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Safe Output-Feedback Adaptive Optimal Control of Affine Nonlinear Systems

Tochukwu E. Ogri, Muzaffar Qureshi, Zachary I. Bell, Wanjiku A. Makumi, Rushikesh Kamalapurkar

TL;DR

A safe control synthesis method that integrates state estimation and parameter estimation within an adaptive optimal control (AOC) and control barrier function (CBF)-based control architecture and leverages recent advancements in deep neural network-based adaptive observers to ensure safety in the presence of state estimation errors.

Abstract

In this paper, we develop a safe control synthesis method that integrates state estimation and parameter estimation within an adaptive optimal control (AOC) and control barrier function (CBF)-based control architecture. The developed approach decouples safety objectives from the learning objectives using a CBF-based guarding controller where the CBFs are robustified to account for the lack of full-state measurements. The coupling of this guarding controller with the AOC-based stabilizing control guarantees safety and regulation despite the lack of full state measurement. The paper leverages recent advancements in deep neural network-based adaptive observers to ensure safety in the presence of state estimation errors. Safety and convergence guarantees are provided using a Lyapunov-based analysis, and the effectiveness of the developed controller is demonstrated through simulation under mild excitation conditions.

Safe Output-Feedback Adaptive Optimal Control of Affine Nonlinear Systems

TL;DR

A safe control synthesis method that integrates state estimation and parameter estimation within an adaptive optimal control (AOC) and control barrier function (CBF)-based control architecture and leverages recent advancements in deep neural network-based adaptive observers to ensure safety in the presence of state estimation errors.

Abstract

In this paper, we develop a safe control synthesis method that integrates state estimation and parameter estimation within an adaptive optimal control (AOC) and control barrier function (CBF)-based control architecture. The developed approach decouples safety objectives from the learning objectives using a CBF-based guarding controller where the CBFs are robustified to account for the lack of full-state measurements. The coupling of this guarding controller with the AOC-based stabilizing control guarantees safety and regulation despite the lack of full state measurement. The paper leverages recent advancements in deep neural network-based adaptive observers to ensure safety in the presence of state estimation errors. Safety and convergence guarantees are provided using a Lyapunov-based analysis, and the effectiveness of the developed controller is demonstrated through simulation under mild excitation conditions.
Paper Structure (16 sections, 6 theorems, 78 equations, 12 figures, 1 algorithm)

This paper contains 16 sections, 6 theorems, 78 equations, 12 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation and Preliminaries
  3. System Description
  4. Control Barrier Functions
  5. Robust safety
  6. Stabilizing Optimal Control Design
  7. Approximate desired control policy
  8. Bellman Error and Simulation of Experience
  9. Update laws for Actor and Critic weights
  10. DNN State Observer Design
  11. Stability Analysis
  12. Simulation Results
  13. Staying Within a Convex Set
  14. Obstacle Avoidance
  15. Discussion of results
  16. ...and 1 more sections

Key Result

Theorem 1

SCC.Ames.Xu.ea2017 Given a set $\mathcal{S} \subset \mathbb{R}^{n}$ and a CBF $h : \mathbb{R}^{n} \to \mathbb{R}$ for the system in eq:dynamics, if $\nabla_{x}h(x)g(x) \neq 0$ for all $x \in \partial \mathcal{S}$, then any locally Lipschitz continuous control policy $\pi:\mathbb{R}^{n} \times \mathb guarantees the system in eq:closedSystem is safe with respect to the sets $(\mathcal{S}, \mathcal{S

Figures (12)

  • Figure 1: Schematic of the proposed control system showing the integration of parameter estimation, state estimation, RL, and CBFs to enable safe adaptive optimal control.
  • Figure 2: Trajectory of error signals over switching intervals.
  • Figure 3: Results for Section \ref{['sim:convexSet']}, safety within a given set (marked by a thick green boundary). The trajectories of the actual states $x$ and the estimated state $\hat{x}$ under the safe controller in \ref{['eq:qp']} (robust CBF) are compared against controllers with standard CBF and without CBF.
  • Figure 4: Estimation errors between the actual states and the estimated states for the experiment in Section \ref{['sim:convexSet']}.
  • Figure 5: Estimated critic weights for the experiment in Section \ref{['sim:convexSet']}.
  • ...and 7 more figures

Theorems & Definitions (13)

  • Definition 1
  • Definition 2
  • Theorem 1
  • Theorem 2
  • Remark 1
  • Theorem 3
  • proof
  • Lemma 1
  • proof
  • Lemma 2
  • ...and 3 more