Logarithm Laws of Self-tuning Regulators


July 24, 2018  15:30-16:30

W303  School of Mathematics, Sichuan University

[lecture]Chanying Li0724-01.png


李婵颖 (中国科学院数学与系统科学研究院)


It was demonstrated that in the Bayesian framework, the logarithm lawGONGSHI.jpg generally characterizes the lower bound to the expected regret in regulation problems. For the Åström-Wittenmark STR problem, [Guo,1995] derived the precise convergence rate of the regret, which achieves the logarithm law exactly. This means the LS-STR is asymptotically efficient. We now prove that for nonlinear uncertain systems, the LS-STR, in some sense, still behaves theoretically superior to other adaptive controllers. The best possible convergence rate for the LS estimator and the logarithm law for regret can be obtained as well for nonlinear systems.


Hui Kou (Sichuan University)

Xu Zhang (Sichuan University)

Jie Zhou (Sichuan University)


Tianyuan Mathematical Center in Southwest China

School of Mathematics, Sichuan University