to that of the second subsystem mentioned above. In the conventional solution to this problem, no states are assumed measurable, and the dimension of the Kalman filter is equal to the dimension of the complete system. In many industrial control problems, the combined control law enables a significant reduction in the dimension of the filter to be achieved. The technique has been proposed for use in dynamic ship positioning control systems, and this problem is discussed.
[1]
M. J. Grimble.
Relationship between Kalman and notch filters used in dynamic ship positioning systems
,
1978
.
[2]
James S. Meditch,et al.
Stochastic Optimal Linear Estimation and Control
,
1969
.
[3]
D. Naidu,et al.
Optimal Control Systems
,
2018
.
[4]
R. E. Kalman,et al.
New Results in Linear Filtering and Prediction Theory
,
1961
.
[5]
U. Shaked.
A general transfer function approach to linear stationary filtering and steady-state optimal control problems
,
1976
.
[6]
Uri Shaked,et al.
A general transfer-function approach to the steady-state linear quadratic Gaussian stochastic control problem
,
1976
.
[7]
R. E. Kalman,et al.
A New Approach to Linear Filtering and Prediction Problems
,
2002
.
[8]
Michael J. Grimble,et al.
The Design of Dynamic Ship Positioning Control Systems Using Extended Kalman Filtering Techniques
,
1979
.