Optimal Stabilization of Linear Stochastic System with Statistically Uncertain Piecewise Constant Drift

Andrey Borisov, Alexey Bosov and Gregory Miller
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Andrey Borisov: Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44/2 Vavilova Str., 119333 Moscow, Russia
Alexey Bosov: Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44/2 Vavilova Str., 119333 Moscow, Russia
Gregory Miller: Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44/2 Vavilova Str., 119333 Moscow, Russia

Mathematics, 2022, vol. 10, issue 2, 1-16

Abstract: The paper presents an optimal control problem for the partially observable stochastic differential system driven by an external Markov jump process. The available controlled observations are indirect and corrupted by some Wiener noise. The goal is to optimize a linear function of the state (output) given a general quadratic criterion. The separation principle, verified for the system at hand, allows examination of the control problem apart from the filter optimization. The solution to the latter problem is provided by the Wonham filter. The solution to the former control problem is obtained by formulating an equivalent control problem with a linear drift/nonlinear diffusion stochastic process and with complete information. This problem, in turn, is immediately solved by the application of the dynamic programming method. The applicability of the obtained theoretical results is illustrated by a numerical example, where an optimal amplification/stabilization problem is solved for an unstable externally controlled step-wise mechanical actuator.

Keywords: Markov jump process; Itô stochastic differential equation; optimal control; quadratic criterion; stochastic filtering; Wonham filter (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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