Measurement scheduling for recursive team estimation

We consider a decentralized LQG measurement scheduling problem in which every measurement is costly, no communication between observers is permitted, and the observers' estimation errors are coupled quadratically. This setup, motivated by considerations from organization theory, models measurement scheduling problems in which cost, bandwidth, or security constraints necessitate that estimates be decentralized, although their errors are coupled. We show that, unlike the centralized case, in the decentralized case the problem of optimizing the time integral of the measurement cost and the quadratic estimation error is fundamentally stochastic, and we characterize the ε-optimal open-loop schedules as chattering solutions of a deterministic Lagrange optimal control problem. Using a numerical example, we describe also how this deterministic optimal control problem can be solved by nonlinear programming.

[1]  Y. Ho,et al.  Team decision theory and information structures in optimal control problems--Part II , 1972 .

[2]  R. Radner,et al.  Economic theory of teams , 1972 .

[3]  L. Arnold.  Stochastic Differential Equations: Theory and Applications , 1992 .

[4]  T. Kailath.  A Note on Least Squares Estimation by the Innovations Method , 1972 .

[5]  R. Radner,et al.  Team Decision Problems , 1962 .

[6]  E B Lee,et al.  Foundations of optimal control theory , 1967 .

[7]  T. Yoshikawa.  Decomposition of dynamic team decision problems , 1978 .

[8]  Michael Athans,et al.  1972 IFAC congress paper: On the determination of optimal costly measurement strategies for linear stochastic systems , 1972 .

[9]  Yu-Chi Ho,et al.  Correction to "Team decision theory and information structures in optimal control problems," Parts I and II , 1972 .

[10]  Harold J. Kushner,et al.  On the optimum timing of observations for linear control systems with unknown initial state , 1964 .

[11]  D. N. P. Murthy,et al.  Parameter estimation for auto-regressive models with uncertain observation , 1980 .

[12]  Steven Michael Barta,et al.  On linear control of decentralized stochastic systems , 1978 .

[13]  J. Bernussou,et al.  An easy way to find gradient matrix of composite matricial functions , 1981 .

[14]  Z. Gajic.  On the quasi-decentralized estimation and control of linear stochastic systems , 1987 .

[15]  Abrahim Lavi,et al.  Optimal observation policies in linear stochastic systems , 1968 .

[16]  L. Meier,et al.  Optimal control of measurement subsystems , 1967 .