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| Optimal Control with Learning on the Fly from Finite to Infinite-DimensionalSystems |
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Citation： |
Feifei MIAO.Optimal Control with Learning on the Fly from Finite to Infinite-DimensionalSystems[J].Chinese Annals of Mathematics B,2026,(5):833~854 |
| Page view： 2
Net amount： 4 |
Authors： |
Feifei MIAO; |
Foundation： |
the National Natural Science Foundation of China (Nos. 12025105,
11971334). |
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| Abstract： |
The main aim of this paper is to extend the Bayesian approach to finding
quadratic optimal control to a wider range of stochastic linear systems. These systems
involve an unknown parameter in the drift term, which is observed through a noisy linear
channel. The author demonstrates the effectiveness of the Bayesian strategy by comparing
the cost it incurs with that of an optimal control that possesses complete knowledge of
the parameter. The findings reveal that the Bayesian strategy minimizes the worst-case
multiplicative regret. Furthermore, the author provides a proof that the corresponding
adaptive scheme is optimal when the unknown system parameter belongs to an infinite
space. This result further validates the effectiveness of the Bayesian strategy in handling
systems with unknown parameters. In summary, this paper contributes to the generalization of the Bayesian strategy for the optimal control in stochastic linear systems with
unknown parameters. It also establishes a theoretical basis for its optimality. |
Keywords： |
Bayesian strategy Kalman-Bucy filter Optimal control Adaptive
control Multiplicative regret |
Classification： |
93C40, 93C41, 93E11 |
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