Model Identification Adaptive Control with $ρ$-POMDP Planning

TL;DR

This work addresses informative input design and model identification adaptive control (MIAC) as belief space planning problems, modeled as partially observable Markov decision processes with belief-dependent rewards (ρ-POMDPs) with an adapted belief-space iterative Linear Quadratic Regulator (BiLQR).

Abstract

Accurate system modeling is crucial for safe, effective control, as misidentification can lead to accumulated errors, especially under partial observability. We address this problem by formulating informative input design and model identification adaptive control (MIAC) as belief space planning problems, modeled as partially observable Markov decision processes with belief-dependent rewards ($ρ$-POMDPs). We treat system parameters as hidden state variables that must be localized while simultaneously controlling the system. We solve this problem with an adapted belief-space iterative Linear Quadratic Regulator (BiLQR). We demonstrate it on fully and partially observable tasks for cart-pole and steady aircraft flight domains. Our method outperforms baselines such as regression, filtering, and local optimal control methods, even under instantaneous disturbances to system parameters.

Figures (3)

• Figure 1: MIAC $\log p(\hat{\theta} \mid a_{1:t}, o_{1:t})$ for BiLQR, Random + EKF, MPC + EKF, and MPC + Regression in one example simulation of the fully observable cart-pole environment (showing the mean trend with error would obscure the BiLQR trend, since the baseline uncertainties in $\log p_{\hat{\theta},\tau}$ are orders of magnitude larger than BiLQR).
• Figure 2: MIAC $\log p(\hat{\theta} \mid a_{1:t}, o_{1:t})$ for BiLQR, Random + EKF, and MPC + EKF in one example simulation of the partially observable aircraft environment.
• Figure 3: Tracking change in pole mass that changes suddenly at time $t = t_c$ for one example simulation with BiLQR.