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Smart Predict-Then-Control: Control-Aware Surrogate Refinement for System Identification

Jiachen Li, Shihao Li, Dongmei Chen

Abstract

This paper introduces Smart Predict Then Control (SPC), a control aware refinement procedure for model based control. SPC refines a prediction oriented model by optimizing a surrogate objective that evaluates candidate models through the control actions they induce. For a fixed surrogate variant under unconstrained control, we establish the smoothness of the surrogate, projected gradient convergence at a sublinear rate of order one over K, and a bias decomposition that yields a conditional transfer diagnostic. On a wind disturbed quadrotor trajectory tracking task, Updated SPC reduces tracking RMSE by 70 percent and closed loop cost by 42 percent relative to the nominal baseline.

Smart Predict-Then-Control: Control-Aware Surrogate Refinement for System Identification

Abstract

This paper introduces Smart Predict Then Control (SPC), a control aware refinement procedure for model based control. SPC refines a prediction oriented model by optimizing a surrogate objective that evaluates candidate models through the control actions they induce. For a fixed surrogate variant under unconstrained control, we establish the smoothness of the surrogate, projected gradient convergence at a sublinear rate of order one over K, and a bias decomposition that yields a conditional transfer diagnostic. On a wind disturbed quadrotor trajectory tracking task, Updated SPC reduces tracking RMSE by 70 percent and closed loop cost by 42 percent relative to the nominal baseline.

Paper Structure

This paper contains 23 sections, 6 theorems, 55 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. PROBLEM FORMULATION
  3. METHOD
  4. Initialization
  5. Auxiliary Evaluation Parameter
  6. Scenario-Based Control Computation
  7. SPC Surrogate Loss
  8. Fixed-Surrogate SPC Algorithm
  9. THEORETICAL ANALYSIS
  10. Regularity of the Surrogate
  11. Convergence of Projected-Gradient SPC
  12. Bias Decomposition and Conditional Transfer
  13. EXPERIMENTS
  14. Setup
  15. Results
  16. ...and 8 more sections

Key Result

Proposition 4

Under Assumptions as:theta_compact_revised--as:Fi_reg_revised, the following hold for each $i$:

Figures (2)

  • Figure 1: Overview of the SPC refinement pipeline.
  • Figure 2: Wind-disturbed quadrotor trajectory tracking.

Theorems & Definitions (15)

  • Definition 1: Deployment metric
  • Remark 1: Not reweighting
  • Remark 2: Updated-surrogate variant
  • Proposition 4: Smoothness of optimizer map/ surrogate
  • Theorem 5: Gradient convergence
  • Proposition 6: Bias decomposition
  • Theorem 8: Conditional transfer
  • Lemma 9: Rollout smoothness
  • proof
  • proof
  • ...and 5 more