Extended Timed Petri Net Modelling Approach for a Class of Hybrid Dynamic Systems

Hybrid dynamical systems (HDS) exhibit the interaction of both continuous and discrete dynamic behaviours, providing a highly realistic representation of physical systems. This framework has attracted extensive research due to its ability to model and analyze complex systems accurately. Among the tools employed in this domain, Petri nets have emerged as a valuable approach for capturing the behaviour of HDS. This work presents an Extended Timed Continuous Petri Nets (ETCPN) framework for effectively modelling discrete-time hybrid dynamical systems (HDS). This extension allows the integration of the ordinary strengths and timed continuous Petri nets, enabling them to capture the intricate dynamics of these systems. It permits the combination of these Petri net formalisms to describe hybrid dynamics behaviours effectively. The investigation unfolds through an analytical depiction of the HDS, followed by schematic modelling, and is subsequently validated through a numerical simulation model. The viability of the ETCPN modelling frame-work is explored through an analytical description of HDS, schematic construction of the ETCPN model, and corresponding numerical simulation for validation. The results highlight the ability of ETCPNs as a modelling tool for the analysis and simulation of discrete-time hybrid dynamical systems.