Note on control for hybrid stochastic systems by intermittent feedback rooted in discrete observations of state and mode with delays

Lichao Feng; Dongxue Li; Chunyan Zhang; Yanmei Yang; Lichao Feng; Dongxue Li; Chunyan Zhang; Yanmei Yang

doi:10.3934/era.2024002

Electronic Research Archive

2024, Volume 32, Issue 1: 17-40. doi: 10.3934/era.2024002

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Note on control for hybrid stochastic systems by intermittent feedback rooted in discrete observations of state and mode with delays

College of Science, North China University of Science and Technology, Tangshan 063210, China

Received: 17 August 2023 Revised: 22 November 2023 Accepted: 28 November 2023 Published: 12 December 2023

For a hybrid stochastic system, most existing feedback controllers need to observe modes at continuous times, which is feasible when the system's mode is observable and does not incur any cost. However, in most cases, the mode is not readily apparent, and identifying it always incurs a certain expense. Therefore, in order to reduce control costs, when designing a feedback controller, both the state and the mode should be observed at discrete moments. This paper introduces an intermittent feedback controller for stabilizing an unstable hybrid stochastic system through discrete delayed observations of state and mode. By utilizing M-matrix theory, intermittent control approach, and the comparison principle, we propose sufficient conditions for the stabilization theory of hybrid stochastic systems. An illustrative example is taken to validate the proposed theory.
- hybrid stochastic system,
- discrete observations,
- delay,
- intermittent feedback control
Citation: Lichao Feng, Dongxue Li, Chunyan Zhang, Yanmei Yang. Note on control for hybrid stochastic systems by intermittent feedback rooted in discrete observations of state and mode with delays[J]. Electronic Research Archive, 2024, 32(1): 17-40. doi: 10.3934/era.2024002

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Abstract

For a hybrid stochastic system, most existing feedback controllers need to observe modes at continuous times, which is feasible when the system's mode is observable and does not incur any cost. However, in most cases, the mode is not readily apparent, and identifying it always incurs a certain expense. Therefore, in order to reduce control costs, when designing a feedback controller, both the state and the mode should be observed at discrete moments. This paper introduces an intermittent feedback controller for stabilizing an unstable hybrid stochastic system through discrete delayed observations of state and mode. By utilizing M-matrix theory, intermittent control approach, and the comparison principle, we propose sufficient conditions for the stabilization theory of hybrid stochastic systems. An illustrative example is taken to validate the proposed theory.

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