Finite-time Safety and Reach-avoid Verification of Stochastic Discrete-time Systems

Conceptos Básicos

This paper proposes novel barrier-like sufficient conditions to compute both lower and upper bounds of the probability that a stochastic discrete-time system will exit a safe set or reach a target set within a given bounded time horizon.

Resumen

The paper studies finite-time safety and reach-avoid verification for stochastic discrete-time dynamical systems. The goal is to determine lower and upper bounds of the probability that, within a predefined finite-time horizon, a system starting from an initial state in a safe set will either exit the safe set (safety verification) or reach a target set while remaining within the safe set until the first encounter with the target (reach-avoid verification).

The key highlights are:

1. The paper introduces novel barrier-like sufficient conditions for characterizing these probability bounds, which either complement existing ones or fill gaps.
2. For finite-time safety verification, the proposed conditions in Theorem 1 and 2 provide both lower and upper bounds, going beyond existing works that only offered upper bounds.
3. For finite-time reach-avoid verification, the conditions in Theorem 3 and 5 also compute both lower and upper bounds of the probability.
4. The proposed conditions are more expressive than previous barrier function-based methods, allowing for a wider range of parameters.
5. The effectiveness of the proposed conditions is demonstrated on two numerical examples using semi-definite programming.

Estadísticas

None.

Citas

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Ideas clave extraídas de

Finite-time Safety and Reach-avoid Verification of Stochastic Discrete-time Systems

by Bai Xue a las arxiv.org 04-30-2024

https://arxiv.org/pdf/2404.18118.pdf

Consultas más profundas

What are the potential applications of the proposed finite-time safety and reach-avoid verification techniques beyond the numerical examples provided

The proposed finite-time safety and reach-avoid verification techniques have a wide range of potential applications beyond the numerical examples provided in the paper. One key application is in autonomous systems, such as self-driving cars or drones, where ensuring safety and reaching specific targets within a finite time frame is crucial. These techniques can also be applied in robotics for tasks like path planning and obstacle avoidance. In the aerospace industry, these verification methods can be used for flight control systems to guarantee safe operation and adherence to predefined trajectories. Additionally, in healthcare systems, these techniques can be utilized for patient monitoring and ensuring timely responses to critical events. Overall, the applications extend to various domains where the verification of safety and reach-avoid properties in stochastic systems is essential for reliable and efficient operation.

How could the barrier-like conditions be further extended or generalized to handle more complex system dynamics or temporal specifications

The barrier-like conditions proposed in the paper for finite-time safety and reach-avoid verification can be further extended or generalized to handle more complex system dynamics or temporal specifications. One way to enhance these conditions is by incorporating learning-based approaches to adaptively adjust the barrier functions based on real-time system behavior. Additionally, integrating probabilistic models or Bayesian techniques can improve the accuracy of the probability bounds calculated. Extending the conditions to handle multi-agent systems or networked systems can also broaden their applicability. Furthermore, exploring different types of barrier functions or optimization techniques can enhance the efficiency and scalability of the verification process for larger and more intricate systems.

Are there any connections or synergies between the finite-time verification approach in this paper and other formal methods like model checking or theorem proving

There are significant connections and synergies between the finite-time verification approach presented in this paper and other formal methods like model checking and theorem proving. Model checking techniques can be used to verify the correctness of system models against temporal properties, complementing the finite-time verification for stochastic systems. Theorem proving, on the other hand, provides a formal and rigorous way to establish the correctness of system behavior based on logical reasoning. By integrating these formal methods with the finite-time verification approach, a more comprehensive and robust verification framework can be developed. The combination of these techniques can offer a more thorough analysis of system properties, ensuring safety, reach-avoid guarantees, and compliance with temporal specifications in a wide range of applications.