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APECS: Adaptive Personalized Control System Architecture

Marius F. R. Juston, Alex Gisi, William R. Norris, Dustin Nottage, Ahmet Soylemezoglu

TL;DR

The Adaptive Personalized Control System (APECS) addresses human-in-the-loop control without direct plant models by learning a Lipschitz-bounded, sector-bounded controller that maps human input to a safe, personalized command. It combines an $L$-Lipschitz neural network with a saturating, elementwise $p(\phantom{a})$ and a trainable scale $L_t$ to enforce a controlled Lipschitz behavior, while training via a weighted loss that balances human imitation and expert reference via an analytically derived optimal weight $\\gamma^*$. The key contributions include the APECS architecture, a novel elementwise sector bounding of the network output, a derivation of worst-case loss bounds for both expert and human operators, and an explicit procedure to set the loss balance and Lipschitz level. Empirically, APECS yields a $4.5\%$ RMSE improvement over a veteran human operator and a $9\%$ improvement over a standard feed-forward NN in trajectory-tracking tasks, with robustness to varying Lipschitz constraints. This work advances shared autonomy by enabling personalized, safe operator-assisted control through formal Lipschitz guarantees and data-driven weighting of human and expert performance.

Abstract

This paper presents the Adaptive Personalized Control System (APECS) architecture, a novel framework for human-in-the-loop control. An architecture is developed which defines appropriate constraints for the system objectives. A method for enacting Lipschitz and sector bounds on the resulting controller is derived to ensure desirable control properties. An analysis of worst-case loss functions and the optimal loss function weighting is made to implement an effective training scheme. Finally, simulations are carried out to demonstrate the effectiveness of the proposed architecture. This architecture resulted in a 4.5% performance increase compared to the human operator and 9% to an unconstrained feedforward neural network trained in the same way.

APECS: Adaptive Personalized Control System Architecture

TL;DR

The Adaptive Personalized Control System (APECS) addresses human-in-the-loop control without direct plant models by learning a Lipschitz-bounded, sector-bounded controller that maps human input to a safe, personalized command. It combines an -Lipschitz neural network with a saturating, elementwise and a trainable scale to enforce a controlled Lipschitz behavior, while training via a weighted loss that balances human imitation and expert reference via an analytically derived optimal weight . The key contributions include the APECS architecture, a novel elementwise sector bounding of the network output, a derivation of worst-case loss bounds for both expert and human operators, and an explicit procedure to set the loss balance and Lipschitz level. Empirically, APECS yields a RMSE improvement over a veteran human operator and a improvement over a standard feed-forward NN in trajectory-tracking tasks, with robustness to varying Lipschitz constraints. This work advances shared autonomy by enabling personalized, safe operator-assisted control through formal Lipschitz guarantees and data-driven weighting of human and expert performance.

Abstract

This paper presents the Adaptive Personalized Control System (APECS) architecture, a novel framework for human-in-the-loop control. An architecture is developed which defines appropriate constraints for the system objectives. A method for enacting Lipschitz and sector bounds on the resulting controller is derived to ensure desirable control properties. An analysis of worst-case loss functions and the optimal loss function weighting is made to implement an effective training scheme. Finally, simulations are carried out to demonstrate the effectiveness of the proposed architecture. This architecture resulted in a 4.5% performance increase compared to the human operator and 9% to an unconstrained feedforward neural network trained in the same way.

Paper Structure

This paper contains 15 sections, 1 theorem, 28 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Formulation
  4. APECS Architecture
  5. Lipschitz Constraint
  6. Lipschitz bounding
  7. Training
  8. Maximum expert operator loss
  9. Maximum human operator loss
  10. Equal weighting
  11. Experiment
  12. Conclusion
  13. Link
  14. $\gamma^*$ Constraint Satisfication
  15. Neural network initialization proof

Key Result

Proposition 1

The $\gamma^*$, defined as eqn:optimal_gamma, satisfies the conditions in eqn:gammaConditions for all $\alpha$.

Figures (11)

  • Figure 1: APECS Architecture
  • Figure 2: APECS Process Control Diagram
  • Figure 3: Default Controller trajectory following
  • Figure 4: Loss comparison for $\gamma = 0$
  • Figure 5: Total loss $\gamma = 0$
  • ...and 6 more figures

Theorems & Definitions (1)

  • Proposition 1