A Stochastic Decentralized Control Problem with Noisy Communication

Autor:	Kambiz Shoarinejad, Jason L. Speyer, Ioannis Kanellakopoulos
Rok vydání:	2002
Předmět:	Stochastic control Mathematical optimization Asymptotic analysis Control and Optimization Asymptotically optimal algorithm Transmission (telecommunications) Applied Mathematics Witsenhausen's counterexample Decentralised system Communication channel Mathematics Counterexample
Zdroj:	SIAM Journal on Control and Optimization. 41:975-990
ISSN:	1095-7138 0363-0129
DOI:	10.1137/s0363012901385629
Popis:	A simple decentralized stochastic control problem is considered where the nonclassical nature of the information pattern is induced by the uncertainty on the information transmission in the system. This is, in fact, a reformulation of the Witsenhausen counterexample, where the first station is allowed to send its information to the second station through a noisy channel. Nonconvexity of the problem in this new formulation has been established, and it is shown how this formulation relates to a classical problem and the Witsenhausen problem, respectively, when the transmission noise intensity goes to zero or infinity. Assuming small transmission noise intensity, we then use an asymptotic approach in order to find an approximated cost. A necessary condition for asymptotically optimal strategies has been obtained using a variational approach, and it is shown that the linear strategies, with slightly different coefficients than the noiseless transmission case, satisfy the necessary condition.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::45a9bb5df4e4ecad4a17a1285b812a2e https://doi.org/10.1137/s0363012901385629 Zobrazit plný text záznamu Plný text ve formátu PDF