Learning-Based Adaptive Optimal Control for Flotation Processes Subject to Input Constraints

Zhongmei Li, Mengzhe Huang, Jianyong Zhu, Weihua Gui, Zhong Ping Jiang, Wenli Du

Research output: Contribution to journalArticlepeer-review


This article presents a learning-based adaptive optimal control approach for flotation processes subject to input constraints and disturbances using adaptive dynamic programming (ADP) along with double-loop iteration. First, the principle of the operational pattern is adopted to preset reagents' addition based on the feeding condition. Then, this article leverages a deep learning model, which is composed of multiple neural layers to detect flotation indexes directly from the raw froth images. After that, the tracking error between the detected flotation indexes and the reference values can be minimized by using ADP-based double-loop iteration. Particularly, a policy-iteration (PI) method is utilized for the proposed learning-based ADP algorithm. In the inner loop, the optimal control problem is formulated as a linear quadratic regulator (LQR) problem using the low-gain feedback design method. In the outer loop, the design parameters, i.e., weighting matrices, are tuned automatically to satisfy the input constraints. Finally, the analytical results demonstrate that the proposed scheme can guarantee asymptotic tracking in the presence of actuator saturation and disturbances.

Original languageEnglish (US)
Pages (from-to)252-264
Number of pages13
JournalIEEE Transactions on Control Systems Technology
Issue number1
StatePublished - Jan 1 2023


  • Actuator saturation
  • adaptive dynamic programming (ADP)
  • deep learning (DL) model
  • flotation processes
  • reagents' control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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