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Related papers: Optimality of broken extremals

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Optimal control problems with symmetries often admit a non stationary turnpike property called trim turnpike, which characterizes the convergence of optimal solutions to certain symmetry induced trajectories called trim primitives. In this…

Optimization and Control · Mathematics 2026-04-27 Sofya Maslovskaya , Sina Ober-Blöbaum , Boris Wembe

We derive necessary conditions for optimality in control problems governed by hyperbolic partial differential equations in Goursat-Darboux form. The conditions consist of a set of Hamiltonian equations in Goursat form, side conditions for…

Optimization and Control · Mathematics 2007-05-23 S. A. Belbas

The paper is devoted to the study of the unconditional extremal problem for a fractional linear integral functional defined on a set of probability distributions. In contrast to results proved earlier, the integrands of the integral…

Optimization and Control · Mathematics 2019-06-14 Peter Shnurkov , Kseniia Adamova

In this paper, we consider a geometric formalism for optimal control of underactuated mechanical systems. Our techniques are an adaptation of the classical Skinner and Rusk approach for the case of Lagrangian dynamics with higher-order…

Mathematical Physics · Physics 2015-05-14 L. Colombo , D. Martin de Diego , M. Zuccalli

We investigate variants of Goddard's problems for nonvertical trajectories. The control is the thrust force, and the objective is to maximize a certain final cost, typically, the final mass. In this report, performing an analysis based on…

Optimization and Control · Mathematics 2009-04-20 Frédéric Bonnans , Pierre Martinon , Emmanuel Trélat

We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…

Optimization and Control · Mathematics 2015-03-19 Morten Vierling

Let $T>0$ fixed. We consider the optimal control problem for analytic affine systems: $\ds{\dot{x}=f\_0(x)+\sum\_{i=1}^m u\_if\_i(x)}$, with a cost of the form: $\ds{C(u)=\int\_0^T \sum\_{i=1}^m u\_i^2(t)dt}$. For this kind of systems we…

Optimization and Control · Mathematics 2016-08-16 Emmanuel Trélat

The paper presents results about strong metric subregularity of the optimality mapping associated with the system of first-order necessary optimality conditions for a problem of optimal control of a semilinear parabolic equation. The…

Optimization and Control · Mathematics 2025-11-19 Alberto Domínguez Corella , Nicolai Jork , Vladimir M. Veliov

In this paper, we derive a version of the Pontryagin maximum principle for general finite-dimensional nonlinear optimal sampled-data control problems. Our framework is actually much more general, and we treat optimal control problems for…

Optimization and Control · Mathematics 2015-12-09 Loïc Bourdin , Emmanuel Trélat

In this paper we combine two main topics in mechanics and optimal control theory: contact Hamiltonian systems and Pontryagin Maximum Principle. As an important result, among others, we develop a contact Pontryagin Maximum Principle that…

Optimization and Control · Mathematics 2020-06-26 Manuel de León , Manuel Lainz , Miguel C. Muñoz-Lecanda

We study the Pontryagin maximum principle by deriving necessary and sufficient conditions for a class of optimal control problems arising in non exchangeable mean field systems, where agents interact through heterogeneous and asymmetric…

Optimization and Control · Mathematics 2025-06-09 Idris Kharroubi , Samy Mekkaoui , Huyên Pham

This paper investigates optimal control problems formulated over a class of piecewise-smooth vector fields. Instead of optimizing over the discontinuous system directly, we instead formulate optimal control problems over a family of…

Dynamical Systems · Mathematics 2019-04-02 Tyler Westenbroek , Xiaobin Xiong , Aaron D Ames , S Shankar Sastry

In addition to the theoretical value of challenging optimal control problmes, recent progress in autonomous vehicles mandates further research in optimal motion planning for wheeled vehicles. Since current numerical optimal control…

Optimization and Control · Mathematics 2013-01-29 Hamidreza Chitsaz

In the present paper we deal with fully nonlinear two-dimensional smooth control systems with scalar input $\dot{q} = \bs{f}(q,u)$, $q \in M$, $u \in U$, where $M$ and $U$ are differentiable smooth manifolds of respective dimensions two and…

Optimization and Control · Mathematics 2012-06-06 Ulysse Serres

Fractional optimal control problems via a wide class of fractional operators with a general analytic kernel are introduced. Necessary optimality conditions of Pontryagin type for the considered problem are obtained after proving a Gronwall…

Optimization and Control · Mathematics 2021-09-24 Faical Ndairou , Delfim F. M. Torres

In this paper we are concerned with generalised L 1-minimisation problems, i.e. Bolza problems involving the absolute value of the control with a control-affine dynamics. We establish sufficient conditions for the strong local optimality of…

Optimization and Control · Mathematics 2021-01-28 Francesca Chittaro , Laura Poggiolini

This work addresses an optimal control problem for a semilinear elliptic equation in two-dimensional space, characterized by an exponential nonlinearity and a singular source term. The source is modeled as a finite linear combination of…

Optimization and Control · Mathematics 2025-05-28 Vu Huu Nhu

We consider an optimal control problem governed by a class of boundary value problem with the spectral Dirichlet fractional Laplacian. Some sufficient condition for the existence of optimal processes is stated. The proof of the main result…

Analysis of PDEs · Mathematics 2017-12-29 Dorota Bors

In this paper error analysis for finite element discretizations of Dirichlet boundary control problems is developed. For the first time, optimal discretization error estimates are established in the case of three dimensional polyhedral and…

Numerical Analysis · Mathematics 2024-01-05 Johannes Pfefferer , Boris Vexler

We study in optimal control the important relation between invariance of the problem under a family of transformations, and the existence of preserved quantities along the Pontryagin extremals. Several extensions of Noether theorem are…

Optimization and Control · Mathematics 2007-05-23 Delfim F. M. Torres