Adaptive quantile control for stochastic system

Area of Science:

• Control Engineering
• Statistical Signal Processing
• Stochastic Systems

Background:

• Adaptive control relies on accurate parameter estimation for stochastic systems.
• Recursive least squares methods are limited to systems with Gaussian noise.
• Non-Gaussian noise distributions present challenges for traditional adaptive control.

Purpose of the Study:

• To propose a novel adaptive quantile control method for stochastic systems with non-Gaussian noise.
• To develop a Bayesian quantile sum estimator for online parameter estimation.
• To demonstrate the practical applicability and effectiveness of the proposed control strategy.

Main Methods:

• Modeling system noise using the Asymmetric Laplace Distribution.
• Online parameter estimation via a Bayesian quantile sum estimator combining recursive quantile estimations and Bayesian posterior probabilities.
• Constructing the adaptive quantile control law using the certainty equivalence principle.

Main Results:

• The proposed adaptive quantile control effectively handles systems with sharp and thick-tailed noise distributions.
• The Bayesian quantile sum estimator provides accurate online parameter estimation.
• The developed controller is computationally efficient and suitable for Micro Controller Unit implementation.

Conclusions:

• Adaptive quantile control offers a robust alternative to traditional methods for stochastic systems with non-Gaussian noise.
• The Bayesian quantile sum estimator is a key innovation for accurate parameter estimation in such systems.
• The proposed approach is practical for real-world applications due to its low computational demands.