Maximally Permissive Supervisory Control with Forcible Events

Core Concepts

This paper proposes a supervisory control theory that allows the supervisor to not only enable/disable events, but also force specific events (called forcible events) that can preempt uncontrollable events. The authors define a notion of forcible-controllability that captures the interplay between controllability of a supervisor and the uncontrollable events provided by a plant in the setting with event forcing. They show the existence of a maximally permissive, forcibly-controllable, nonblocking supervisor and provide an algorithm to compute such a supervisor.

Abstract

The paper introduces a supervisory control theory that extends the traditional Ramadge-Wonham framework by allowing the supervisor to force specific events, called forcible events, in addition to enabling/disabling events. This enriched interaction mechanism between the supervisor and the plant enables the supervisor to preempt uncontrollable events.

The key contributions are:

1. Definition of forcible-controllability: This notion captures the interplay between the controllability of a supervisor and the uncontrollable events provided by the plant in the setting with event forcing. Forcible-controllability allows the supervisor to use forcible events to preempt uncontrollable events.

2. Existence of maximally permissive supervisor: The authors show that a maximally permissive, forcibly-controllable, nonblocking supervisor exists for any given plant and specification.

3. Synthesis algorithm: An algorithm is provided to compute the maximally permissive, forcibly-controllable, nonblocking supervisor. The algorithm maintains sets of nonblocking states, bad states, and states where forcing is applied to handle the absence of the transitivity property for forcibly-controllable sublanguages.

4. Illustration: Two small case studies are presented to illustrate the approach.

The paper generalizes the classical supervisory control theory by incorporating the notion of forcible events, which allows the supervisor to preempt uncontrollable events. This enriched interaction mechanism can lead to more permissive supervisors compared to the traditional approach.

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Key Insights Distilled From

Supervisory Control Theory with Event Forcing

by Michel Renie... at arxiv.org 04-15-2024

https://arxiv.org/pdf/2404.08469.pdf

Deeper Inquiries

What are some potential real-world applications of the proposed supervisory control theory with forcible events

The proposed supervisory control theory with forcible events has several potential real-world applications. One application could be in autonomous vehicles, where the supervisor can force certain actions (such as emergency braking) to preempt potential accidents or collisions. Another application could be in industrial automation, where the supervisor can force specific events to ensure safety protocols are followed or to optimize production processes. Additionally, in cybersecurity systems, the supervisor could force certain actions to prevent security breaches or unauthorized access.

How does the performance of the maximally permissive supervisor compare to a traditional supervisor in terms of permissiveness and computational complexity

The maximally permissive supervisor generated by the proposed approach offers greater permissiveness compared to a traditional supervisor. The traditional supervisor in supervisory control theory typically focuses on enabling or disabling events, while the maximally permissive supervisor with forcible events can preempt uncontrollable events by forcing specific actions. This additional capability enhances the permissiveness of the supervisor, allowing for more flexibility in controlling the system's behavior. In terms of computational complexity, the proposed approach may involve additional considerations for handling forcible events, but the benefits of increased permissiveness may outweigh the slight increase in complexity.

Can the proposed approach be extended to handle other types of control mechanisms, such as timed events or probabilistic transitions, in addition to forcible events

The proposed approach can potentially be extended to handle other types of control mechanisms, such as timed events or probabilistic transitions, in addition to forcible events. By incorporating timing constraints or probabilistic behaviors into the supervisory control framework, the system can respond to events based on specific timing requirements or probabilistic outcomes. This extension would require adapting the algorithm to consider timing constraints or probabilistic transitions in addition to forcible events, expanding the capabilities of the supervisory control system to handle a wider range of scenarios.