1. AUTOMATIC CONTROL THEORY II Slovak University of Technology Faculty of Material Science and Technology in Trnava

2. Modeling Complex Systems A complex adaptive system has the following characteristics  it persists in spite of changes in the diverse individual components of which it is comprised  the interactions between those components are responsible for the persistence of the system  the system itself engages in adaptation or learning

3. Modeling Complex Systems a system is complex when  it moves between order and disorder without becoming fixed in either state a system adapts when  it responds to information by changing

4. Modeling Complex Systems adaptation and Finding Excellent Solutions a complex adaptive system receives a stream of data about itself and its surroundings it identifies particular regularities and compresses them into a concise "schema“  one of many possible ones related by mutation or substitution

5. Modeling Complex Systems the schema can supply  descriptions of certain aspects of the real world  predictions of events that are to happen in the real world  prescriptions for behavior of the complex adaptive system in the real world the descriptions can turn out to be  more accurate  or less accurate

6. Modeling Complex Systems the predictions can turn out to be  more reliable  or less reliable the prescriptions for behavior can turn out to  lead to favorable  or unfavorable outcomes

7. Modeling Complex Systems a complex adaptive system  interacts with the environment  creates schemata, which are compressed and generalized regularities experienced in those interactions  behaves in ways consistent with these schemata  incorporates feedback from the environment to modify and adapt its schemata for greater success

8. Modeling Complex Systems Self-Organization in Complex Systems not every system is a complex adaptive system certain conditions must be met in order for a system to self-organize the system must include a large number of agents the agents must interact in a nonlinear fashion

9. Modeling Complex Systems if there aren't enough components or they are prevented from interacting  you won't see patterns emerge or evolve the nature of the interactions must be nonlinear the motion of the whole is not only greater than, but different than the sum of the motions of the parts  due to nonlinear interactions among the parts or between the parts and the environment

10. Modeling Complex Systems Complex Adaptive Systems Summarized complex adaptive systems involve agents whose local, non-linear interactions result in self- organization by the system as a whole complex adaptive systems exist in a mixed condition between order and chaos that enables them to achieve stability and flexibility simultaneously

11. Modeling Complex Systems The agents in a complex adaptive system thrive by devising excellent solutions to difficult problems, rather than by finding best or perfect solutions Complex adaptive systems find excellent solutions by creating schemata based on regularities identified as successful, behaving in ways consistent with these schemata, and incorporating feedback to adapt the schemata for greater success

12. Modeling Complex Systems examining what may be happening in self- organizing complex systems  using computer simulations main components of the modeling environment are  turtles  patches  observer

13. Modeling Complex Systems turtles  individual agents in the system  they can represent any kind of agent from a molecule to a person patches  the environment in which the turtles operate is divided into patches

14. Modeling Complex Systems patch size and movement by turtles within and between patches is determined by the program designer patches are not necessarily passive, but typically are, active components of the system commands may apply either to turtles or to patches

15. Modeling Complex Systems observer  can issue commands that affect both patches and turtles variables within a model may be set up as sliders the sliders can be manipulated while the model is running