Full Information H 2 Control of Borel-Measurable Markov Jump Systems with Multiplicative Noises

Hongji Ma and Yang Wang
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Hongji Ma: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Yang Wang: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Mathematics, 2021, vol. 10, issue 1, 1-13

Abstract: This paper addresses an H 2 optimal control problem for a class of discrete-time stochastic systems with Markov jump parameter and multiplicative noises. The involved Markov jump parameter is a uniform ergodic Markov chain taking values in a Borel-measurable set. In the presence of exogenous white noise disturbance, Gramian characterization is derived for the H 2 norm, which quantifies the stationary variance of output response for the considered systems. Moreover, under the condition that full information of the system state is accessible to measurement, an H 2 dynamic optimal control problem is shown to be solved by a zero-order stabilizing feedback controller, which can be represented in terms of the stabilizing solution to a set of coupled stochastic algebraic Riccati equations. Finally, an iterative algorithm is provided to get the approximate solution of the obtained Riccati equations, and a numerical example illustrates the effectiveness of the proposed algorithm.

Keywords: H 2 control; markov chain; borel set; gramian; riccati equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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