Related papers: $L^1$-Minimization for Mechanical Systems
This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smooth elliptic PDE. The control enters the state equation not…
In this paper we analyse the optimality of broken Pontryagin extremal for an n-dimensional affine control system with a control parameter, taking values in a k- dimensional closed ball. We prove the optimality of broken normal extremals…
We consider the time-optimal control by magnetic fields of a spin 1/2 particle in a dissipative environment. This system is used as an illustrative example to show the role of singular extremals in the control of quantum systems. We analyze…
We study the singular stochastic optimal control problem with model uncertainty, where the necessary conditions determined by the corresponding maximum principle are trivial. Robust integral form and pointwise second order necessary…
In this article we study optimal control problems for systems that are affine with respect to some of the control variables and nonlinear in relation to the others. We consider finitely many equality and inequality constraints on the…
The objective of this article is to apply recent developments in geometric optimal control to analyze the time minimum control problem of dissipative two-level quantum systems whose dynamics is governed by the Lindblad equation. We focus…
We consider an optimal control problem governed by a one-dimensional elliptic equation that involves univariate functions of bounded variation as controls. For the discretization of the state equation we use linear finite elements and for…
We investigate the bang-bang property for fairly general classes of $L^\infty-L^1$ constrained bilinear optimal control problems in two cases: that of the one-dimensional torus, in which case we consider parabolic equations, and that of…
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…
Maximum hands-off control is a control that has the minimum L0 norm among all feasible controls. It is known that the maximum hands-off (or L0-optimal) control problem is equivalent to the L1-optimal control under the assumption of…
The purpose of this paper is to establish the first and second order necessary conditions for stochastic optimal controls in infinite dimensions. The control system is governed by a stochastic evolution equation, in which both drift and…
We consider the exact penalization of the incompressibility condition $div(u)=0$ for the velocity field of a Bingham fluid in terms of the $L^1$-norm. This penalization procedure results in a nonsmooth optimization problem for which we…
Reduced quasilinear (QL) and nonlinear (gradient-driven) models with scale separations, commonly used to interpret experiments and to forecast turbulent transport levels in magnetised plasmas are tested against nonlinear models without…
The study is devoted to mathematical modeling and optimal control design of longitudinal motions of a rectilinear elastic rod. The control inputs are a force, which is normal to the cross section and distributed piecewise constantly along…
The Pontryagin's Maximum Principle allows, in most cases, the design of optimal controls of affine nonlinear control systems by considering the sign of a smooth function. There are cases, although, where this function vanishes on a whole…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…
Pointwise minimum norm control laws for hybrid dynamical systems are proposed. Hybrid systems are given by differential equations capturing the continuous dynamics or flows, and by difference equations capturing the discrete dynamics or…
Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…
In this manuscript, we consider a control system governed by a general ordinary differential equation on a Riemannian manifold, with its endpoints satisfying some inequalities and equalities, and its control constrained to a closed convex…
In this paper, we first investigate necessary optimality conditions for problems governed by systems describing the flow of an incompressible second grade fluid. Next, we study the asymptotic behavior of the optimal solution when the…