# Haut PDF Some results on the optimal control with unilateral state constraints

### Some results on the optimal control with unilateral state constraints

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### A SECOND-ORDER MAXIMUM PRINCIPLE IN OPTIMAL CONTROL UNDER STATE CONSTRAINTS

**results**and to inves- tigate second-order necessary optimality conditions using second-order ...In

**the**context of

**optimal**

**control**theory this approach was applied in [17, 18] by ...

38

### Nonlinear H ∞ -control under unilateral constraints

**the**restitution rule is assumed at

**the**collision time ...facilitate

**the**exposition capabilities of

**the**developed synthesis and its robustness features are first illustrated

**with**a ...

33

### Nonlinear state feedback H-infinity-control of mechanical systems under unilateral constraints

**the**hybrid model of interest subject to an

**unilateral**constraint and

**the**H ∞ -

**control**problem is then ...of

**the**problem in question to exist, and a

**state**feedback con- ...

7

### Lipschitz solutions of optimal control problems with state constraints of arbitrary order

**the**Lipschitz continuity of

**the**solution of an

**optimal**

**control**problem is of interest for obtaining error bounds for

**the**discretization, see Dontchev and Hager ...in

**the**...

21

### On second order necessary conditions in infinite dimensional optimal control with state constraints

**the**

**constraints**, see

**the**exact definition of tangents in Section ...our

**results**apply to

**optimal**

**control**problems involving

**some**classes of PDEs, see [17], [18], [21] ...

7

### Error estimates for the Euler discretization of an optimal control problem with first-order state constraints

**the**paper. In Section 2 we introduce

**the**problem and

**the**assumptions adopted in

**the**paper, and we

**state**our main result (Theorem ...for

**the**

**control**,

**state**, ...

26

### On some optimal control problems governed by a state equation with memory

**the**Cauchy problem is studied in details. Section 3 deals

**with**

**the**existence of

**optimal**controls,

**the**material of these sections is rather standard but is included for

**the**...

26

### Deterministic mean field games with control on the acceleration and state constraints

**the**graph of

**the**multivalued map Γ opt : Θ Ñ Γ, px, vq ÞÑ Γ opt rx, vs is closed in

**the**sense given in Proposition ...accurate

**results**In dimension one and for a running cost quadratic in ...

37

### The Mayer and Minimum Time Problems with Stratified State Constraints *

**the**dynamics F is considered to be uppersemi-continuous on

**the**set K whereas in [20] it is assumed to be Lipschitz ...continuous.

**The**paper is organized as ...along

**with**

**the**...

20

### Stability Analysis of Optimal Control Problems with a Second-order State Constraint

**results**for

**state**

**constraints**of first-order have been obtained by Malanowski [18] and Dontchev and Hager ...[9].

**The**difficulty of pure

**state**

**constraints**is

**the**...

37

### Value function and optimal trajectories for a maximum running cost control problem with state constraints. Application to an abort landing problem.

**the**general case where

**the**set of

**state**

**constraints**K is a non-empty closed subset of R d (K ( R d ),

**the**value function is merely ...requires

**some**assumptions that involve an ...

29

### Some Results on Reset Control systems

**the**main

**results**of this thesis, namely

**the**study of reset

**control**systems

**with**magnitude limitation on

**the**...estimating

**the**stability region and performance ...

141

### Nonlinear H_inf -Control of Mechanical Systems under Unilateral Constraints on the Position

**with**

**some**positive definite functions = : , > = 0, … , ? for all @ > 0 and ? ∈ ℤ such that C ≤ ...consistent

**with**

**the**notion of dissipativity introduced by Willems (1972) and Hill ...

7

### On some stochastic control problems with state constraints

**the**value function satisfies a special kind of nonlinear partial differ- ential equation called

**the**Hamilton-Jacobi-Bellman (HJB) ...for

**optimal**

**control**problems set in a deterministic ...

156

### Direct and indirect methods in optimal control with state constraints and the climbing trajectory of an aircraft

**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 ...

24

### Minimal controllability time for the heat equation under unilateral state or control constraints

**with**

**the**convergence result given in § 5.3 of

**the**minimal time for

**the**discretized problem, to

**the**minimal time of

**the**continuous one, as N t and N x tend to +∞ ...

41

### Optimal control of a parabolic equation with time-dependent state constraints

**the**set of C ∞ functions over Q, (78) holds.

**The**conclusion ...of

**the**alternative formulation that is useful when for- mulating shooting algorithms; see Bonnans and Hermant [15] for related ...

28

### Optimal Control of Aerospace Systems with Control-State Constraints and Delays

**the**critical behavior coming out from applying indirect methods to (OCP) τ consists of

**the**integration of mixed-type equations that arise from system ...(6.4).

**The**convergence ...

224

### On the shooting algorithm for optimal control problems with state constraints

**the**no-gap second-order optimality conditions and

**the**characterization of

**the**well-posedness of

**the**shooting algorithm, obtained in [18, 21] and [19], respectively, for an ...

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