Summary
The expected value of a random cost may be viewed either as its first moment or as its first cumulant. Recently, the Kalman control gain formulas have been generalized to finite linear combinations of cost cumulants, when the systems are described in continuous time. This paper initiates the investigation of cost cumulant control for discrete-time systems. The cost variance is minimized, subject to a cost mean constraint. A new version of Bellman’s optimal cost recursion equation is obtained and solved for the case of full-state measurement. Application is made to the First Generation Structural Benchmark for seismically excited buildings.
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Notes
- 1.
The assumptions that be diagonal and be positive definite have been made for convenience only.
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Cosenza, L., Sain, M.K., Diersing, R.W., Won, CH. (2008). Cumulant Control Systems: The Cost-Variance, Discrete-Time Case. In: Won, CH., Schrader, C., Michel, A. (eds) Advances in Statistical Control, Algebraic Systems Theory, and Dynamic Systems Characteristics. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4795-7_2
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DOI: https://doi.org/10.1007/978-0-8176-4795-7_2
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