A Survey on Optimal Control Problems with Differential-Algebraic Equations

Gerdts, Matthias

doi:10.1007/978-3-319-11050-9_3

Cited by 6 publications

(4 citation statements)

References 92 publications

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“…However, the calculcation of gradients using the adjoint approach may not be the most suitable one if non-linear control and/or state constraints are present in the optimal control problem. In this case the sensitivity approach is preferable, details can be found in Gerdts [25].…”

Section: Remark 43mentioning

confidence: 99%

Approximation of reachable sets using optimal control algorithms

Baier¹,

Gerdts²,

Xausa³

2013

NACO

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Section: Remark 43mentioning

confidence: 99%

Approximation of reachable sets using optimal control algorithms

Baier¹,

Gerdts²,

Xausa³

2013

NACO

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“…The above nonlinear optimization problem is solved by a sequential quadratic programming (SQP) method [5,9]. As in [13] we use an Armijo type line-search procedure for the augmented Lagrangian function in our implementation.…”

Section: Optimal Control Problemmentioning

confidence: 99%

Path-Planning with Collision Avoidance in Automotive Industry

Landry

Gerdts

Henrion

et al. 2013

IFIP Advances in Information and Communication Technology

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Abstract. An optimal control problem to find the fastest collision-free trajectory of a robot is presented. The dynamics of the robot is governed by ordinary differential equations. The collision avoidance criterion is a consequence of Farkas's lemma and is included in the model as state constraints. Finally an active set strategy based on backface culling is added to the sequential quadratic programming which solves the optimal control problem.Keywords: Optimal control, collision avoidance, backface culling, active set strategy. Collision AvoidanceIn automotive industry robots have to work simultaneously on the same workpiece. The challenge is to find for each robot the fastest trajectory that avoids any collision with the surrounding obstacles and the other robots. We start with the establishment of the collision avoidance criterion.For simplicity, we suppose that only one obstacle is present in the workspace. As in [7,8] a collision detection can be obtained when the robot is approximated by a union of convex polyhedra. This union is called P and it given bywhere n P is the number of polyhedra in P . If p i denotes the number of faces inSimilarly, the obstacle is approximated by the following union of convex poly-where n Q is the number of polyhedra in Q. If q j is the number of faces in Q (j) , then C (j) ∈ R qj ×3 and d (j) ∈ R qj for j = 1, . . . , n Q . In the following, n P , A, b D.

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“…In the past couple decades, DAEs have become a very important generalization of ordinary differential equations (ODEs) and have numerous applications in mathematical modeling of various dynamical processes; see e.g. [3,5,13,31] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

“…This means that the maximum principles derived in [11] can only be applied to control of seDAEs with index one. Recently some necessary optimality conditions for control of DAEs with higher indexes have been derived [31,25,13].…”

Section: Introductionmentioning

confidence: 99%

Necessary Optimality Conditions for Implicit Control Systems with Applications to Control of Differential Algebraic Equations

2017

Set-Valued Var. Anal

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In this paper we derive necessary optimality conditions for optimal control problems with nonlinear and nonsmooth implicit control systems. Implicit control systems have wide applications including differential algebraic equations (DAEs). The challenge in the study of implicit control system lies in that the system may be truly implicit, i.e., the Jacobian matrix of the constraint mapping may be singular. Our necessary optimality conditions hold under the so-called weak basic constraint qualification plus the calmness of a perturbed constraint mapping. Such constraint qualifications allow for singularity of the Jacobian and hence is suitable for implicit systems. Specifying these results to control of semi-explicit DAEs we obtain necessary optimality conditions for control of semi-explicit DAEs with index higher than one.

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A Survey on Optimal Control Problems with Differential-Algebraic Equations

Cited by 6 publications

References 92 publications

Approximation of reachable sets using optimal control algorithms

Approximation of reachable sets using optimal control algorithms

Path-Planning with Collision Avoidance in Automotive Industry

Necessary Optimality Conditions for Implicit Control Systems with Applications to Control of Differential Algebraic Equations

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