# Minicourse on behavioral systems theory- Lecture 6: System identification

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## Abstract

The Behavioral Approach to Systems Theory The Behavioral Approach to Systems Theory Paolo Rapisarda, Un. of Southampton, U.K. & Jan C. Willems, K.U. Leuven, Belgium MTNS 2006 Kyoto, Japan, July 24–28, 2006 Lecture 6: System Identification Lecturer: Jan C. Willems Issues to be discussed • Remarks on deterministic versus stochastic system identification. • Deterministic SYSID via the notion of the most powerful unfalsified model (MPUM) • What is subspace identification? • Algorithms for state construction • by past/future intersection • (by oblique projection) • by recursive annihilator computation Issues to be discussed • Remarks on deterministic versus stochastic system identification. • Deterministic SYSID via the notion of the most powerful unfalsified model (MPUM) • What is subspace identification? • Algorithms for state construction • by past/future intersection • (by oblique projection) • by recursive annihilator computation Issues to be discussed • Remarks on deterministic versus stochastic system identification. • Deterministic SYSID via the notion of the most powerful unfalsified model (MPUM) • What is subspace identification? • Algorithms for state construction • by past/future intersection • (by oblique projection) • by recursive annihilator computation General Introduction SYSID MATHEMATICAL MODEL OBSERVED DATA MODEL CLASS Basic difficulties: trade-off between overfitting and predictability learning essential features / rejecting non-essential ones SYSID Data: an ‘observed’ vector time-series w˜(1), w˜(2), . . . , w˜(T ) w(t) ∈ Rw T finite, infinite, or T →∞ ⇓ A dynamical model from a model class, e.g. a LTIDS R0w(t) + R1w(t + 1) + · · · + RLw(t + L) = 0 or R0w(t) + R1w(t + 1) + · · · + RLw(t + L) = M0ε(t) + · · · + MLε(t + L) SYSID ‘deterministic’ ID variables observed MODEL w Model class: R0w(t) + R1w(t + 1) + · · ·+ RLw(t + L) = 0 SYSID algorithm: w˜(1), w˜(2), . . . , w˜(T ) 7→ Rˆ0

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