Optimality Zone Algorithms for Hybrid Systems: Efficient Algorithms for Optimal Location and Control Computation

2006 ◽  
pp. 123-137 ◽  
Author(s):  
Peter E. Caines ◽  
M. Shahid Shaikh
Keyword(s):  
Hybrid Systems ◽  
Optimal Location ◽  
Efficient Algorithms ◽  
And Control

scholarly journals Theory of hybrid dynamical systems and its applications to biological and medical systems

2010 ◽  
Vol 368 (1930) ◽  
pp. 4893-4914 ◽  
Author(s):  
Kazuyuki Aihara ◽  
Hideyuki Suzuki
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamical Systems ◽  
Mathematical Modelling ◽  
Systems Theory ◽  
Control Systems ◽  
Hybrid Systems ◽  
Hybrid Dynamical Systems ◽  
Medical Systems ◽  
Theme Issue ◽  
And Control

In this introductory article, we survey the contents of this Theme Issue. This Theme Issue deals with a fertile region of hybrid dynamical systems that are characterized by the coexistence of continuous and discrete dynamics. It is now well known that there exist many hybrid dynamical systems with discontinuities such as impact, switching, friction and sliding. The first aim of this Issue is to discuss recent developments in understanding nonlinear dynamics of hybrid dynamical systems in the two main theoretical fields of dynamical systems theory and control systems theory. A combined study of the hybrid systems dynamics in the two theoretical fields might contribute to a more comprehensive understanding of hybrid dynamical systems. In addition, mathematical modelling by hybrid dynamical systems is particularly important for understanding the nonlinear dynamics of biological and medical systems as they have many discontinuities such as threshold-triggered firing in neurons, on–off switching of gene expression by a transcription factor, division in cells and certain types of chronotherapy for prostate cancer. Hence, the second aim is to discuss recent applications of hybrid dynamical systems in biology and medicine. Thus, this Issue is not only general to serve as a survey of recent progress in hybrid systems theory but also specific to introduce interesting and stimulating applications of hybrid systems in biology and medicine. As the introduction to the topics in this Theme Issue, we provide a brief history of nonlinear dynamics and mathematical modelling, different mathematical models of hybrid dynamical systems, the relationship between dynamical systems theory and control systems theory, examples of complex behaviour in a simple neuron model and its variants, applications of hybrid dynamical systems in biology and medicine as a road map of articles in this Theme Issue and future directions of hybrid systems modelling.

scholarly journals New Software Tool for Modeling and Control of Discrete-Event and Hybrid Systems Using Timed Interpreted Petri Nets

2020 ◽  
Vol 10 (15) ◽  
pp. 5027 ◽  
Author(s):  
Erik Kučera ◽  
Oto Haffner ◽  
Peter Drahoš ◽  
Ján Cigánek ◽  
Roman Leskovský  ◽  
...  
Keyword(s):  
Petri Nets ◽  
Hybrid Systems ◽  
Industry 4.0 ◽  
Discrete Event Systems ◽  
Production Systems ◽  
Discrete Event ◽  
Software Tool ◽  
Modeling And Control ◽  
Event Systems ◽  
And Control

For the development of modern complex production processes in Industry 4.0, it is appropriate to effectively use advanced mathematical models based on Petri nets. Due to their versatility in modeling discrete-event systems, Petri nets are an important support in creating new platforms for digitized production systems. The main aim of the proposed article is to design a new software tool for modeling and control of discrete-event and hybrid systems using Arduino and similar microcontrollers. To accomplish these tasks, a new tool called PN2ARDUINO based on Petri nets is proposed able to communicate with the microcontroller. Communication with the microcontroller is based on the modified Firmata protocol hence, the control algorithm can be implemented on all microcontrollers that support this type of protocol. The developed software tool was successfully verified in control of laboratory systems. In addition, it can be used for education and research purposes as it offers a graphical environment for designing control algorithms for hybrid and mainly discrete-event systems. The proposed software tool can improve education and practice in cyber-physical systems (Industry 4.0).

Sign in / Sign up

Export Citation Format

Share Document