@Misc{Berberich2018a,
  author       = {Berberich, J. and K{\"o}hler, J. and Allg{\"o}wer, F. and M{\"u}ller, M. A.},
  title        = {Indefinite linear quadratic optimal control: periodic dissipativity and turnpike properties},
  howpublished = {Viennese Conference on Optimal Control and Dynamic Games},
  month        = {July},
  year         = {2018},
  abstract     = {This talk is about discrete-time indefinite linear quadratic (LQ)
	optimal control problems in the presence of constraints on states
	and inputs. In the recent literature, a characterization of the optimal
	trajectories of LQ-problems was given in terms of strict dissipativity
	and turnpike properties at steady-states, provided that the stage
	cost is positive semidefinite. By taking the particular shape of
	the constraints into account, we show that these results can be generalized
	to indefinite cost functions and periodic orbits. In particular,
	sufficient conditions for strict dissipativity with respect to periodic
	orbits and steady-states in constrained indefinite LQ-problems are
	discussed. It is shown that the corresponding optimal periodic orbit
	can be computed explicitly using a non-strict dissipation inequality
	and is, in many cases, located on the boundary of the constraints.
	A similar technique is applied to analyze strict dissipativity at
	steady-states, where some of the arguments simplify. In particular,
	negative eigenvalues of the cost, the exact shape of the constraints,
	and the location of the optimal steady-state are highly intertwined
	and allow for an intuitive geometric interpretation.},
  pubtype      = {talk},
}

{"_id":"8KYbPcpWmu5KCxNKB","bibbaseid":"berberich-khler-allgwer-mller-indefinitelinearquadraticoptimalcontrolperiodicdissipativityandturnpikeproperties-2018","downloads":0,"creationDate":"2018-11-29T07:13:47.809Z","title":"Indefinite linear quadratic optimal control: periodic dissipativity and turnpike properties","author_short":["Berberich, J.","Köhler, J.","Allgöwer, F.","Müller, M. A."],"year":2018,"bibtype":"misc","biburl":"http://www.ist.uni-stuttgart.de/.content/publication_database/ist.bib","bibdata":{"bibtype":"misc","type":"misc","author":[{"propositions":[],"lastnames":["Berberich"],"firstnames":["J."],"suffixes":[]},{"propositions":[],"lastnames":["Köhler"],"firstnames":["J."],"suffixes":[]},{"propositions":[],"lastnames":["Allgöwer"],"firstnames":["F."],"suffixes":[]},{"propositions":[],"lastnames":["Müller"],"firstnames":["M.","A."],"suffixes":[]}],"title":"Indefinite linear quadratic optimal control: periodic dissipativity and turnpike properties","howpublished":"Viennese Conference on Optimal Control and Dynamic Games","month":"July","year":"2018","abstract":"This talk is about discrete-time indefinite linear quadratic (LQ) optimal control problems in the presence of constraints on states and inputs. In the recent literature, a characterization of the optimal trajectories of LQ-problems was given in terms of strict dissipativity and turnpike properties at steady-states, provided that the stage cost is positive semidefinite. By taking the particular shape of the constraints into account, we show that these results can be generalized to indefinite cost functions and periodic orbits. In particular, sufficient conditions for strict dissipativity with respect to periodic orbits and steady-states in constrained indefinite LQ-problems are discussed. It is shown that the corresponding optimal periodic orbit can be computed explicitly using a non-strict dissipation inequality and is, in many cases, located on the boundary of the constraints. A similar technique is applied to analyze strict dissipativity at steady-states, where some of the arguments simplify. In particular, negative eigenvalues of the cost, the exact shape of the constraints, and the location of the optimal steady-state are highly intertwined and allow for an intuitive geometric interpretation.","pubtype":"talk","bibtex":"@Misc{Berberich2018a,\n author = {Berberich, J. and K{\\\"o}hler, J. and Allg{\\\"o}wer, F. and M{\\\"u}ller, M. A.},\n title = {Indefinite linear quadratic optimal control: periodic dissipativity and turnpike properties},\n howpublished = {Viennese Conference on Optimal Control and Dynamic Games},\n month = {July},\n year = {2018},\n abstract = {This talk is about discrete-time indefinite linear quadratic (LQ)\n\toptimal control problems in the presence of constraints on states\n\tand inputs. In the recent literature, a characterization of the optimal\n\ttrajectories of LQ-problems was given in terms of strict dissipativity\n\tand turnpike properties at steady-states, provided that the stage\n\tcost is positive semidefinite. By taking the particular shape of\n\tthe constraints into account, we show that these results can be generalized\n\tto indefinite cost functions and periodic orbits. In particular,\n\tsufficient conditions for strict dissipativity with respect to periodic\n\torbits and steady-states in constrained indefinite LQ-problems are\n\tdiscussed. It is shown that the corresponding optimal periodic orbit\n\tcan be computed explicitly using a non-strict dissipation inequality\n\tand is, in many cases, located on the boundary of the constraints.\n\tA similar technique is applied to analyze strict dissipativity at\n\tsteady-states, where some of the arguments simplify. In particular,\n\tnegative eigenvalues of the cost, the exact shape of the constraints,\n\tand the location of the optimal steady-state are highly intertwined\n\tand allow for an intuitive geometric interpretation.},\n pubtype = {talk},\n}\n\n","author_short":["Berberich, J.","Köhler, J.","Allgöwer, F.","Müller, M. A."],"key":"Berberich2018a","id":"Berberich2018a","bibbaseid":"berberich-khler-allgwer-mller-indefinitelinearquadraticoptimalcontrolperiodicdissipativityandturnpikeproperties-2018","role":"author","urls":{},"metadata":{"authorlinks":{}}},"search_terms":["indefinite","linear","quadratic","optimal","control","periodic","dissipativity","turnpike","properties","berberich","köhler","allgöwer","müller"],"keywords":[],"authorIDs":[],"dataSources":["EXg9RjjTit3R3tBWv"]}