In most real cases transition probabilities between operational modes of Markov jump linear systems cannot be computed exactly and are time-varying. We take into account this aspect by considering Markov jump linear systems where the underlying Markov chain is polytopic and time- inhomogeneous, i.e. its transition probability matrix is varying over time, with variations that are arbitrary within a polytopic set of stochastic matrices. We address and solve for this class of systems the infinite-horizon optimal control problem. In particular, we show that the optimal controller can be obtained from a set of coupled algebraic Riccati equations, and that for mean square stabilizable systems the optimal finite-horizon cost corresponding to the solution to a parsimonious set of coupled difference Riccati equations converges exponentially fast to the optimal infinite-horizon cost related to the set of coupled algebraic Riccati equations. All the presented concepts are illustrated on a numerical example showing the efficiency of the provided solution.

Linear quadratic regulation of polytopic time-inhomogeneous Markov jump linear systems

Zacchia Lun, Yuriy
;
2019-01-01

Abstract

In most real cases transition probabilities between operational modes of Markov jump linear systems cannot be computed exactly and are time-varying. We take into account this aspect by considering Markov jump linear systems where the underlying Markov chain is polytopic and time- inhomogeneous, i.e. its transition probability matrix is varying over time, with variations that are arbitrary within a polytopic set of stochastic matrices. We address and solve for this class of systems the infinite-horizon optimal control problem. In particular, we show that the optimal controller can be obtained from a set of coupled algebraic Riccati equations, and that for mean square stabilizable systems the optimal finite-horizon cost corresponding to the solution to a parsimonious set of coupled difference Riccati equations converges exponentially fast to the optimal infinite-horizon cost related to the set of coupled algebraic Riccati equations. All the presented concepts are illustrated on a numerical example showing the efficiency of the provided solution.
2019
978-3-907144-00-8
File in questo prodotto:
File Dimensione Formato  
ECC_2019_4094.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Nessuna licenza
Dimensione 402.95 kB
Formato Adobe PDF
402.95 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
1903.03091.pdf

accesso aperto

Tipologia: Documento in Pre-print
Licenza: Creative commons
Dimensione 220.22 kB
Formato Adobe PDF
220.22 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11771/12677
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
social impact