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MAPS: A Mode-Aware Probabilistic Scheduling Framework for LPV-Based Adaptive Control

Taehun Kim, Guntae Kim, Cheolmin Jeong, Chang Mook Kang

TL;DR

MAPS presents a unified framework that merges IMM-based real-time mode estimation with LPV gain scheduling to tackle friction-induced uncertainties in DC motor control. By using mode probabilities as convex interpolation weights for online gain synthesis, MAPS achieves friction-aware adaptation without explicit friction modeling. The approach is supported by theoretical stability guarantees under a common Lyapunov function and robustness to scheduling mismatch, with exponential stability under bounded estimation error. Empirical validation on Simulink and a Hardware-in-the-Loop testbed demonstrates superior state estimation accuracy and improved reference tracking under varying friction and external loads, highlighting practical real-time applicability and broad generalizability to other parameter-varying systems.

Abstract

This paper proposes Mode-Aware Probabilistic Scheduling (MAPS), a novel adaptive control framework tailored for DC motor systems experiencing varying friction. MAPS uniquely integrates an Interacting Multiple Model (IMM) estimator with a Linear Parameter-Varying (LPV) based control strategy, leveraging real-time mode probability estimates to perform probabilistic gain scheduling. A key innovation of MAPS lies in directly using the updated mode probabilities as the interpolation weights for online gain synthesis in the LPV controller, thereby tightly coupling state estimation with adaptive control. This seamless integration enables the controller to dynamically adapt control gains in real time, effectively responding to changes in frictional operating modes without requiring explicit friction model identification. Validation on a Hardware-in-the-Loop Simulation (HILS) environment demonstrates that MAPS significantly enhances both state estimation accuracy and reference tracking performance compared to Linear Quadratic Regulator (LQR) controllers relying on predefined scheduling variables. These results establish MAPS as a robust, generalizable solution for friction-aware adaptive control in uncertain, time-varying environments, with practical real-time applicability.

MAPS: A Mode-Aware Probabilistic Scheduling Framework for LPV-Based Adaptive Control

TL;DR

MAPS presents a unified framework that merges IMM-based real-time mode estimation with LPV gain scheduling to tackle friction-induced uncertainties in DC motor control. By using mode probabilities as convex interpolation weights for online gain synthesis, MAPS achieves friction-aware adaptation without explicit friction modeling. The approach is supported by theoretical stability guarantees under a common Lyapunov function and robustness to scheduling mismatch, with exponential stability under bounded estimation error. Empirical validation on Simulink and a Hardware-in-the-Loop testbed demonstrates superior state estimation accuracy and improved reference tracking under varying friction and external loads, highlighting practical real-time applicability and broad generalizability to other parameter-varying systems.

Abstract

This paper proposes Mode-Aware Probabilistic Scheduling (MAPS), a novel adaptive control framework tailored for DC motor systems experiencing varying friction. MAPS uniquely integrates an Interacting Multiple Model (IMM) estimator with a Linear Parameter-Varying (LPV) based control strategy, leveraging real-time mode probability estimates to perform probabilistic gain scheduling. A key innovation of MAPS lies in directly using the updated mode probabilities as the interpolation weights for online gain synthesis in the LPV controller, thereby tightly coupling state estimation with adaptive control. This seamless integration enables the controller to dynamically adapt control gains in real time, effectively responding to changes in frictional operating modes without requiring explicit friction model identification. Validation on a Hardware-in-the-Loop Simulation (HILS) environment demonstrates that MAPS significantly enhances both state estimation accuracy and reference tracking performance compared to Linear Quadratic Regulator (LQR) controllers relying on predefined scheduling variables. These results establish MAPS as a robust, generalizable solution for friction-aware adaptive control in uncertain, time-varying environments, with practical real-time applicability.

Paper Structure

This paper contains 31 sections, 3 theorems, 62 equations, 10 figures, 6 tables.

Table of Contents

  1. Introduction
  2. System Modeling
  3. DC Motor Model
  4. State-Space Representation
  5. Viscous Friction Coefficient Identification
  6. Filter Design
  7. Simulation Modeling
  8. Standard Kalman Filter
  9. Interacting Multiple Model
  10. Controller Design
  11. Discrete-Time Linear Quadratic Regulator Theory
  12. Linear Parameter Varying System
  13. Closed-loop Stability Analysis of MAPS
  14. Experimental Setup and Scenario
  15. Experimental Environments
  16. ...and 16 more sections

Key Result

Lemma 1

Let $\mathrm{\Phi}^{[i]}$ be the vertex systems of a discrete-time polytopic LPV model. Assume that for each $i$, a stabilizing state feedback gain $K^{[i]}$ is designed such that the following inequality holds: for some symmetric positive definite matrix $P \succ 0$. Then, any convex combination of these systems, defined as is quadratically stable. Here, $\mathrm{\Phi}^{\text{cl}}_{k}$ denotes

Figures (10)

  • Figure 1: MAPS framework architecture.
  • Figure 2: Friction characteristics showing coulomb/viscous regions.
  • Figure 3: Experimental Architecture
  • Figure 4: State estimation comparison: IMM-KF(red) vs. standard KF(blue).
  • Figure 5: State estimation error comparison: IMM-KF(red) vs. standard KF(blue).
  • ...and 5 more figures

Theorems & Definitions (10)

  • Remark
  • Lemma 1: Quadratic Stability of Polytopic Vertex Systems
  • proof
  • Theorem 1: Stability of MAPS-Gain Scheduled LPV Control
  • proof
  • Remark
  • Remark
  • Theorem 2: Exponential Stability of MAPS-Gain LPV Control under Parameter Estimation Error
  • proof
  • Remark