Closed loop stability of measure-driven impulsive control systems

Code, Warren J.; Silva, Geraldo Nunes

doi:10.1007/s10883-010-9085-9

Cited by 8 publications

(9 citation statements)

References 15 publications

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“…Our solution concept most closely resembles that of Wolenski and Žabić [20] and matches that of Code and Silva [7]. Optimality conditions for MDIs include [17], where the measure is scalar while F is Lipschitz in x, measurable in t, and the impulsive map G is continuous in (t, x), Lipschitz in x.…”

mentioning

confidence: 83%

“…We also assume that μ takes values in the closed cone K ⊆ R m . We now provide the concept of solution for (3.2); we adopt the extension in [7], which is similar to the extension [21] of [12,13], but employs the measure-differential inclusion framework. Denote R := R ∪ {±∞}.…”

Section: Impulsive System Solution Concept and Time Reparametrizationmentioning

confidence: 99%

“…Applying this to each of the relevant trajectories in our optimal control problem, we obtain a new optimal control problem with the same cost function, a related differential inclusion with no measure involved, but with the sacrifice that the time interval endpoint becomes a choice variable. This differs from the solution concepts used in, for example, [9,13,17,20] where jumps give rise to dynamic subsystems on a unit interval; the time stretch we use here (also used in [7] and [6]) weights instants and produces subsystems on intervals of varying length where the jump dynamics of G are active.…”

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confidence: 99%

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Optimal Control of Non-convex Measure-driven Differential Inclusions

Code

Loewen

2010

Set-Valued Anal

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Necessary conditions for optimality in control problems with differentialinclusion dynamics have recently been developed in the non-convex case by Clarke, Vinter, and others. Using appropriate reparametrizations of the time variable, we extend these results to systems whose dynamics involve a differential inclusion where a vector-valued measure appears. An auxiliary result central to our proof is an extension of existing free end-time necessary conditions to Clarke's stratified framework.

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mentioning

confidence: 83%

Section: Impulsive System Solution Concept and Time Reparametrizationmentioning

confidence: 99%

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confidence: 99%

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Optimal Control of Non-convex Measure-driven Differential Inclusions

Code

Loewen

2010

Set-Valued Anal

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“…Based on his work, [4,6,12] generalized the idea to consider discontinuous inputs, and in general, the functions of bounded variation. From stability point of view, the work of [11] talks about stabilization in terms of existence of an input function that makes some Lyapunov function decrease along the trajectories of the system (2).…”

Section: Literature Overviewmentioning

confidence: 99%

Stability notions for a class of nonlinear systems with measure controls

Tanwani

Brogliato

Prieur

2015

Math. Control Signals Syst.

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We consider the problem of stability in a class of differential equations which are driven by a differential measure associated with inputs of locally bounded variation. After discussing some existing notions of solution for such systems, we derive Lyapunov-based conditions on the system's vector fields for asymptotic stability under a specific class of inputs. These conditions are based on the stability margin of the Lebesgue-integrable and the measure-driven components of the system. For more general inputs which do not necessarily lead to asymptotic stability, we then derive conditions such that the maximum norm of the resulting trajectory is bounded by some function of the total variation of the input, which generalizes the notion of integral input-to-state stability in measure-driven systems.

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“…From stability point of view, the work of Code and Silva [2010] talks about stabilization in terms of existence of an input function that makes some Lyapunov function decrease along the trajectories of the system (2).…”

Section: Introductionmentioning

confidence: 99%

On Stability of Measure Driven Differential Equations

Tanwani

Brogliato

Prieur

2013

IFAC Proceedings Volumes

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International audienceWe consider the problem of stability in a class of differential equations which are driven by a differential measure associated with the inputs of locally bounded variation. After discussing some existing notions of solution for such systems, we derive conditions on the system's vector fields for asymptotic stability under a specific class of inputs. These conditions present a trade-off between the Lebesgue-integrable and the measure-driven components of the system. In case the system is not asymptotically stable, we derive weaker conditions such that the norm of the resulting trajectory is bounded by some function of the total variation of the input, which generalizes the notion of integral input-to-state stability in measure-driven systems

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Closed loop stability of measure-driven impulsive control systems

Cited by 8 publications

References 15 publications

Optimal Control of Non-convex Measure-driven Differential Inclusions

Optimal Control of Non-convex Measure-driven Differential Inclusions

Stability notions for a class of nonlinear systems with measure controls

On Stability of Measure Driven Differential Equations

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