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Nonlinear Reachable Set Computation and Model Predictive Control for Safe Hypersonic Re-entry of Atmospheric Vehicles

Jinaykumar Patel, Kamesh Subbarao

Abstract

This paper investigates the application of reachability analysis to the re-entry problem faced by vehicles entering Earth's atmosphere. The study delves into the time evolution of reachable sets for the system, particularly when subject to nonlinear implicit controls, given the potential damage from the intense heat generated during hypersonic re-entry. Our proposed methodology leverages zonotopes and constrained zonotopes to ensure compliance with safety specifications. Furthermore, we utilize Model Predictive Control for detailed trajectory planning. To substantiate our methodology, we provide detailed simulations that not only tackle nonlinear re-entry scenarios but also illustrate trajectory planning using MPC.

Nonlinear Reachable Set Computation and Model Predictive Control for Safe Hypersonic Re-entry of Atmospheric Vehicles

Abstract

This paper investigates the application of reachability analysis to the re-entry problem faced by vehicles entering Earth's atmosphere. The study delves into the time evolution of reachable sets for the system, particularly when subject to nonlinear implicit controls, given the potential damage from the intense heat generated during hypersonic re-entry. Our proposed methodology leverages zonotopes and constrained zonotopes to ensure compliance with safety specifications. Furthermore, we utilize Model Predictive Control for detailed trajectory planning. To substantiate our methodology, we provide detailed simulations that not only tackle nonlinear re-entry scenarios but also illustrate trajectory planning using MPC.
Paper Structure (24 sections, 27 equations, 6 figures, 3 tables, 2 algorithms)

This paper contains 24 sections, 27 equations, 6 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Representation of the System and Control Parameters
  4. Reachability
  5. Set Representations: A Primer
  6. Computation of the Reachable Set for a Nonlinear System
  7. Computation of the Set of Linearization Errors
  8. Heat Transfer Analysis
  9. Heat Rate Constraint
  10. Model Predictive Control
  11. Cost Function
  12. Constraints
  13. Reachable Safe Sets:
  14. Control Inputs:
  15. Implementation
  16. ...and 9 more sections

Figures (6)

  • Figure 1: Reachable set tube (Altitude vs Velocity) and heat rate limit
  • Figure 2: Zonotope reachable sets evolution
  • Figure 3: Constrained zonotope reachable sets evolution given the heating limit (red-line)
  • Figure 4: Altitude vs Time
  • Figure 5: Velocity vs Time
  • ...and 1 more figures