Related papers: Lecture Note for Bounded Controls in Continuous-Ti…
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…
Pontryagin's Maximum Principle is an outstanding result for solving optimal control problems by means of optimizing a specific function on some particular variables, the so called controls. However, this is not always enough for solving all…
We reconsider the variational integration of optimal control problems for mechanical systems based on a direct discretization of the Lagrange-d'Alembert principle. This approach yields discrete dynamical constraints which by construction…
Quantum optimal control is a set of methods for designing time-varying electromagnetic fields to perform operations in quantum technologies. This tutorial paper introduces the basic elements of this theory based on the Pontryagin maximum…
The key element of the approach to the theory of necessary conditions in optimal control discussed in the paper is reduction of the original constrained problem to unconstrained minimization with subsequent application of a suitable…
We study time-inconsistent recursive stochastic control problems, i.e., for which the Bellman principle of optimality does not hold. For this class of problems classical optimal controls may fail to exist, or to be relevant in practice, and…
We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal…
We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
We describe a reformulation (following Hales (2017)) of a 1934 conjecture of Reinhardt on pessimal packings of convex domains in the plane as a problem in optimal control theory. Several structural results of this problem including its…
In this article, the sufficient Pontryagin's maximum principle for infinite horizon discounted stochastic control problem is established. The sufficiency is ensured by an additional assumption of concavity of the Hamiltonian function.…
A Hamiltonian algorithm, both theoretical and numerical, to obtain the reduced equations implementing Pontryagine's Maximum Principle for singular linear-quadratic optimal control problems is presented. This algorithm is inspired on the…
We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…
In this work, we investigate the optimal control problem for continuous-time Markov decision processes with the random impact of the environment. We provide conditions to show the existence of optimal controls under finite-horizon criteria.…
This paper deals with optimal control problems described by a controlled version of Moreau's sweeping process governed by convex polyhedra, where measurable control actions enter additive perturbations. This class of problems, which…
We establish a geometric Pontryagin maximum principle for discrete time optimal control problems on finite dimensional smooth manifolds under the following three types of constraints: a) constraints on the states pointwise in time, b)…
We provide an improvment of the maximum principle of Pon-tryagin of the optimal control problems, for a system governed by an ordinary differential equation, in presence of final constraints, in the setting of the piece-wise differentiable…
Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…
Controllability maximization problem under sparsity constraints is a node selection problem that selects inputs that are effective for control in order to minimize the energy to control for desired state. In this paper we discuss the…
In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order $\alpha\in(0,1)$ in time. The…