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Auto-Optimization with Active Learning in Uncertain Environment: A Predictive Control Approach

Yuan Tan, Jun Yang, Zhongguo Li, Wen-Hua Chen, Shihua Li

TL;DR

The paper tackles auto-optimization of model predictive control in unknown environments by integrating exploitation-focused MPC with active learning. It introduces EO-MPC to guarantee parameter convergence via virtual excitation in the terminal set and extends to AL-MPC that predicts future data and actively explores the environment to reduce uncertainty. The authors prove recursive feasibility and convergence for both frameworks and validate them on numerical benchmarks, photovoltaic MPPT, and phototropic nano-drone control, showing faster adaptation and improved tracking. This work offers a practical, robust approach for real-time operation under environmental uncertainty with demonstrated applicability to energy systems and autonomous platforms.

Abstract

This paper presents an auto-optimal model predictive control (MPC) framework enhanced with active learning, designed to autonomously track optimal operational conditions in an unknown environment,where the conditions may dynamically adjust to environmental changes. First, an exploitation-oriented MPC (EO-MPC) is proposed, integrating real-time sampling data with robust set-based parameter estimation techniques to address the critical challenge of parameter identification. By introducing virtual excitation signals into the terminal constraint and establishing a validation mechanism for persistent excitation condition, the EO-MPC effectively resolves the issue of insufficient persistent excitation in parameter identification. Building upon this foundation, an active learning MPC (AL-MPC) approach is developed to integrate both available and virtual future data to resolve the fundamental conflict between tracking an unknown optimal operational condition and parameter identification. The recursive feasibility and convergence of the proposed methods are rigorously established, and numerous examples substantiate the reliability and effectiveness of the approach in practical applications.

Auto-Optimization with Active Learning in Uncertain Environment: A Predictive Control Approach

TL;DR

The paper tackles auto-optimization of model predictive control in unknown environments by integrating exploitation-focused MPC with active learning. It introduces EO-MPC to guarantee parameter convergence via virtual excitation in the terminal set and extends to AL-MPC that predicts future data and actively explores the environment to reduce uncertainty. The authors prove recursive feasibility and convergence for both frameworks and validate them on numerical benchmarks, photovoltaic MPPT, and phototropic nano-drone control, showing faster adaptation and improved tracking. This work offers a practical, robust approach for real-time operation under environmental uncertainty with demonstrated applicability to energy systems and autonomous platforms.

Abstract

This paper presents an auto-optimal model predictive control (MPC) framework enhanced with active learning, designed to autonomously track optimal operational conditions in an unknown environment,where the conditions may dynamically adjust to environmental changes. First, an exploitation-oriented MPC (EO-MPC) is proposed, integrating real-time sampling data with robust set-based parameter estimation techniques to address the critical challenge of parameter identification. By introducing virtual excitation signals into the terminal constraint and establishing a validation mechanism for persistent excitation condition, the EO-MPC effectively resolves the issue of insufficient persistent excitation in parameter identification. Building upon this foundation, an active learning MPC (AL-MPC) approach is developed to integrate both available and virtual future data to resolve the fundamental conflict between tracking an unknown optimal operational condition and parameter identification. The recursive feasibility and convergence of the proposed methods are rigorously established, and numerous examples substantiate the reliability and effectiveness of the approach in practical applications.

Paper Structure

This paper contains 27 sections, 7 theorems, 47 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Motivation
  3. Related Work
  4. Contributions
  5. Notation
  6. Problem Description
  7. System dynamics and constraints
  8. The unknown environment
  9. Control objective and challenges
  10. Exploitation-Oriented MPC
  11. Robust set-based parameter estimation
  12. Persistent excitation
  13. Cost function
  14. Terminal constraint set design
  15. Optimization problem
  16. ...and 12 more sections

Key Result

Lemma 1

Under Assumption 1, if the regressor $\phi(y_k)$ satisfies the PE condition for Eq. (eq19), the estimated parameter set $\Theta_k$ converges to the true parameter set $\{\theta^*\}$ as $k \to \infty$ with probability 1.

Figures (5)

  • Figure 1: The parameter set $\Theta_{k}$ is bounded by the constraints shown in red, and the parameter estimate $\bar{\theta}_k$ lies inside this set. The predicted bounds are shown as dashed blue lines, which depend on the control input variables $u_{i|k}$. The blue shaded region shows the resulting predicted parameter set $\hat{\Theta}_{i|k}$.
  • Figure 2: Example 1: estimated parameter set at time steps $k \in \{0,1, 3, 5, 10, 50\}$ for different algorithms.
  • Figure 3: Example 1: simulation results for the numerical example.
  • Figure 4: Example 2: simulation results for MPPT.
  • Figure 5: Example 3: simulation results for phototropic control.

Theorems & Definitions (9)

  • Remark 1
  • Remark 2
  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Lemma 3
  • Theorem 2
  • Theorem 3
  • Theorem 4