## 2. Attributes for the built in class Real

In order to superimpose information on variable declarations, two new attributes are introduced for the built-in type Real. Firstly, it should be possible to specify that a variable, or parameter, is free in the optimization. Modelica parameters are normally considered to be fixed after the initialization step, but in the case of optimization, some parameters may rather be considered to be free. In optimal control formulations, the control inputs should be marked as free, to indicate that they are indeed optimization variables. For these reasons, a new attribute for the built-in type Real, `free`

, of boolean type is introduced. By default, this attribute is set to `false`

.

Secondly, an attribute, `initialGuess`

, is introduced to enable the user to provide an initial guess for variables and parameters. In the case of free optimization parameters, the `initialGuess`

attribute provides an initial guess to the optimization algorithm for the corresponding parameter. In the case of variables, the `initialGuess`

attribute is used to provide the numerical solver with an initial guess for the entire optimization interval. This is particularly important if a simultaneous or multiple-shooting algorithm is used, since these algorithms introduce optimization variables corresponding to the values of variables at discrete points over the interval. Note that such initial guesses may be needed both for control and state variables. For such variables, however, the proposed strategy for providing initial guesses may sometimes be inadequate. In some cases, a better solution is to use simulation data to initialize the optimization problem. This approach is also supported by the Optimica compiler. In the double integrator example, the control variable *u* is a free optimization variable, and accordingly, the `free`

attribute is set to `true`

. Also, the `initialGuess`

attribute is set to 0.0.

optimization DIMinTime
DoubleIntegrator di(u(free=true,
initialGuess=0.0));
input Real u = di.u;
end DIMinTime;