# Introduction

The vle extension **vle.discrete-time** can be used to model and simulate
discrete time atomic models into VLE. Discrete time atomic models are models
that compute at time *t* outputs of variables *v1, …, vn* taking into account
values of variables *v1,…, vn*, given a user specified parameter *D*, at times

*t, t - D, t - 2 * D,…*,

The packages related to this extension are:

**vle.discrete-time**provides the discrete time extension itself.**vle.discrete-time.decision**provides a decision agent having a discrete time dynamic. It embeds a*KnowledgeBase*from package**vle.extension.decision**. This is an experimental package.**vle.discrete-time_test**provides tests for discrete time models.

Evolution of state variables *vi* is described by C++ equation syntax close to
mathematical formulation. These expressions must be written in the
*compute* function.

For example the expression *V1 = V1(-1) + V2() + V3(-2)* computes, at current
time *t*, the value of *V1* as the sum of the value of *V1* at time
*t - D*, the current value of *V2* and the value of *V3* at time
*t - 2*D*.

**Fig:** A discrete-time model with 6 variables, 3 can be
updated from external event (inputs), 3 are sent by default at each time step
on the network (outputs)

The interface (input and output ports) is given for an example in the above
figure. Note that variables *v1, …, v3* are not necessary
inputs they could also be outputs. And variables *v4, …, v6* could also
have their input ports.

# Writing atomic models

The *vle/discrete-time/TemporalValues.hpp* API provides functionnalities
to handle variables (double, vector or polymorphic *vle::value*) and their
history. Particularly, access operators are defined for these data structures.
Available variables types are :

- double. To use a temporal value of type double, you must use the struct
*vle::discrete_time::Var*(see examples below). - vector of double. To use a temporal value of type vector of double,
you must use the struct
*vle::discrete_time::Vect*. *vle::value::Value*: To use a temporal value of this type you must use the struct*vle::discrete_time::ValueVle*.

Temporal values maintain an historic of updates with dates and
are browseable using access operator. Updates can be directly set
by a *devs::Dynamic* if the temporal value is declared
(in constructor or not) using the function *Var::init*,
*Vect::init* or *ValueVle::init* (see lines 13, 14 in code).

**Fig:** Example of updates for a temporal value of type *Var*.

In example depicted in the above figure, at current time *t*, the state
of historic of *Var* *S* is:

*[t1, a1],[t2, a3],[t3, a2],[t4, a1]*.

Operator *()* on *S* will give one of the update value. The signal is
supposed to be piecewise constant function. Then

*S(-0.3)*returns value at time*t - 0.3 * D*, ie*a1*.*S(-3.6)*returns value at time*t - 3.6 * D*, ie*a3*.*S()*returns last update value, ie*a1*.

Operator *=* of *Var* allows to set an update
(for example into the *compute* function of discrete-time model).

For Vectors (struct *Vect*):

*S[1](-0.3)*returns value at time*t - 0.3 * D*for the dimension 1.*S[0](-3.6)*returns value at time*t - 3.6 * D*for the dimension 0.*S[2]()*returns last update vector at index 2.*S[2]=1.5*updates value of*S*at dim 2 with 1.5.

Below is given an example of dynamic for an atomic model that relies
on the extension **vle.discrete-time**.

```
class MyModel : public DiscreteTimeDyn
{
public:
//Declaration of variables
Var x;
Vect y;
Var z; // used in this module as an input
MyModel(const vd::DynamicsInit& model,
const vd::InitEventList& events) :
DiscreteTimeDyn(model, events)
{
//Initialisation of variables from experimental conditions
x.init(this, "x", events);
y.init(this, "y", events);
//Overwrite initialisations (Optionnal)
x.init_value(3.0);
x.history_size(3);
y.dim(2)
}
void compute(const vd::Time& /*time*/)
{
x = x(-1) - y[1]() / z();
y[0] = z() - 1;
y[1] = y[0]() + 1;
}
};
```

# Configuring atomic models

To configure discrete time atomic models, one can use the parameters from the
*vpz* conditions listed below. The *X* refers to an internal variable
(a real, a vector or a vle value).

