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dc.contributor.authorFerrante, A.
dc.contributor.authorNtogramatzidis, Lorenzo
dc.date.accessioned2017-11-28T06:36:57Z
dc.date.available2017-11-28T06:36:57Z
dc.date.created2017-11-28T06:21:45Z
dc.date.issued2017
dc.identifier.citationFerrante, A. and Ntogramatzidis, L. 2017. On the generalized algebraic Riccati equations. IFAC-PapersOnLine. 50 (1): pp. 9555-9560.
dc.identifier.urihttp://hdl.handle.net/20.500.11937/58801
dc.identifier.doi10.1016/j.ifacol.2017.08.1653
dc.description.abstract

Three hundred years have passed since Jacopo Francesco Riccati analyzed a quadratic differential equation that would have been of crucial importance in many fields of engineering and applied mathematics. Indeed, countless variations and generalizations of this equation have been considered as they proved to be the right mathematical tool to address important problems. This paper is focused on a generalized version of the matrix Riccati equation where the matrix that in the classical Riccati equation is inverted can be singular: we analyze the equation obtained by substituting the inverse operator with the Moore-Penrose pseudo-inverse. The equations obtained by this substitution are known as generalized Riccati equations. The relation between these equations — both in continuos-time and in discrete-time — and singular Linear Quadratic (LQ) optimal control problem are examined. A geometric characterization of the set of solutions of the generalized Riccati equation is illustrated. It is shown that in this general setting there are LQ optimal control problems for which the optimal closed-loop system is stable also in cases where the Riccati equation does not possess a stabilizing solution.

dc.relation.sponsoredbyhttp://purl.org/au-research/grants/arc/DP160104994
dc.titleOn the generalized algebraic Riccati equations
dc.typeJournal Article
dcterms.source.volume50
dcterms.source.number1
dcterms.source.startPage9555
dcterms.source.endPage9560
dcterms.source.issn2405-8963
dcterms.source.titleIFAC-PapersOnLine
curtin.departmentDepartment of Mathematics and Statistics
curtin.accessStatusFulltext not available


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