Optimal Scheduling of Scalar Gauss-Markov Systems With a Terminal Cost Function

• Published in: IEEE transactions on automatic control Vol. 54; no. 5; pp. 1100 - 1105
• Main Authors: Savage, C.O., La Scala, B.F.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additive noise; Applied sciences; Australia; Computer science; control theory; systems; Control theory. Systems; Cost engineering; Cost function; Estimated state error variance (ESEV); Exact sciences and technology; Gaussian processes; Kalman filters; Mathematical models; Operational research and scientific management; Operational research. Management science; Optimal scheduling; Optimization; Particle measurements; Processor scheduling; Proving; Scalars; Scheduling; Scheduling, sequencing; State estimation; Terminals; Time measurement; Tracking; Target tracking; Gaussian process; Error estimation; Optimal policy; Estimated state error variance (ESEV); Multiple target; Scheduling
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2009.2012994

In this technical note, we consider the problem of optimal measurement scheduling for a particular class of Gauss-Markov systems. These type of scheduling problems arise in applications such as multi-target tracking and sensor management. General solutions to such problems in the Gauss-Markov framework are still the subject of ongoing research. Here, for the first time, we present a set of results for scalar systems, where we consider optimality in the context of minimizing a terminal cost. Complete proofs are given in each case. In some cases, proof outlines have been previously available; other cases are presented here for the first time. For the class of problems considered we demonstrate that simple index policies are optimal. We further examine practical problems in which suboptimal solutions may suffice. Numerical examples are presented for each case.