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Risk-Aware MPC for Stochastic Systems with Runtime Temporal Logics

Maico H. W. Engelaar, Zengjie Zhang, Mircea Lazar, Sofie Haesaert

TL;DR

The paper tackles runtime allocation of STL specifications for linear stochastic systems with additive disturbances by introducing a provably correct risk-aware tube-MPC framework. It leverages probabilistic reachable tubes to convert STL constraints into risk-bounded mixed-integer conditions and performs real-time rescheduling to accept or reject new specifications while preserving previous guarantees. The main contributions are the formalization of runtime specification handling, recursive feasibility proofs, and a practical two-dimensional motion-planning validation showing correct risk management under dynamic tasks. This approach enables flexible, task-adaptive control in multi-robot and human-robot collaboration scenarios with rigorous probabilistic performance guarantees.

Abstract

This paper concerns the risk-aware control of stochastic systems with temporal logic specifications dynamically assigned during runtime. Conventional risk-aware control typically assumes that all specifications are predefined and remain unchanged during runtime. In this paper, we propose a novel, provably correct model predictive control scheme for linear systems with additive unbounded stochastic disturbances that dynamically evaluates the feasibility of runtime signal temporal logic specifications and automatically reschedules the control inputs accordingly. The control method guarantees the probabilistic satisfaction of newly accepted specifications without sacrificing the satisfaction of the previously accepted ones. The proposed control method is validated by a robotic motion planning case study.

Risk-Aware MPC for Stochastic Systems with Runtime Temporal Logics

TL;DR

The paper tackles runtime allocation of STL specifications for linear stochastic systems with additive disturbances by introducing a provably correct risk-aware tube-MPC framework. It leverages probabilistic reachable tubes to convert STL constraints into risk-bounded mixed-integer conditions and performs real-time rescheduling to accept or reject new specifications while preserving previous guarantees. The main contributions are the formalization of runtime specification handling, recursive feasibility proofs, and a practical two-dimensional motion-planning validation showing correct risk management under dynamic tasks. This approach enables flexible, task-adaptive control in multi-robot and human-robot collaboration scenarios with rigorous probabilistic performance guarantees.

Abstract

This paper concerns the risk-aware control of stochastic systems with temporal logic specifications dynamically assigned during runtime. Conventional risk-aware control typically assumes that all specifications are predefined and remain unchanged during runtime. In this paper, we propose a novel, provably correct model predictive control scheme for linear systems with additive unbounded stochastic disturbances that dynamically evaluates the feasibility of runtime signal temporal logic specifications and automatically reschedules the control inputs accordingly. The control method guarantees the probabilistic satisfaction of newly accepted specifications without sacrificing the satisfaction of the previously accepted ones. The proposed control method is validated by a robotic motion planning case study.
Paper Structure (12 sections, 3 theorems, 20 equations, 4 figures, 1 table, 1 algorithm)

This paper contains 12 sections, 3 theorems, 20 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. introduction
  2. Preliminaries and Problem Statement
  3. Class of Systems
  4. Signal Temporal Logic
  5. Problem Statement
  6. Risk-Aware Tube-MPC design with Rescheduling
  7. Probabilistic Reachable Tubes
  8. Risk-Aware Tube-MPC Constraints Design
  9. Risk-Aware Tube-MPC Rescheduling
  10. Theoretical Analysis
  11. Numerical Simulation
  12. Conclusion

Key Result

Theorem 4

Let specification $\phi$ be assigned at time $k$ to the system Eq:NomErr with normalized dynamics. If the nominal trajectory $\{z(k), \cdots, z(N)\}$ with $z(k)=x(k)$ and nominal controls $\{v(k), \cdots, v(N-1)\}$ satisfies Eq:STLCon with $\{\rho(k), \cdots, \rho(N)\}$ strictly positive, than $\mat

Figures (4)

  • Figure 1: Illustration of the classical specification problem.
  • Figure 2: Illustration of the dynamic specification problem. Here, a new task is accepted at times $k=0$, $k=1$, and $k=4$, while at time $k=2$, a task is rejected.
  • Figure 3: The developed approach: real-time specifications, PRTs and risks are dynamically updated and integrated within a deterministic tube-MPC problem, which yields a control update.
  • Figure 4: The red, orange and green trajectory show robotic movement planned at $k=5$, $k=15$ and $k=20$ respectively. The blue trajectory shows the robots' actual movement.

Theorems & Definitions (8)

  • Definition 1
  • Definition 2: Probabilistic Reachable Sets
  • Remark 1
  • Definition 3
  • Remark 2
  • Theorem 4
  • Theorem 5
  • Lemma 6: Risk-Aware Tube Lemma