Averaging, aggregation and optimal control of stochastic hybrid systems with singularly perturbed Morkovian switching behavior

Ching Chih Tsai*, Abraham H. Haddad

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations

Abstract

This paper develops methodologies for the averaging, aggregation and optimal control of stochastic hybrid systems whose state equations depend on continuous-time and nearly completely decomposable finite state Markov chains. Such Markovian switching models consist of several identified groups of strongly interacting states. The random sample solution processes of the system state can be well approximated by deterministic trajectories, for the duration of intervals of which the switching process takes values in different groups. Aggregated models are derived, by utilizing averaging and aggregation ideas, to describe the global behavior for the original systems. By modifying concepts of stochastic stabilizability and controllability in [15], necessary and sufficient conditions are established by the perturbation approach. Based on these properties, near-optimum finite and infinite time Markovian jump linear quadratic control problems are explored as well and corresponding averaged cost functions are studied. All the results are shown to hold when the system state and the group index can be exactly measured. Finally, an illustrative example is provided to demonstrate the aforementioned techniques.

Original languageEnglish (US)
Pages (from-to)1868-1872
Number of pages5
JournalProceedings of the American Control Conference
Volume2
StatePublished - Dec 1 1994
EventProceedings of the 1994 American Control Conference. Part 1 (of 3) - Baltimore, MD, USA
Duration: Jun 29 1994Jul 1 1994

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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