Setting Parameter Constraints with a Range (System Identification Toolkit)

If you have prior knowledge of a parameter, you can set constraints by providing upper and lower limits for the parameter. With the limit range, the SI Estimate Partially Known State-Space Model VI randomly selects a value within the range as an initial guess of the parameter. From this initial value, the VI then performs optimization to minimize the difference between the estimated output and the measured real output. The goal of constraint optimization is to find a global optimum, or the smallest difference between the estimated output and the real output, with parameters of physical meaning. Successfully finding the global optimum depends on the limit range you set and the random initial value the SI Estimate Partially Known State-Space Model VI selects.

To increase the possibility of finding the global optimum, complete the following steps:

1. Use prior knowledge to set the range as narrow as possible.
2. Perform multiple estimates with the range you set. You might get different optimization results because the SI Estimate Partially Known State-Space Model VI randomly selects an initial value within the range each time you run the VI. If you repeatedly obtain the same result, this result might be the optimum you want to find. If you obtain inconsistent results, either choose the result that best meets the system requirements, or continue with step 3 to adjust the limit range.
3. Select one of the previous results you got in step 2 according to the prior knowledge you have of the system. Narrow the range in which the result falls. Run the SI Estimate Partially Known State-Space Model VI multiple times. A consistent result you get might be the optimum you want to find. Otherwise, repeat this step until you find a consistent result.

You set limits in the SI Estimate Partially Known Continuous Transfer Function Model VI the same way you do in the SI Estimate Partially Known State-Space Model VI.