Characterizations of detectability notions in terms of discontinuous dissipation functions

Krichman, Mikhail; Sontag, Eduardo D.

doi:10.1080/00207170210141842

Cited by 5 publications

(7 citation statements)

References 15 publications

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“…In nonlinear setups similar to the one adopted here, we are enforced to consider c.l. versions of detectability as in [6] and [12].…”

Section: A Closed-loop Detectabilitymentioning

confidence: 97%

“…We can also write ( + J N )d(x t ) d(x t ) + J N (xt) = V (xt), which can be substituted in (12), leading to V (x t ) 0V (x t+ N ) > (=( + J N ))V (x t ) 0 N or equivalently 1 V (x t ) > V (x t+ N ) 0 N; whenever x t 6 = 0 (14) where 1 = 1 0 =( + J N ). Note from (13) that < + + J N since from Definition 3, d(z) J N (z) J N d(z) for N N d (see also (2) and (5)).…”

Section: A Closed-loop Detectabilitymentioning

confidence: 99%

“…More precisely, we show that V N is contractive along the state trajectory on a sequence of time instants of variable step size t d or N d (see Theorem 1), to some extent parallelling a general integral dissipation inequality of [12] in the context of continuous-time, input-output to state stability. A key notion of closed-loop detectability (cl-detectability) is introduced in this technical note, and employed in the construction of V N .…”

Section: Introductionmentioning

confidence: 97%

“…There is a recent study by [6] on stability that does not require any special end point condition, leading to conditions on N that, in particular scenarios, are similar to the one obtained in Theorem 1. However, the detectability notion in [6] is characterized in terms of continuous dissipation functions that may not exist for discontinuous f and c and can be difficult to obtain even for continuous f and c [12], as explained in Remark 1. Stability was also studied in [1], [8] for large enough N , under strong assumptions such as f being C 2 , c being strictly positive and controllability-like conditions.…”

Section: Introductionmentioning

confidence: 99%

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Uniform Approximation of Infinite Horizon Control Problems for Nonlinear Systems and Stability of the Approximating Controls

Costa

Val

2009

IEEE Trans. Automat. Contr.

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This technical note addresses the approximation of the infinite horizon problem and the stability of the approximating controls generated by the receding horizon method. The setup takes into account systems and costs that may be nonlinear and discontinuous, with possibly state and control constraints, allowing for a wide range of problems. A detectability notion is introduced that matches standard regularity conditions such as existence of bounds for the cost, and does not require any continuity hypothesis. It is shown that the receding horizon controls associated with the finite horizon problems are approximating solutions for the infinite horizon problem, for a large enough horizon. Exponential stability of the controlled system and estimates for horizons ensuring stability and approximation of the infinite horizon problem are also studied.

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“…In nonlinear setups similar to the one adopted here, we are enforced to consider c.l. versions of detectability as in [6] and [12].…”

Section: A Closed-loop Detectabilitymentioning

confidence: 97%

Section: A Closed-loop Detectabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Uniform Approximation of Infinite Horizon Control Problems for Nonlinear Systems and Stability of the Approximating Controls

Costa

Val

2009

IEEE Trans. Automat. Contr.

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“…Two papers were submitted, one of which has appeared and the other one is in press; see [3] and [4]. In another line of work partially supported by the grant, we worked on ISS-type small-gain results.…”

Section: Summary Of Main Accomplishmentsmentioning

confidence: 99%

Input to State Stability and Related Notions

Sontag¹

2001

Self Cite

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The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for r maintaining the data needed, and completing and reviewing the collection of information. Approval for public release; distribution is unlimited. SUPPLEMENTARY NOTESThe views, opinions and/or findings contained in this report are those of the authors and should not be construed as an official U.S. o vernment position, policy or decision, unless so designated by other documentation. ABSTRACTThis AASERT grant provided graduate student support to complement the research carried out under grant F49620-98-1-0242. The main emphasis'of this subproject was the complete characterization of IOSS, which a notion of well-posed detectability, and related concepts, resulting in necessary and "sufficient characterizations in terms of dissipation inequalities, as well as the construction of norm-observers for finite-dimensional nonlinear systems. ABSTRACTThis AASERT grant provided graduate student support to complement the research carried out under grant F49620-98-1-0242. The main emphasis of this subproject was the complete characterization of IOSS, which is a notion of well-posed detectability, and related concepts, resulting in necessary and sufficient characterizations in terms of dissipation inequalities, as well as the construction of norm-observers for finite-dimensional nonlinear systems.

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