A measurable upper semicontinuous viability theorem for tubes

Frankowska, Hélène; Plaskacz, Sławomir

doi:10.1016/0362-546x(94)00299-w

Cited by 40 publications

(28 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this last paper F is supposed to be bounded, to have convex compact images and the constraints are given by an inequality. Then viability theorems from [14,15] are used.…”

Section: Introductionmentioning

confidence: 99%

Regularity of Solution Maps of Differential Inclusions Under State Constraints

Bettiol

Frankowska

2006

Set-Valued Anal

Self Cite

View full text Add to dashboard Cite

Consider a differential inclusion under state constraintswhere F is an unbounded set-valued map with closed and convex images, which is measurable in t and k(t)-Lipschitz in x (with k(·) ∈ L 1 ) and K ⊂ R n is a closed set with smooth boundary. We provide sufficient conditions for the set-valued map ξ 0 S K [t0,T ] (ξ 0 ) associating to each initial point ξ 0 ∈ K the set of all solutions to the above constrained differential inclusion starting at ξ 0 to be pseudo-Lipschitz on K. This result is applied to investigate local Lipschitz continuity of the value function for the constrained Bolza problem of optimal control theory. Mathematics Subject Classifications (2000)34A60 · 49K24 · 54C60.

show abstract

“…In this last paper F is supposed to be bounded, to have convex compact images and the constraints are given by an inequality. Then viability theorems from [14,15] are used.…”

Section: Introductionmentioning

confidence: 99%

Regularity of Solution Maps of Differential Inclusions Under State Constraints

Bettiol

Frankowska

2006

Set-Valued Anal

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the second section we will introduce some notations and recall a viability theorem due to Frankowska and Plaskacz (see [10]) for differential inclusions with dynamics that are merely measurable in time and upper semicontinuous in the state variable. In Sect.…”

Section: L(t X(t) U(t))dtmentioning

confidence: 99%

“…Since the set Γ is sleek and has nonempty interior, N Γ (·) ∩ S n−1 is upper semicontinuous and therefore there existsη > 0 such that 10) and assume that ε…”

Section: Lemma 32 Let γ Be As In (33) Then For Anymentioning

confidence: 99%

Hölder estimates for trajectories of differential inclusions and HJB equations with state constraints

Facchi¹,

Hoehener²

2012

Nonlinear Differ. Equ. Appl.

View full text Add to dashboard Cite

Abstract. We consider the differential inclusionẋ ∈ F (t, x), with F measurable in t and Lipschitz in x, together with the state constraint x(t) ∈ Ω and prove the existence of neighboring trajectories lying in the interior of Ω. Using this result, we can characterize the Value Function of the Bolza Problem as the unique lower semicontinuous solution to the corresponding Hamilton-Jacobi-Bellman equation.Mathematics Subject Classification. 34A60, 34H05, 49K15, 49L25, 93C15.

show abstract

“…Remark 1 A simplified property of differential inclusion had been got in reference [ 4 ] by Frankowska and Plaskacz, but they only omitted the last factor of linear growth condition (3). ~,'(t) E F(t,,rK(x)), ~,(0) = x0 E K (7) satisfyx(t) 6 K, Vt E I.…”

Section: Let Z(t) = X(rmentioning

confidence: 99%

Periodic viable trajectories of differential inclusions

Wang¹

1999

Appl Math Mech

View full text Add to dashboard Cite

A measurable upper semicontinuous viability theorem for tubes

Cited by 40 publications

References 5 publications

Regularity of Solution Maps of Differential Inclusions Under State Constraints

Regularity of Solution Maps of Differential Inclusions Under State Constraints

Hölder estimates for trajectories of differential inclusions and HJB equations with state constraints

Periodic viable trajectories of differential inclusions

Contact Info

Product

Resources

About