Discrete-Time Control for Systems of Interacting Objects with Unknown Random Disturbance Distributions: A Mean Field Approach
| Autor: | J. Adolfo Minjárez-Sosa, Héctor Jasso-Fuentes, Carmen G. Higuera-Chan |
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| Rok vydání: | 2015 |
| Předmět: |
Stochastic control
0209 industrial biotechnology Control and Optimization Markov chain Optimality criterion Differential equation Applied Mathematics 010102 general mathematics Mathematical analysis 02 engineering and technology 01 natural sciences 020901 industrial engineering & automation Asymptotically optimal algorithm Mean field theory Control theory Convergence (routing) Applied mathematics 0101 mathematics Mathematics |
| Zdroj: | Applied Mathematics & Optimization. 74:197-227 |
| ISSN: | 1432-0606 0095-4616 |
| Popis: | We are concerned with stochastic control systems composed of a large number of N interacting objects sharing a common environment. The evolution of each object is determined by a stochastic difference equation where the random disturbance density $$\rho $$ź is unknown for the controller. We present the Markov control model (N-model) associated to the proportions of objects in each state, which is analyzed according to the mean field theory. Thus, combining convergence results as $$N\rightarrow \infty $$Nźź (the mean field limit) with a suitable statistical estimation method for $$\rho $$ź, we construct the so-named eventually asymptotically optimal policies for the N-model under a discounted optimality criterion. A consumption-investment problem is analyzed to illustrate our results. |
| Databáze: | OpenAIRE |
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