In this episode I talk to Professor Paolo Rapisarda about a bunch of interesting theoretical (but very useful) aspects of control, including his work on behavioural systems theory, model reduction, Willems’ fundamental lemma, and data-driven control.

You can find the transcript at: https://docs.google.com/document/d/1xosQlyCazjngvrydEdlSX917p84v4GY8Maljp5J8MQY/edit?usp=sharing

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Paolo Rapisarda: https://www.southampton.ac.uk/people/5x2hb9/professor-paolo-rapisarda

Introduction

State maps for linear systems: https://eprints.soton.ac.uk/264646/1/State_maps.pdf

Harry Trentelman: https://research.rug.nl/en/persons/harry-trentelman

Jan Willems: https://homes.esat.kuleuven.be/~sistawww/smc/jwillems/

PhD thesis: https://research.rug.nl/en/publications/linear-differential-systems-2

Behavioural systems

Epic Jan Willems behavioural systems paper: https://skoge.folk.ntnu.no/prost/proceedings/cpc6-jan2002/willems.pdf

State maps

LTV paper:https://eprints.soton.ac.uk/457114/1/State_for_linear_discrete_time_varying_systems.pdf

Leibnitz rule: https://www.cuemath.com/calculus/leibniz-rule/

Dissipativity

Jan Willem’s paper: https://link.springer.com/article/10.1007/bf00276493

Jan Willem’s optimal control paper: https://ieeexplore.ieee.org/abstract/document/1099831

Quadratic differential forms: https://epubs.siam.org/doi/10.1137/S0363012996303062

Balancing

Siep Weiland: https://ieeexplore.ieee.org/author/37301202100

Keith Glover: https://www.eng.cam.ac.uk/profiles/kg103

H-infinity model order reduction: https://ieeexplore.ieee.org/document/701085

1980 Moore balancing paper: https://ieeexplore.ieee.org/document/1102568

Kalman decomposition: https://en.wikipedia.org/wiki/Kalman_decomposition

Arjan van der Schaft: https://scholar.google.nl/citations?user=BIPifjAAAAAJ&hl=en

Hamiltonian systems: https://www.unige.ch/~hairer/poly_geoint/week1.pdf

Port Hamiltonianity:https://www.annualreviews.org/content/journals/10.1146/annurev-control-081219-092250

Jacqueline Scherpen: https://research.rug.nl/en/persons/jacqueline-scherpen

Balancing of Port-Hamiltonian systems: https://research.rug.nl/files/2999949/2003ProcIFACWorkshopLHMNCLopezlena.pdf

Balancing for non-linear systems: https://research.rug.nl/files/3318296/1993ProcECCScherpen.pdf

Fundamental lemma

Ivan Markovski: https://scholar.google.com/citations?user=qSl_3FQAAAAJ&hl=en

Continuous-time work: https://www.sciencedirect.com/science/article/pii/S016769112400238X

Chebychev polynomials: https://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html

Kanat Camblibel: https://scholar.google.com/citations?user=aeWjKPcAAAAJ&hl=en

Sufficient condition modification of Willems’s lemma: https://arxiv.org/abs/2405.18962

Experimental implementation: https://arxiv.org/abs/2407.12509

Data-driven control

Data-driven ILC:https://ieeexplore.ieee.org/abstract/document/10384133

DeePC: https://arxiv.org/abs/1811.05890

Jonathan Mayo-Maldonado: https://scholar.google.co.uk/citations?user=W-vnMBwAAAAJ&hl=en

Extra questions

Aizerman’s conjecture: https://en.wikipedia.org/wiki/Aizerman%27s_conjecture