[Paper Review] Modeling and analysis using hybrid Petri nets

Latéfa Ghomri, Hassane Alla|arXiv (Cornell University)|Jun 12, 2007

Petri Nets in System Modeling12 references4 citations

TL;DR

This paper proposes hybrid Petri net (HPN) models for modeling and analyzing hybrid dynamic systems (HDS), extending discrete Petri nets through fluidification to continuous models and introducing two distinct HPN formalisms: one for deterministic HDS and another for nondeterministic HDS. The key contribution is a unified framework enabling modeling, analysis, and controller synthesis for complex hybrid systems using formal, mathematically grounded HPN structures.

ABSTRACT

This paper is devoted to the use of hybrid Petri nets (PNs) for modeling and control of hybrid dynamic systems (HDS). Modeling, analysis and control of HDS attract ever more of researchers' attention and several works have been devoted to these topics. We consider in this paper the extensions of the PN formalism (initially conceived for modeling and analysis of discrete event systems) in the direction of hybrid modeling. We present, first, the continuous PN models. These models are obtained from discrete PNs by the fluidification of the markings. They constitute the first steps in the extension of PNs toward hybrid modeling. Then, we present two hybrid PN models, which differ in the class of HDS they can deal with. The first one is used for deterministic HDS modeling, whereas the second one can deal with HDS with nondeterministic behavior. Keywords: Hybrid dynamic systems; D-elementary hybrid Petri nets; Hybrid automata; Controller synthesis

Motivation & Objective

• Address the growing need for formal modeling and analysis techniques for hybrid dynamic systems (HDS) that combine discrete and continuous behaviors.
• Extend classical discrete Petri nets to handle continuous dynamics through fluidification of markings, forming the foundation for hybrid modeling.
• Develop two distinct hybrid Petri net models: one for deterministic HDS and another for systems with nondeterministic behavior.
• Enable formal controller synthesis and system analysis within a unified formalism based on hybrid Petri nets.
• Provide a theoretical framework that supports both modeling and verification of hybrid systems using hybrid automata and Petri net extensions.

Proposed method

• Introduce continuous Petri net models by fluidifying discrete markings, transforming discrete token counts into continuous fluid levels.
• Propose a first hybrid Petri net model tailored for deterministic hybrid dynamic systems, integrating continuous and discrete transitions.
• Develop a second hybrid Petri net model capable of representing systems with nondeterministic behavior, enhancing modeling flexibility.
• Utilize the formalism of hybrid automata to structure the behavior of the proposed HPN models, ensuring compatibility with existing hybrid system theory.
• Apply controller synthesis techniques within the HPN framework to enable automatic generation of control policies for hybrid systems.
• Leverage the duality between Petri nets and hybrid automata to ensure consistency and correctness in system modeling and analysis.

Experimental results

Research questions

• RQ1 How can discrete Petri nets be extended to model hybrid systems with both discrete and continuous dynamics?
• RQ2 What formalism enables the representation of deterministic hybrid dynamic systems using hybrid Petri nets?
• RQ3 How can hybrid Petri nets be adapted to model systems with nondeterministic behavior?
• RQ4 What is the role of fluidification in transitioning from discrete to continuous Petri net models?
• RQ5 Can controller synthesis be effectively performed within the proposed hybrid Petri net framework?

Key findings

• The fluidification of discrete Petri net markings successfully produces continuous Petri net models, forming a foundational step toward hybrid modeling.
• The proposed deterministic hybrid Petri net model enables accurate modeling and analysis of systems with predictable continuous and discrete dynamics.
• The extended HPN model for nondeterministic systems supports the representation of systems with multiple possible behaviors, enhancing modeling expressiveness.
• The integration of hybrid automata concepts into the HPN framework ensures formal consistency and supports rigorous system analysis.
• Controller synthesis is feasible within the proposed HPN framework, enabling automated generation of control strategies for hybrid systems.
• The approach provides a unified formalism that supports both modeling and verification of hybrid dynamic systems, with applications in system design and control.