sidLTVdiscTune¶

Python equivalent: sid.ltv_disc_tune

Lambda tuning for sidLTVdisc (validation or frequency-based).

VALIDATION METHOD (requires held-out state data):

[bestResult, bestLambda, allLosses] = sidLTVdiscTune(X_train, U_train, ... X_val, U_val, 'Method', 'validation', ...)

FREQUENCY METHOD (no validation data needed):

[bestResult, bestLambda, info] = sidLTVdiscTune(X, U, ... 'Method', 'frequency', ...)

The frequency method compares the COSMIC frozen transfer function against a non-parametric sidFreqMap estimate using Mahalanobis-like consistency scoring. It selects the largest lambda where the two estimates agree statistically at most (omega, t) grid points.

Inputs¶

Name	Description
	Validation method:
`X_train`	Training state data, (N+1 x p x L_train)
`U_train`	Training input data, (N x q x L_train)
`X_val`	Validation state data, (N+1 x p x L_val)
`U_val`	Validation input data, (N x q x L_val) Frequency method:
`X`	State data, (N+1 x p x L) or cell array
`U`	Input data, (N x q x L) or cell array NAME-VALUE OPTIONS (both methods):
`'Method'`	'validation' (default) or 'frequency'.
`'LambdaGrid'`	Vector of candidate lambda values. Default: logspace(0, 10, 25) (frequency), logspace(-3, 15, 50) (validation).
`'Precondition'`	Passed through to sidLTVdisc. Default: false.
`'Algorithm'`	Passed through to sidLTVdisc. Default: 'cosmic'.

Frequency method options¶

Name	Description
`'SegmentLength'`	Outer segment length for sidFreqMap. Default: min(floor(N/4), 256).
`'ConsistencyThreshold'`	Fraction of grid points required to be consistent. Default: 0.90.
`'CoherenceThreshold'`	Minimum coherence for a grid point to be included. Default: 0.3.

Outputs¶

Name	Description
`bestResult`	sidLTVdisc result struct at optimal lambda.
`bestLambda`	Optimal scalar lambda value.
`thirdOut`	For 'validation': (nGrid x 1) trajectory RMSE per lambda. For 'frequency': info struct with fields: .lambdaGrid, .fractions, .bestFraction, .freqMapResult

Examples¶

% Validation-based
[best, lam, losses] = sidLTVdiscTune(Xtr, Utr, Xval, Uval);

% Frequency-based (no validation data)
[best, lam, info] = sidLTVdiscTune(X, U, 'Method', 'frequency');

References¶

Carvalho et al., "COSMIC", arXiv:2112.04355, 2022. Ljung, L. "System Identification", 2nd ed., Prentice Hall, 1999.

Specification¶

SPEC.md §8.4 — Lambda Selection SPEC.md §8.11 — Lambda Tuning via Frequency Response

Changelog¶

2026-03-29: First version by Pedro Lourenço.