Optimal adaptive control: A non-linear separation theorem†
作者:
D. G. LAINIOTIS,
J. G. DESHPANDE,
T. N. UPADHYAY,
期刊:
International Journal of Control
(Taylor Available online 1972)
卷期:
Volume 15,
issue 5
页码: 877-888
ISSN:0020-7179
年代: 1972
DOI:10.1080/00207177208932202
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
For the quadratic cost, non-linear, adaptive stochastic control problem with linear plant and measurement models excited by white gaussian noise, and unknown time-invariant model parameters, the optimal stochastic control is obtained and shown to separate (‘non-linear separation theorem’) into a bank of model-conditional deterministic controller gains and a corresponding bank of known non-linear functional of the model-conditional, causal, mean-square state-vector estimates. This separation may also be viewed as a decomposition of the optimal, non-linear adaptive control into a bank of model-conditional, optimal, non-adaptive linear controls, one for each admissible value fof the unknown parameter θ and a nonlinear part, namely the bank of aposteriorimodel probabilities, which incorporate the adaptive nature, of the optimal adaptive control. Results are given for a special case of the above problem— namely, uncertainty in the measurement matrix—that exhibit drastically reduced computational requirements. In this special case, we have explicit separation between control and estimation, and it is shown that only one deterministic controller is required to be used with the non-linear, adaptive, mean-square state-vector estimate.
点击下载:
PDF (406KB)
返 回