This term refers to at least two kind of systems. According to the values of the time variable, there are continuous time systems and discrete time systems. In continuous time systems, the changes in the variables may occur at any moment of time in a given interval. In discrete time systems, variables can only change at "discrete" time moments (Discrete in this case, means isolated.) For example, a digital controller takes measurements at fixed (typically, periodic) moments of time, and changes the decision variable (controlled input) at some fixed (typically, periodic) moments of time. The states of the controlled plant however change continuously. So a plant that is controlled with a digital controller can be modelled as a hybrid system, in the sense of continuous time and discrete time. However, if you look at the values that the state variables may take, there are systems in which the states evolve continuously, and systems in which the states may only take discrete values. A switch is the simplest example of a discrete state system, since it can only be ON and OFF. Now, since variables in a computer are stored numerically, ultimately in binary form, a digital controller is nothing else but a very complex system of switches. So a plant that is controlled with a digital controller can be seen as a hybrid system consisting of a continuous state system (the plant) and a discrete state system (the controller).

For both kinds of hybrid systems and their control, there is extensive literature. Hope this answer helps you find a way out there.

You may find a good introduction and a few examples in:

02/2013; In book: Modeling, Analysis and Design of Hybrid Systems, Publisher: Springer - Verlag 2002, Editors: S. Engell, G. Frehse, E. Schnieder

A hybrid system is the combination of different approaches. For example, discrete system linked to other system whose behavior can be descripted by a continuous domain time. For example, a fuzzy system combined with a nonlinear system. There are many possibilities.

I just look at the Wikipedia article on the HS, and can point out that there are no words about control, just about modelling... So, I perceive it as a sign of methodological misunderstanding... The topicstarter had made the right question, and it seems to me the HS gurus don't have any definition that can help to differ HS from so called behavioristic systems, or reactive systems, or event-driven systems, or just a control system. Also, lack of words about control make me think that there is no clear differentiation between control object and control algorithm in the field. As to the question about control -- as I see systems of the HS-class can be controlled by any event-driven approach used on the PLC level of automation (simple one by the SFC language (from IEC 61131-3), complex one by the Reflex language... FSM-based, hyperprocess-based, or Petri net-based language)... Also have a look at "Shanmugham S. G., Roberts C. A. Application of graphical specification methodologies to manufacturing control logic development: a classification and comparison // Int. J. Computer integrated manufacturing. 1998. V. 11. No 2." that covers graphic solutions for the task...

have a nice day, Vladimir E. Zyubin

Moufid: thank you for the enlightment... It seems to me, the above (Hysteresis, Manual transmission, Bouncing ball, Temperature control system, Water-level monitor, Multiple collisions...) is just an eclectic set. In some cases it is a modelling problem (hystersis, bouncing ball, multiple collisions), in some cases it is an ordinary PID control (temperature control system), in some cases it is a data aquisition system (water-level monitor)... "Hybrid systems" sounds like a buzz-words that is used to cover scholastic research activity... No definition, no strict field of tasks...

Well, for me it seems to be not a very usefull discussion. I answered and referred to a book I think it is better to read it first. It is in English and containers the outcome of a six-years focus research program funded by the German Research Foundation (DFG). There were not only stupid guys in the committee.

With best regards, Hans-Michael Hanisch

Hans-Michael: do you insist I need to buy the book in orded to understand what the smart guys mean when they say "hybrid system"?!

with best regards, Vladimir

I do not insist, but it should be helpful anyway. I guess you have a library... By the way, not all of the authors were so very smart, but I think that it is a good overview. And it contains more than academic examples.

With best regards, Hans-Michael Hanisch

Moufid: Thank you for the link. But... Do you think the definition "Hybrid systems are dynamical systems with interacting continuous-time dynamics (modeled, for example, by differential equations) and discrete-event dynamics (modeled, for example, by automata)." is exact and helpful?

The problems I see within the sentence are the following:

1. Why does the sentence (that pretend to be a definition) include examples?

2. Why does the sentence have words about modeling and about moreover means of modeling? A modeled thing is just a model of the thing. As I suspect it is just a software model.

3. A system with dynamics is just a dynamical system by definition, so there is no needs to point out that the system is dynamical.

So the sentence can be reduced to the following:

"Hybrid systems are software models of systems with interacting continuous-time dynamics and discrete-event dynamics"

It is just formal problems... If we will try to dig a bit deeper we can make the following questions: why don't we see that the discrete-event dynamics is just a set of continuous-time dynamics(es) ? So, the statement can be reduced to the following one:

"Hybrid systems are software models of systems with discrete-event dynamics"...

