Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

State and Input Constrained Adaptive Tracking Control of Uncertain Euler-Lagrange Systems with Robustness and Feasibility Analysis

Poulomee Ghosh, Shubhendu Bhasin

TL;DR

This work addresses tracking for uncertain Euler-Lagrange systems under user-defined state and input constraints in the presence of bounded disturbances. It integrates a Barrier Lyapunov Function (BLF) for state constraint satisfaction with a saturated control law and projection-based adaptive updates to achieve feasible, robust tracking without optimization. A verifiable feasibility condition $C1$ links the input bound $\bar{\tau}$ to state bounds and disturbance levels, ensuring the existence of a feasible policy and bounded closed-loop signals. Simulation on a two-link manipulator confirms constraint satisfaction and improved performance over a robust adaptive baseline, highlighting practical applicability to safety-critical robotic systems.

Abstract

This paper proposes an adaptive tracking controller for uncertain Euler-Lagrange (E-L) systems with user-defined state and input constraints in presence of bounded external disturbances. A barrier Lyapunov function (BLF) is employed for state constraint satisfaction, integrated with a saturated controller that ensures the control input remains within pre-specified bounds. To the best of the authors' knowledge, this is the first result on tracking control of state and input-constrained uncertain E-L systems that provides verifiable conditions for the existence of a feasible control policy. The efficacy of the proposed controller in terms of constraint satisfaction and tracking performance is demonstrated through simulation on a robotic manipulator system.

State and Input Constrained Adaptive Tracking Control of Uncertain Euler-Lagrange Systems with Robustness and Feasibility Analysis

TL;DR

This work addresses tracking for uncertain Euler-Lagrange systems under user-defined state and input constraints in the presence of bounded disturbances. It integrates a Barrier Lyapunov Function (BLF) for state constraint satisfaction with a saturated control law and projection-based adaptive updates to achieve feasible, robust tracking without optimization. A verifiable feasibility condition links the input bound to state bounds and disturbance levels, ensuring the existence of a feasible policy and bounded closed-loop signals. Simulation on a two-link manipulator confirms constraint satisfaction and improved performance over a robust adaptive baseline, highlighting practical applicability to safety-critical robotic systems.

Abstract

This paper proposes an adaptive tracking controller for uncertain Euler-Lagrange (E-L) systems with user-defined state and input constraints in presence of bounded external disturbances. A barrier Lyapunov function (BLF) is employed for state constraint satisfaction, integrated with a saturated controller that ensures the control input remains within pre-specified bounds. To the best of the authors' knowledge, this is the first result on tracking control of state and input-constrained uncertain E-L systems that provides verifiable conditions for the existence of a feasible control policy. The efficacy of the proposed controller in terms of constraint satisfaction and tracking performance is demonstrated through simulation on a robotic manipulator system.

Paper Structure

This paper contains 8 sections, 2 theorems, 40 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Proposed Methodology
  4. Input Constraint Satisfaction Using Saturated Control Design
  5. State Constraint Satisfaction using BLF
  6. Feasibility Analysis
  7. Simulation Results
  8. Conclusion

Key Result

Lemma 1

For any positive constant $\kappa$, let $\Omega_r := \{r \in \mathbb{R}^n : \|r\|<\kappa\}\subset \mathbb{R}^n$ and $\Psi:=\mathbb{R}^N\times \Omega_r \subset \mathbb{R}^{N+n}$ be open sets. Consider the system dynamics given by $\mu:=[r^T,\xi^T]^T\in \Psi$, where $\xi$ is the augmentation of the unconstrained states and the function $f:\mathbb{R}_{+}\times \Psi \rightarrow \mathbb{R}^{N+n}$ is m

Figures (9)

  • Figure 1: Caption
  • Figure 2: Feasibility regions for Case 1
  • Figure 3: Feasibility region for Case 2
  • Figure 4: Feasibility region for Case 3
  • Figure 5: Feasibility region for (\ref{['plant']}).
  • ...and 4 more figures

Theorems & Definitions (7)

  • Remark 1
  • Lemma 1
  • proof
  • Remark 2
  • Theorem 1
  • proof
  • Remark 3