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1 Modeling Systems
Fig. 1.1 Simplest dynamic model with a response to a given external influence
outside the model. In open models, some of the variables are external, as depicted in
Fig. 1.1. They are used to receive and transmit information from the outside, that is,
from other components. External variables are of several kinds:
• inputs whose values can only be changed externally;
• outputs whose values vary within the model and can be transferred to other objects
(models);
• contacts and streams; their values can change both inside the model and outside.
By the presence or absence of the internal structure of the model are divided into
elementary and composite. Elementary models contain only variables and the law
of evolution (behavior), and they are also called one component. In turn, composite
models can also contain local components, that is, other models, and the connections
between them. These models are often called multi-component or simply component.
According to the type of model time, models are continuous, discrete, and hybrid
(continuous–discrete). Time can be modeled in different ways depending on the task.
As a model of continuous time, the segment of the real axis [0, T ] is usually taken,
where the value of T is determined by the objectives of the experiment. The time
variable t at a given interval varies continuously with a constant speed. The state
variables in this case change continuously depending on time, and the model of the
dynamic system is continuous, as shown in Fig. 1.2a.
There are, however, models in which it makes sense to monitor only the fact of
the occurrence of events, without being interested in the time of their occurrence.
Successive events can be renumbered, and we get a sequence of time samples—
renumbered clock cycles. In this case, time (t) takes a finite number of integer values
equal to the number of ticks in the model. Then, the state variables change discretely,
and the system model is called discrete, as shown in Fig. 1.2b.
The combination of segments of continuous time, between which there are discrete
cycles, is a model of hybrid time. It is modeled as follows. Before occurrence of some
conditions, called an event, time has a continuous behavior, and the variables change
continuously. Sections with continuous time are called states. As soon as an event
occurs, continuous time “freezes,” the local discrete clocks turn on, and the variables
change discretely. After all discrete actions have been completed, the discrete time
stops, and the continuous time starts to change again (from the point at which it
“stopped”). Such events in the model can be as many as one like. Models using
this type of time are called hybrid. The states of the hybrid system are described
by systems of differential or differential–algebraic equations. Events are defined by
logical predicates; discrete actions are correctly described algorithmically. Hybrid
1 Modeling Systems
Fig. 1.1 Simplest dynamic model with a response to a given external influence
outside the model. In open models, some of the variables are external, as depicted in
Fig. 1.1. They are used to receive and transmit information from the outside, that is,
from other components. External variables are of several kinds:
• inputs whose values can only be changed externally;
• outputs whose values vary within the model and can be transferred to other objects
(models);
• contacts and streams; their values can change both inside the model and outside.
By the presence or absence of the internal structure of the model are divided into
elementary and composite. Elementary models contain only variables and the law
of evolution (behavior), and they are also called one component. In turn, composite
models can also contain local components, that is, other models, and the connections
between them. These models are often called multi-component or simply component.
According to the type of model time, models are continuous, discrete, and hybrid
(continuous–discrete). Time can be modeled in different ways depending on the task.
As a model of continuous time, the segment of the real axis [0, T ] is usually taken,
where the value of T is determined by the objectives of the experiment. The time
variable t at a given interval varies continuously with a constant speed. The state
variables in this case change continuously depending on time, and the model of the
dynamic system is continuous, as shown in Fig. 1.2a.
There are, however, models in which it makes sense to monitor only the fact of
the occurrence of events, without being interested in the time of their occurrence.
Successive events can be renumbered, and we get a sequence of time samples—
renumbered clock cycles. In this case, time (t) takes a finite number of integer values
equal to the number of ticks in the model. Then, the state variables change discretely,
and the system model is called discrete, as shown in Fig. 1.2b.
The combination of segments of continuous time, between which there are discrete
cycles, is a model of hybrid time. It is modeled as follows. Before occurrence of some
conditions, called an event, time has a continuous behavior, and the variables change
continuously. Sections with continuous time are called states. As soon as an event
occurs, continuous time “freezes,” the local discrete clocks turn on, and the variables
change discretely. After all discrete actions have been completed, the discrete time
stops, and the continuous time starts to change again (from the point at which it
“stopped”). Such events in the model can be as many as one like. Models using
this type of time are called hybrid. The states of the hybrid system are described
by systems of differential or differential–algebraic equations. Events are defined by
logical predicates; discrete actions are correctly described algorithmically. Hybrid