Inverse models are a good way to build controllers if the system can be inverted properly. If inversion is a problem, then using forward models is a much safer method. Forward models come with a caveat though. We are given a desired behavior. However, the behavior is an output in a forward model. We can not just set the query to the desired behavior and ask for a prediction. It is necessary to search through the space of possible actions to find the one that predicts the behavior we want.
Fortunately, Vizier can do exactly that. At this point, we will introduce the Optex command, which can do a variety of model inversion, optimization, and experiment design tasks. It has the flexibility to do many things, but we'll start with a simple example.
Optex -> New
Project name forward
Use current data ON
Continue
Minimize expression
OUTPUT Variable weight 0.0
OUTPUT Target value 0.4
OUTPUT Target weight 1.0
OK
Choose
The default Optex search algorithm is called PMAX. It looks for the input that will produce the best output as defined in the Taskspec. In this example, ``goodness'' was defined as minimizing the squared difference between the desired behavior and the actual behavior. Optex suggested action 0.06. You can use Predict to verify that this action does produce a behavior near 0.4. Notice that there is more than one action that will produce the desired behavior. 0.72 will also work. Optex has chosen between the two of these arbitrarily. We can constrain Vizier's search so that it only considers actions above 0.5, and ask it to choose again. Then it selects 0.72.
Optex makes a dialogue box that stays on the screen after Optex commands have been completed. Subsequent Optex commands can then be run from that dialogue box. The dialogue box can be removed by selecting ``Quit.'' It can then be recalled by selecting ``Resume'' from the Optex menu.
Optex -> Edit -> Taskspec -> INPUT Low 0.5
OK
Choose