"System is a model of system"... Is it good definition? Nop. So, it seems to me, the right answer on the topicstarter's question looks like:

"Hybrid systems are systems with discrete-event dynamics. The people who say they deal with hybrid system mean they deal with software modeling of discrete-event systems".

with best regards, Vladimir

Dear Dr. Moufid Bouhentala Ali: I do realise that a lot of words have been produced within the so called hybrid system theory... As to me the IEC 61131-3 languages were known much before 1993 (when the IEC 61131-3 doc has been produced). These languages were invented to program programmable logic controllers (or PLCs) in order to construct control systems, i. e. "a system that senses, switches, or regulates another system" ( http://www.collinsdictionary.com/dictionary/english/control-system?showCookiePolicy=true )... "There are two common classes of control systems, with many variations and combinations: logic or sequential controls, and feedback or linear controls" ( http://en.wikipedia.org/wiki/Control_system ). So, I can not catch why somebody use the words "hybrid systems" to name systems that are called "control systems".

Dear all,

The Wikipedia definition is crap. It is absolutely wrong to rely on that. For me is too late today to write a longer comment, but actually it should be taught at any undergraduate lecture on control systems. Please note that I am an engineer...

With best regards, Hans-Michael Hanisch

Dear Dr. Hanish, you are absolutely right in your critics of Wikipedia, but I (as an engineer as well) don't see some principal uncertainty in the quote. Also please note that engineering community practically does not use the term "hybrid systems". Have a look at http://control.com/search.php?search_string=%22hybrid+systems%22

(It is an archive that collects millions of messages posted by engineers on control systems topics: SCADA, DCS, PLC, OPC, IEC 61131-3, IEC 61499, HMI, communications, motion control, engineering, languages, software to name a few) And there are a lot of people you know (as I suspect): Dr. Steinhoff, Dr. Vyutkin, Dr. Haase are among them.

Please be a bit more tolerant to the Wikipedia articles and the authors that can have their own opinion and (as I think) are practical engineers as well.

Regards, Vladimir E. Zyubin

Dear all,

I MUST come back to my criticisms regarding wikipedia. In my understanding, wikipedia was thought to be some kind of an encyclopedia and NOT a chatroom for exchanging opinions that do not correspond to reality.

I cite the article in wikipedia:

"There are two common classes of control systems, with many variations and combinations: logic or sequential controls, and feedback or linear controls. There is also fuzzy logic, which attempts to combine some of the design simplicity of logic with the utility of linear control. Some devices or systems are inherently not controllable."

What is, for example, with nonlinear control? It is not in the definition. That is the same as I would claim that the western border of Russia is the Ural Mountains. ALL Russians would agree that this is crap.

A second example: What about logic closed-loop control? No feedback? Sorry, have a look at, for example, manufacturing sites in the automotive industry. Could you believe that there is no feedback in the control system? Would you drive a car that is manufactured in this way?

A third example: Linear feedforward control. There is no feedback in such systems. This is part of the basic course in automatic control for undergraduate students. Would you pass an exam with a definition like above?

I could continue. My conclusion: Saying that this is crap is not a question of tolerance but a fact.

Bye and best regards, Hans-Michael Hanisch

Dear Hans-Michael,

You are deadly right in your critics of some Wikipedia's articles. But who is without sin? Even the sun has spots... To err is human, and so on.

I personally mention the article just to point out that the control systems definition looks very similar to the hybrid systems definition.

"A control system is a device, or set of devices to manage, command, direct or regulate the behavior of other device(s) or system(s)." (and American Heritage Dictionary, Britannica Concise Encyclopedia, McGraw-Hill Science & Technology Encyclopedia, Columbia Encyclopedia say the same -- have a look at http://www.answers.com/topic/control-system)

"Hybrid systems are dynamical systems with interacting continuous-time dynamics (modeled, for example, by differential equations) and discrete-event dynamics (modeled, for example, by automata)."

"The term "hybrid system" has many meanings, one of which is: a dynamical system whose evolution depends on a coupling between variables that take values in a continuum and variables that take values in a finite or countable set."(Arian van der Schaft and Hans Schumacher, An Introduction to Hybrid Dynamical Systems // Lecture Notes in Control and Information Sciences, Springer. 2000)

I see no differences between control systems and hybrid systems from a practical engineering point of industrial automation. (Well, but academician words about a continuum :-)

So I (as an engineer specialized in industrial automation) just joint to the former question: what is the difference between control systems and hybrid systems I (and other engineers) have not dealt with before?!

Best wishes, Vladimir E. Zyubin

Any switching in continous systems would result in a hybrid system. Hybrid comes from digital (switching) + continous. In this regard, I would highly recommend the book of switched linear systems by Z. Sun that gives excellent analysis on the switched systems.