Assume that we have data who looks like this from a dynamical system $G(s)$ e.g mass-spring-damper system. Where the output is the position of the mass and input is the applied force onto the mass.
Then we cut the data into several different images:
In this case, we can use arrays of fixed size that contains the data.
Questions:
- Assuming that we have a reference signal that output signal shall follow. Is it possible for us to compute the input signals if we have a neural network model?
Example: If we have a desire reference signal that looks like this 
and our output signal looks like this What input signal should we use then to make the output signal follows the desire reference signal?
- Is it possible to compute a neural network model if we have like thousands of different arrays with fixed size that contains data?
Example: What tools should I use? Can I use least squares / pseudo least squares to compute the weights for the neural network?
- Can neural network be a good controller for heavy nonlinear systems where fuzzy models or recursive adaptive controllers are normally used?
Example: We collect enormous massive data, train a model by using linear algebra and then we implement the weights onto an embedded system?