Defining Initial Parameter Values and a Mesh (Control Design and Simulation Module)

After you define the parameter space using the minimum and maximum values of each parameter, you must specify the initial values of each parameter. These initial parameter values determine where the Sequential Quadratic Programming (SQP) algorithm begins the search for optimal values. However, if you choose only a single initial set of initial values, the SQP algorithm might return local optimal values. Local optimal values are values that minimize the cost function within only a subset of parameter space. Local optimal values are not the true solution to the SQP algorithm because the true optimal values might exist outside the parameter space the algorithm searched.

To mitigate this problem, you can execute the SQP algorithm several times, using a different set of initial parameter values each time. If you use a large enough range of initial parameter values within the given parameter space, you can be relatively confident that the SQP algorithm finds the global optimal values.

You can implement this strategy by defining an initial parameters mesh. The initial parameters mesh defines the distribution pattern of these sets of initial values and the total number of initial value sets to generate. You can choose from four patterns depending on the needs of the problem: Uniform grid, Uniform random, Quasirandom, and Random walk.

Each pattern has unique characteristics and strengths. For example, the simplest possible option is the uniform grid, which generates a specified number of equally-spaced locations in the parameter space. However, the uniform random and quasirandom options often provide better coverage of the parameter space while using a fewer number of points than the uniform grid option. The random walk option biases the search to explore close to the initial values but eventually explores a larger region of parameter space. This option is useful if you think a particular parameter space contains the optimal values and you want to focus on a certain region of that space, such as the center.

Use the Initial Parameters parameter of the SIM Optimal Design VI to specify initial parameter values. Use the Initial Parameters Mesh parameter of this VI to define an initial parameters mesh.