Steady-State Control Reference and Token Conservation Laws in Continuous Petri Net Systems

This paper addresses several questions related to the control of timed continuous Petri nets under infinite server semantics. First, some results regarding equilibrium states and control actions are given. In particular, it is shown that the considered systems are piecewise linear, and for every lin...

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Bibliographic Details
Published in:IEEE transactions on automation science and engineering 2008-04, Vol.5 (2), p.307-320
Main Authors: Mahulea, C., Ramirez-Trevino, A., Recalde, L., Silva, M.
Format: Article
Language:English
Subjects:
Applied sciences
Approximation
Computer science
control theory
systems
Continuous time systems
Control system analysis
Control system synthesis
Control systems
Control theory. Systems
Controllability
Discrete event systems
Distributed control systems
Dynamical systems
Dynamics
Exact sciences and technology
Fluid dynamics
Linear systems
Logistics
Manufacturing
Mathematical analysis
Mathematical problems
Operational research and scientific management
Operational research. Management science
Optimal control
Optimization
Petri nets
Piecewise linear techniques
Polynomials
Semantics
Steady state
Transitions
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Summary:This paper addresses several questions related to the control of timed continuous Petri nets under infinite server semantics. First, some results regarding equilibrium states and control actions are given. In particular, it is shown that the considered systems are piecewise linear, and for every linear subsystem the possible steady states are characterized. Second, optimal steady-state control is studied, a problem that surprisingly can be computed in polynomial time, when all transitions are controllable and the objective function is linear. Third, an interpretation of some controllability aspects in the framework of linear dynamic systems is presented. An interesting finding is that noncontrollable poles are zero valued.
ISSN:1545-5955
1558-3783
DOI:10.1109/TASE.2007.893504