Related papers: Bang--bang trajectories with a double switching ti…
In this paper we consider the problem of structural stability of strong local optimisers for the minimum time problem in the case when the nominal problem has a bang-bang strongly local optimal control which exhibits a double switch.
In this paper we give sufficient conditions for a Pontryagin extremal trajectory, consisting of two bang arcs followed by a singular one, to be a strong local minimizer for a Mayer problem. The problem is defined on a manifold $M$ and the…
This paper is concerned with necessary and sufficient second-order conditions for finite-dimensional and infinite-dimensional constrained optimization problems. Using a suitably defined directional curvature functional for the admissible…
This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain…
Second order systems whose drift is defined by the gradient of a given potential are considered, and minimization of the $L^1$-norm of the control is addressed. An analysis of the extremal flow emphasizes the role of singular trajectories…
The paper puts forward sufficient conditions for local controllability of a control dynamical system. The results obtained are meaningful in the case when the linear approximation to this system is not completely controllable. As a…
In this paper we study the structural stability of a bang-singular-bang extremal in the minimum time problem between fixed points. The dynamics is single-input and control-affine. On the nominal problem ($r = 0$), we assume the coercivity…
While the Pontryagin Maximum Principle can be used to calculate candidate extremals for optimal orbital transfer problems, these candidates cannot be guaranteed to be at least locally optimal unless sufficient optimality conditions are…
We investigate optimality conditions for optimization problems constrained by a class of variational inequalities of the second kind. Based on a nonsmooth primal-dual reformulation of the governing inequality, the differentiability of the…
In an earlier paper (https://doi.org/10.1137/21M1393315), the Switch Point Algorithm was developed for solving optimal control problems whose solutions are either singular or bang-bang or both singular and bang-bang, and which possess a…
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…
A remarkably simple result is found for the optimal protocol of drivings for a general two-level Hamiltonian which transports a given initial state to a given final state in minimal time. If one of the three possible drivings is…
This paper is a continuation of the work by the same authors on the Cartan group equipped with the sub-Finsler $\ell_\infty$ norm. We start by giving a detailed presentation of the structure of bang-bang extremal trajectories. Then we prove…
We consider bilinear optimal control problems, whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient second-order conditions for bang-bang controls, which guarantee…
We prove both necessary and sufficient second order conditions of extrema for variational problems involving any higher order continuously twice differentiable Lagrangians with multi-valued dependent functions of several variables. Our…
This article connects the theory of extremal doubly stochastic measures to the geometry and topology of optimal transportation. We begin by reviewing an old question (# 111) of Birkhoff in probability and statistics [4], which is to give a…
Second-order optimality conditions of the bilevel programming problems are dependent on the second-order directional derivatives of the value functions or the solution mappings of the lower level problems under some regular conditions,…
We study a parabolic boundary control problem with one spatial dimension, control constraints of box type, and an objective function that measures the $L^2$-distance to a desired terminal state. It is shown that, for a certain choice of the…
We study the optimal control problem for a control-affine system, where we want to minimize the $L^1$ norm of the control. First, we show how Pontryagin Maximum Principle (PMP) applies to this problem and we divide the extremal trajectories…
In this paper we derive new second-order optimality conditions for a very general set-constrained optimization problem where the underlying set may be nononvex. We consider local optimality in specific directions (i.e., optimal in a…