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Priority-driven Constraints Softening in Safe MPC for Perturbed Systems

Ying Shuai Quan, Mohammad Jeddi, Francesco Prignoli, Paolo Falcone

TL;DR

The paper tackles maintaining hard constraint satisfaction in safe MPC for systems subject to disturbances and unknown constraints by introducing a priority-driven online constraint softening mechanism. A learning-based component predicts suitable relaxations of adjustable constraints, guided by disturbance variation and a contraction-based terminal design, enabling recursive feasibility and safety. The approach comprises an uncertainty-responsive SMPC with slack variables, a slope-restricted neural network to bound and predict slack, Lipschitz/SDP-based guarantees, and a priority-driven algorithm to select which constraints to soften in real time. Simulation in autonomous driving demonstrates collision-avoidance guarantees under unforeseen obstacle motion, with notable reductions in online computation compared to fully slack-based approaches. Overall, the method offers a practically viable, disturbance-responsive SMPC framework for safety-critical, perturbation-prone environments.

Abstract

This paper presents a safe model predictive control (SMPC) framework designed to ensure the satisfaction of hard constraints for systems perturbed by an external disturbance. Such safety guarantees are ensured, despite the disturbance, by online softening a subset of adjustable constraints defined by the designer. The selection of the constraints to be softened is made online based on a predefined priority assigned to each adjustable constraint. The design of a learning-based algorithm enables real-time computation while preserving the original safety properties. Simulations results, obtained from an automated driving application, show that the proposed approach provides guarantees of collision-avoidance hard constraints despite the unpredicted behaviors of the surrounding environment.

Priority-driven Constraints Softening in Safe MPC for Perturbed Systems

TL;DR

The paper tackles maintaining hard constraint satisfaction in safe MPC for systems subject to disturbances and unknown constraints by introducing a priority-driven online constraint softening mechanism. A learning-based component predicts suitable relaxations of adjustable constraints, guided by disturbance variation and a contraction-based terminal design, enabling recursive feasibility and safety. The approach comprises an uncertainty-responsive SMPC with slack variables, a slope-restricted neural network to bound and predict slack, Lipschitz/SDP-based guarantees, and a priority-driven algorithm to select which constraints to soften in real time. Simulation in autonomous driving demonstrates collision-avoidance guarantees under unforeseen obstacle motion, with notable reductions in online computation compared to fully slack-based approaches. Overall, the method offers a practically viable, disturbance-responsive SMPC framework for safety-critical, perturbation-prone environments.

Abstract

This paper presents a safe model predictive control (SMPC) framework designed to ensure the satisfaction of hard constraints for systems perturbed by an external disturbance. Such safety guarantees are ensured, despite the disturbance, by online softening a subset of adjustable constraints defined by the designer. The selection of the constraints to be softened is made online based on a predefined priority assigned to each adjustable constraint. The design of a learning-based algorithm enables real-time computation while preserving the original safety properties. Simulations results, obtained from an automated driving application, show that the proposed approach provides guarantees of collision-avoidance hard constraints despite the unpredicted behaviors of the surrounding environment.

Paper Structure

This paper contains 15 sections, 3 theorems, 25 equations, 6 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Notation
  3. Safe MPC
  4. Priority-driven softened Safe MPC
  5. Uncertainty-Responsive SMPC
  6. Learning Uncertainty-Responsive SMPC
  7. NN with slope-restricted nonlinearity
  8. Lipschitz continuity analysis
  9. Relaxed consistency condition and recursive feasibility
  10. Priority-driven soft-constrained MPC
  11. Simulation Result
  12. Vehicle Model and System Constraints
  13. Date Collection and Training
  14. Simulation scenario
  15. Conclusion

Key Result

Proposition 1

batkovic2022safe Suppose that Assumptions a:cont, a:rec_ref, a:terminal, a:unknown_constraints, and a:safe hold, and that Problem (eq:nmpc) is feasible for the initial state ${\mathbf{x}}_k$. Then, system (eq:sys) in a closed loop with the solution of (eq:nmpc) applied in receding horizon is safe (r

Figures (6)

  • Figure 1: Two time instances of the scenario. Yellow shaded region denotes the predicted position of a pedestrian. Sensing the pedestrian, ego vehicle plans a trajectory (yellow/green/blue line indicating high/medium/low speed) within the sensing range.
  • Figure 2: Infeasibility indicator $\mathcal{F}^1$ from $\text{NN}^1_{E^1}$.
  • Figure 3: Closed-loop trajectories with NNs and (\ref{['eq:unmpc']}).
  • Figure 4: Computation time of applying NN and (\ref{['eq:unmpc']})).
  • Figure 5: Closed-loop trajectories with softened MPC (design 1).
  • ...and 1 more figures

Theorems & Definitions (8)

  • Definition 1: Safety
  • Proposition 1
  • proof
  • Definition 2
  • Theorem 1
  • Definition 3: Safety
  • Theorem 2
  • proof