TY - JOUR
T1 - Optimum design of measurement channels and control policies for linear-quadratic stochastic systems
AU - Başar, Tamer
AU - Bansal, Rajesh
N1 - Funding Information:
* This work was supported in part by the US Department of Energy under Grant DE-FG-02-88-ER-13939, and in part by the Joint Services Electronics Program under Grant N00014-90-J-1270. Correspondence to: T. Ba§ar, Coordinated Science Laboratory, University of Illinois, 1308 Main Street, Urbana, IL 61801, USA.
PY - 1994/3/10
Y1 - 1994/3/10
N2 - In the design of optimal controllers for linear-quadratic stochastic systems, a standard assumption is that the measurement channels are fixed and linear, and the measurement noise is Gaussian. In this paper we relax the first part of this restriction and raise the issue of the derivation of optimum measurement structures as a part of the overall design. Toward this end, we take the measuement process as one given by a Wiener integral, and modify the cost function so that it now places some soft constraints on the measurement strategy. Using some results from information theory, we show that the scalar version (for both finite and infinite horizons) of this joint design problem admits an optimum, dictating linear designs for both the controller and the measurement strategy. For the vector version, however, it is possible for a nonlinear design to improve over the best linear one. In both cases, best linear designs involve the solutions of nonlinear (deterministic) optimal control problems.
AB - In the design of optimal controllers for linear-quadratic stochastic systems, a standard assumption is that the measurement channels are fixed and linear, and the measurement noise is Gaussian. In this paper we relax the first part of this restriction and raise the issue of the derivation of optimum measurement structures as a part of the overall design. Toward this end, we take the measuement process as one given by a Wiener integral, and modify the cost function so that it now places some soft constraints on the measurement strategy. Using some results from information theory, we show that the scalar version (for both finite and infinite horizons) of this joint design problem admits an optimum, dictating linear designs for both the controller and the measurement strategy. For the vector version, however, it is possible for a nonlinear design to improve over the best linear one. In both cases, best linear designs involve the solutions of nonlinear (deterministic) optimal control problems.
KW - Decentralized systems
KW - Dynamic optimization
KW - LQG design
KW - Optimum signal design
KW - Stochastic control
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U2 - 10.1016/0377-2217(94)90261-5
DO - 10.1016/0377-2217(94)90261-5
M3 - Article
AN - SCOPUS:0028396597
SN - 0377-2217
VL - 73
SP - 226
EP - 236
JO - European Journal of Operational Research
JF - European Journal of Operational Research
IS - 2
ER -