How to choose relative error bound when using reducespec on sparse LTI model

Hello everyone,

I have a sparse LTI model, named "sys", that I want to reduce with reducespec and balanced truncation.

The final model should have a maximum relative error of e.g. 30%.

I have tried the following:

R = reducespec(sys, "balanced");
R.Options.Goal = "relative";
sysR = getrom(R, MaxError=0.3, Method='truncate');

However, in contrast to the full model, the MOR specification object of the sparse model does not have the "Goal" field under "R.Options", which appears to mean that it cannot be switched to relative error bound.

Unrecognized property 'Goal' for class 'mor.SparseBalancedTruncationOptions'.

Is there another way to switch to the relative error bound, or is there a fundamental underlying reason why this is not applicable to sparse models?

Thank you in advance!

Answer 1

[Simar]

Hi Dires,

The error you are encountering suggests that the “mor.SparseBalancedTruncationOptions” class does not support “Goal” property directly. This limitation might stem from specific challenges and assumptions associated with applying MOR techniques to sparse systems.Though, direct “Goal” option for specifying relative error bounds seems unavailable for sparse models through “reducespec” with balanced truncation, one can still achieve the objective by a more manual approach involving iterative reduction and error checking:

1.Error Estimation:

Use error estimation techniques to iteratively determine the order of reduction that meets your relative error criteria. This can involve:

• Performing a preliminary reduction with a conservative guess on the order.
• Estimating the error between the original and reduced models.
• Adjusting the order based on the estimated error and repeating until the desired error threshold is met.

2. Custom Reduction Loop:

Implement a custom loop that reduces model order step by step, checking relative error at each step. This process continues until the error exceeds the threshold. Here is a conceptual example:

originalOrder = order(sys); % Get the original order of the system 
targetError = 0.3; % 30% target error 
for reducedOrder = originalOrder:-1:1 % Start from the original order and decrement 
    [sysR, info] = balred(sys, reducedOrder); % Perform balanced reduction 
    errorEstimate = norm(sys - sysR, inf) / norm(sys, inf); % Calculate relative error 
    if errorEstimate <= targetError 
        break; % Stop if the target error is met or exceeded 
    end 
end 

3.Use balred Directly:

The “balred” function can be used directly for balanced truncation, as shown in the loop above. While “reducespec” provides a more automated and potentially sophisticated approach, “balred” offers a straightforward mechanism for reduction that, when combined with manual error checking, can achieve the goal.

balred- https://www.mathworks.com/help/control/ref/dynamicsystem.balred.html?searchHighlight=balred&s_tid=srchtitle_support_results_1_balred#mw_37a0a645-cb62-40f8-9fd6-548678262ac0

The fundamental reason for absence of straightforward “Goal” option for relative error bounds in sparse model reduction could be related to the computational complexity and stability of calculating such metrics for sparse systems. Sparse systems often involve large-scale data where efficiency and accuracy in error estimation are more challenging to balance.

Hope it helps!

Best Regards,

Simar