Related papers: Structural stability for bang--singular--bang extr…
When applying methods of optimal control to motion planning or stabilization problems, some theoretical or numerical difficulties may arise, due to the presence of specific trajectories, namely, singular minimizing trajectories of the…
In this paper a priori error estimates are derived for full discretization (in space and time) of time-optimal control problems. Various convergence results for the optimal time and the control variable are proved under different…
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…
A large collection of financial contracts offering guaranteed minimum benefits are often posed as control problems, in which at any point in the solution domain, a control is able to take any one of an uncountable number of values from the…
We study the singularities for minimum time control-affine problems in 4D with 2D controls. After regularization, the problem boils down to the study of a bifurcation around some nilpotent equilibrium in the singular locus. We show that the…
The minimum-time control problem consists in finding a control policy that will drive a given dynamic system from a given initial state to a given target state (or a set of states) as quickly as possible. This is a well-known challenging…
We study the problem of state transition on a finite time interval with minimal energy supply for linear port-Hamiltonian systems. While the cost functional of minimal energy supply is intrinsic to the port-Hamiltonian structure, the…
We propose and analyze a posteriori error estimates for a control-constrained optimal control problem with bang-bang solutions. We consider a solution strategy based on the variational approach, where the control variable is not…
Combining invariant-based inverse engineering, perturbation theory, and Optimal Control Theory, we design fast, transitionless expansions of cold neutral atoms or ions in Gaussian anharmonic traps. Bounding the possible trap frequencies and…
A method is developed for solving bang-bang and singular optimal control problems using adaptive Legendre-Gauss-Radau (LGR) collocation. The method is divided into several parts. First, a structure detection method is developed that…
Necessary conditions for existence of normal extremals in optimal control of systems subject to nonholonomic constraints are derived as solutions of a constrained second order variational problems. In this work, a geometric interpretation…
We analyze space-time finite element methods for the numerical solution of distributed parabolic optimal control problems with energy regularization in the Bochner space $L^2(0,T;H^{-1}(\Omega))$. By duality, the related norm can be…
This paper examines the impulse controllability of degenerate singular parabolic equations through a modern framework focused on finite-time stabilization. Furthermore, we provide an explicit estimate for the exponential decay of the…
Low-thrust engines for interplanetary spacecraft transfers allow cost-effective space missions with flexible launch and arrival dates. To find fuel-optimal trajectories, an optimal control problem is to be solved. Pontryagin's Maximum…
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…
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…
This paper studies a vertical powered descent problem in the context of planetary landing, considering glide-slope and thrust pointing constraints and minimizing any final cost. In a first time, it proves the Max-Min-Max or Max-Singular-Max…
This contribution considers optimal control problems subject to nonlocal conservation laws -- those in which the velocity depends nonlocally (i.e., via a convolution) on the solution -- and the so-called singular limit. First, the existence…
A fundamental problem that the bearing rigidity theory studies is to determine when a framework can be uniquely determined up to a translation and a scaling factor by its inter-neighbor bearings. While many previous works focused on the…
This paper firstly presents the necessary and sufficient conditions for a kind of discrete-time robust stochastic optimal control problem with convex control domains. As it is an "inf sup problem", the classical variational method is…