Basic settings:

**time_step**(double, default 1.0) : the time step of the discrete time atomic model.**dim_X**(int, default 2) : if*X*is a vector, it defines the dimension of the vector. Used only if*X*is a vector.**history_size_X**(uint, default 1) : it gives the size of the history of internal variable*X*.**init_value_X**(vle::Value, default vle::Double(0.0)) : the initial value of the internal variable*X*. It can be a vv::Double for a variable without history, a vv::Tuple for a variable with history or a vv::Table for a vector. Checks are performed with*dim_X*and*history_size_X*.**syncs**(set of strings, default empty): each variable into this set are parameterized with a value of 1 for sync parameter.**sync_X**(uint, default 0): if*sync_X*> 0, the value of*X*at times n **sync_X***time_step*, with n > 0 is expected to be provided by an external event before calling the*compute*function. This option has priority on*syncs*.

Advanced settings for output configurations:

**output_period**(uint, default 1): gives the time step of output. Output will produce values each*time_step***output_period*.**output_period_X**(uint, default 1): a specific value of*output_period*for variable*X*. This option has priority on*output_period*.**output_nil**(bool, default false): if true, the output function will produce a Null value for a variable which last update is not equals to current time, otherwise it will gives the last updated value.**output_nil_X**(bool, default false): a specific value of*output_nil*for variable*X*. This option has priority on*output_nil*.

Advanced settings for debugging:

**snapshot_before**(bool, default false) : if true, a snapshot of variable values is done before the compute function. It can be observed on the port*X_before*.**snapshot_after**(bool, default false) : if true, a snapshot of variable values is done after the compute function. It can be observed on the port*X_after*.**error_no_sync_X**(bool, default false) : if true, the access to*X*at the current time*X()*will send an error if the last time of update of*X*is before the current time.

Advanced settings for multiple update:

**allow_update_X**(bool, default false): if false, the first value set for*X*at a given time step is kept. The following updates for*X*at this time step are ignored.**forcing_X**(a vle Map or Set, default empty): this option can not be used simultaneously with*allow_update*. The map (or set of such map) represents a forcing event. A forcing event forces the model to set a value to*X*at a given time. The map should contain:**time**(double): the time of forcing event**value**(real, vector or vle Value): the value of forcing event**before_output**(bool, default false): true if the forcing event should occur before the output function of the dynamic.

Advanced settings for dynamic management of variables (this configuration can
be dynamically set by an external event on port *dyn_init* with a map):

**dyn_allow**(bool, default false): if true, input ports added for example by an executive are automatically added has state variables after the*compute*function.**dyn_type**(‘Var’, ‘Vect’ or ‘ValueVle’, default ‘Var’): gives the type of new state variables to add. Used only if*dyn_allow*is true.**dyn_sync**(uint, default 0): gives the type of synchronisation of new state variables to add as with*sync_X*. Used only if*dyn_allow*is true.**dyn_init_value**(vle::Value, default vle::Double(0.0)): gives the initial value of new variables as with*init_value_X*. Used only if*dyn_allow*is true.**dyn_dim**(uint, default 2): gives the dimension when creating a new*Vect*. Used only if*dyn_allow*is equal to true and*dyn_type*==*Vect*.

Advanced settings for synchronisation:

**bags_to_eat**(int, default 0) : the number of bags to wait before computing the values of variables (calls of*compute*user function).

# Technical details

**Fig:** The activity diagram of a discrete time model: sequence of calls at
a given time step.

**Fig:** The DEVS state transition graph for discrete-time atomic models.

This extension is intended to improve the functionnalities of extension
**vle.extension.difference-equation**, to improve perfomance results and to
limit the behavior in order to facilitate the coupling with other extensions :

- there is no propagation of the perturbation : it requires a state backup and other extensions do not have this.
- there is no initialization process of the dynamics (no
*initValue*function): synchronisation at the time of instantiation of the atomic model makes it difficult to couple with DSDEVS. - there is no external variables. All variables are internal variables.
- it provides vector of variables and polymorphic vle values.
- It uses a DEVS state approah for the code of transitions