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Achieving Precisely-Assigned Performance Requirements for Spacecraft Attitude Control

Jiakun Lei

TL;DR

The paper addresses the challenge of achieving precisely-assigned performance in spacecraft attitude control by introducing the Precisely-Assigned Performance (PAP) framework. It combines a parametrically defined Reference Performance Function (RPF) with a control barrier-function (CBF) based condition to create a performance-satisfied tube around the desired transient, enforcing a precise settling time, bounded steady-state error, and minimal overshoot. A backstepping-inspired PAP controller, augmented by Sontag’s universal stabilization and a disturbance observer, guarantees convergence into the tube and provides an explicit finite-time bound for reaching the performance region, while remaining singularity-free. The approach is validated numerically on a rigid-body spacecraft under large disturbances and across Monte Carlo trials, demonstrating robust performance, rapid convergence, and avoidance of PPC singularities. This framework offers a practically implementable, computation-friendly alternative to optimization-based safety controllers for high-performance spacecraft attitude tasks.

Abstract

This paper investigates the attitude control problem of spacecraft, with the objective of achieving precise performance criteria including precise settling time, steady-state error, and overshoot elimination. To tackle this challenge, we propose the Precisely-Assigned Performance (PAP) control scheme. Firstly, we utilize a parameterized function to explicitly characterize a reference for the transient responses, termed the Reference Performance Function (RPF). Subsequently, leveraging the concept of the RPF, we define a performance-satisfied tube region and introduce the concept of control barrier functions to derive a sufficient condition for the state trajectory to converge and remain confined within this tube region. By introducing the concept of Sontag's universal formula for stabilization, a PAP controller, constructed based on the backstepping method, is then designed to guide the system to satisfy these affine constraint conditions, and a disturbance observer is further integrated to handle perturbations. Theoretical proofs are presented to demonstrate the controller's capability to establish the boundedness of the overall system and ensure that each state trajectory will converge into the performance-satisfied region within a finite time duration under any conditions. Finally, numerical simulation results are presented to validate the effectiveness of the proposed method.

Achieving Precisely-Assigned Performance Requirements for Spacecraft Attitude Control

TL;DR

The paper addresses the challenge of achieving precisely-assigned performance in spacecraft attitude control by introducing the Precisely-Assigned Performance (PAP) framework. It combines a parametrically defined Reference Performance Function (RPF) with a control barrier-function (CBF) based condition to create a performance-satisfied tube around the desired transient, enforcing a precise settling time, bounded steady-state error, and minimal overshoot. A backstepping-inspired PAP controller, augmented by Sontag’s universal stabilization and a disturbance observer, guarantees convergence into the tube and provides an explicit finite-time bound for reaching the performance region, while remaining singularity-free. The approach is validated numerically on a rigid-body spacecraft under large disturbances and across Monte Carlo trials, demonstrating robust performance, rapid convergence, and avoidance of PPC singularities. This framework offers a practically implementable, computation-friendly alternative to optimization-based safety controllers for high-performance spacecraft attitude tasks.

Abstract

This paper investigates the attitude control problem of spacecraft, with the objective of achieving precise performance criteria including precise settling time, steady-state error, and overshoot elimination. To tackle this challenge, we propose the Precisely-Assigned Performance (PAP) control scheme. Firstly, we utilize a parameterized function to explicitly characterize a reference for the transient responses, termed the Reference Performance Function (RPF). Subsequently, leveraging the concept of the RPF, we define a performance-satisfied tube region and introduce the concept of control barrier functions to derive a sufficient condition for the state trajectory to converge and remain confined within this tube region. By introducing the concept of Sontag's universal formula for stabilization, a PAP controller, constructed based on the backstepping method, is then designed to guide the system to satisfy these affine constraint conditions, and a disturbance observer is further integrated to handle perturbations. Theoretical proofs are presented to demonstrate the controller's capability to establish the boundedness of the overall system and ensure that each state trajectory will converge into the performance-satisfied region within a finite time duration under any conditions. Finally, numerical simulation results are presented to validate the effectiveness of the proposed method.
Paper Structure (29 sections, 5 theorems, 50 equations, 11 figures)

This paper contains 29 sections, 5 theorems, 50 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Formulation
  4. System Modeling
  5. Precisely-Assigned Performance Constraints
  6. Precise Settling Time
  7. Precise Steady-State Error
  8. Maximum Overshoot Elimination
  9. Control Objective
  10. Precisely-Assigned Performance Control Scheme
  11. Main Structure and Logic
  12. Tracking Performance Constraint
  13. PAP Condition
  14. PAP Controller
  15. The Design of the Virtual Control Law
  16. ...and 14 more sections

Key Result

Lemma 1

Given a sufficiently large constant $h > 0$, $|\tanh(hx)|\ge |x|$ holds for $x\in\left[-h_{0},h_{0}\right]$, where $h_{0} \in\left(0,1\right)$ is a positive constant li2016adaptive.

Figures (11)

  • Figure 1: Main Logic of the PAP Control Scheme
  • Figure 2: Illustration of the RPF and the state region satisfies the TPC
  • Figure 3: Illustration Explanation of the above Conclusions
  • Figure 7: Time evolution of $q_{evi}(t)$ and $\rho_{i}(t)$ (Normal Case)
  • Figure 8: Time evolution of $\omega_{si}(t)$ (Normal Case)
  • ...and 6 more figures

Theorems & Definitions (12)

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