[PDF] Top 20 Second-order Analysis for Optimal Control Problems with Pure and Mixed State Constraints

... Key-words: Optimal control, state constraint, higher order, mixed control-state constraint, junction conditions, necessary or sufficient second-order optimality conditions, shooting algo[r] ... Voir le document complet

... deals with Hamilton-Jacobi-Bellman (HJB) approach for some stochas- tic control problems in presence of state ...of problems arises in many chal- lenging applications, and ... Voir le document complet

... the control problem of an aircraft in a climbing phase was modeled as a Mayer optimal control problem with two state constraints of order 1 and with affine ... Voir le document complet

... past for reducing the gap between second-order necessary and sufficient optimality conditions for optimization problems in Banach spaces, with so-called cone constraint ... Voir le document complet

... the optimal control problem at hand is usually reformulated as an infinite dimensional abstract optimization problem involving inequality and equality ...first and second- order ... Voir le document complet

... Algorithm and Numerical Simulations 6.2.1 Solving (OCP) τ by Shooting Methods and Homotopy on Delays As pointed out previously, the critical behavior coming out from applying indirect methods to (OCP) τ ... Voir le document complet

... provide second-order necessary conditions in Pontryagin form for optimal control problems with pure state and mixed control-state ... Voir le document complet

... qualification and to use the alternative formulation of the optimality conditions, introduced in Jacobson, Lele and Speyer [25], rigorously obtained in Maurer [31] and generalized in Bonnans ... Voir le document complet

... Conclusion and Remarks In this paper, we obtain for the first time stability results for optimal control problems with a state constraint of order greater ... Voir le document complet

... of second order optimality conditions for these partially affine problems have been studied by Goh in [27, 28, 26, 30], Dmitruk in [20], Dmitruk and Shishov in [21], Bernstein ... Voir le document complet

... (5) for any suitable second-order tangent z to the constraints, see the exact definition of tangents in Section ...to optimal control problems involving some classes of ... Voir le document complet

... an optimal control problem is of interest for obtaining error bounds for the discretization, see Dontchev and Hager ...Shvartsman and Vinter [19] considered the case of ... Voir le document complet

... solutions for the perturbed problem is ...sensitivity analysis is realized locally, in a neighborhood of a local optimal solution of the reference ...R-strong optimal controls. We say that a ... Voir le document complet

... [20] and derive a new charac- terization of the value function, for Mayer and minimum time problems, in term of unique Bilateral viscosity solution to an adequate Hamilton-Jacobi ...the ... Voir le document complet

... moments constraints Aur´ elien Alfonsi Rafa¨ el Coyaud Virginie Ehrlacher Damiano Lombardi May 14, 2019 Abstract: Optimal Transport (OT) problems arise in a wide range of applications, from physics ... Voir le document complet

... deals with a class of stochastic optimal control problems (SOCP) in presence of ...that for such problems the value function is, in general, discontinuous and its ... Voir le document complet

... 0, for x ∈ R d ...proposed for this class of equations, based on finite difference [37], semi-Lagrangian [28, 43, 45] and finite volume methods ...space and looking for a fixed point of ... Voir le document complet

... that for every p ∈ F (x), we have D ↑ u(t, x)(1, −p) ≤ 0 and (iii) holds ...only with final state constraints (K = R n ...Ω. For the reader’s convenience, we give the main steps ... Voir le document complet

... RELATED PROBLEMS In this section we begin by investigating the same problem when we remove one of the unilateral constraint D a ⊂ Ω or Ω ⊂ D b ...values for the parameter λ, we are able to recover a ... Voir le document complet

... with T -terminal condition given by the smallest function ˆ g ≥ g such that ∂ x 2 ˆ g ≤ ¯ γ(T, ...) with ˜ γ such that F (·, ˜ γ) ≤ C for some C > 0, and obtain that v is actually the ... Voir le document complet