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Periodic Event-Triggered Prescribed Time Control of Euler-Lagrange Systems under State and Input Constraints

Chidre Shravista Kashyap, Karnan A, Pushpak Jagtap, Jishnu Keshavan

Abstract

This article proposes a periodic event-triggered adaptive barrier control policy for the trajectory tracking problem of perturbed Euler-Lagrangian systems with state, input, and temporal (SIT) constraints. In particular, an approximation-free adaptive-barrier control architecture is designed to ensure prescribed-time convergence of the tracking error to a prescribed bound while rejecting exogenous disturbances. In contrast to existing approaches that necessitate continuous real-time control action, the proposed controller generates event-based updates through periodic evaluation of the triggering condition. Additionally, we derive an upper bound on the monitoring period by analysing the performance degradation of the filtered tracking error to facilitate periodic evaluation of the event-triggered strategy. To this end, a time-varying threshold function is considered in the triggering mechanism to reduce the number of triggers during the transient phase of system behaviour. Notably, the proposed design avoids Zeno behaviour and precludes the need for continuous monitoring of the triggering condition. A simulation and experimental study is undertaken to demonstrate the efficacy of the proposed control scheme.

Periodic Event-Triggered Prescribed Time Control of Euler-Lagrange Systems under State and Input Constraints

Abstract

This article proposes a periodic event-triggered adaptive barrier control policy for the trajectory tracking problem of perturbed Euler-Lagrangian systems with state, input, and temporal (SIT) constraints. In particular, an approximation-free adaptive-barrier control architecture is designed to ensure prescribed-time convergence of the tracking error to a prescribed bound while rejecting exogenous disturbances. In contrast to existing approaches that necessitate continuous real-time control action, the proposed controller generates event-based updates through periodic evaluation of the triggering condition. Additionally, we derive an upper bound on the monitoring period by analysing the performance degradation of the filtered tracking error to facilitate periodic evaluation of the event-triggered strategy. To this end, a time-varying threshold function is considered in the triggering mechanism to reduce the number of triggers during the transient phase of system behaviour. Notably, the proposed design avoids Zeno behaviour and precludes the need for continuous monitoring of the triggering condition. A simulation and experimental study is undertaken to demonstrate the efficacy of the proposed control scheme.

Paper Structure

This paper contains 10 sections, 3 theorems, 27 equations, 5 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Problem Statement
  4. Adaptive PETC Design
  5. Stability Analysis
  6. Analysis of the Periodic Event-Triggering Mechanism
  7. Results and Discussion
  8. Simulation results
  9. Experimental Studies
  10. Conclusion

Key Result

Theorem 3.1

Consider the state and input-constrained EL system eq:ptcuel_eom with Propertiesprope1-prope3 and satisfying Assumptionsass:parameter-ass:trajectory. Then the adaptive control policy eq:petc_control_policy under the event-triggered mechanism eq:petc_not_triggered_value ensures that local PTPB stabil

Figures (5)

  • Figure 1: PETC Adaptive Barrier Control Architecture
  • Figure 2: Simulation results for the IIWA 14 robot depicting trajectory tracking under the proposed control policy \ref{['eq:petc_mechanism']} with comparisons against the studies in chen2023adaptivewang2022adaptive for the chosen prescribed time of $T = 4\text{s}$ and $h=0.0002$s.
  • Figure 3: The FR3 robot arm tracking the desired trajectory within the prescribed time $T=4s$. The red dotted and green solid lines denote the desired and traced trajectories respectively.
  • Figure 4: Experimental results for the FR 3 robotic arm tracking a reference trajectory illustrating the satisfaction of state and input constraints using the proposed PETC scheme \ref{['eq:petc_mechanism']} with monitoring period $h = 0.001$s and prescribed time $T=4s$.
  • Figure 5: Experimental results for the FR 3 robotic arm tracking a reference trajectory illustrating the satisfaction of state and input constraints using the proposed control policy \ref{['eq:petc_mechanism']}.

Theorems & Definitions (8)

  • Definition 2.7: csk:2025
  • Remark 2.8
  • Remark 2.9
  • Theorem 3.1
  • Remark 3.2
  • Theorem 3.3: minimum inter-event time
  • Proposition 3.4
  • Remark 3.5