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We investigate a control process described by a linear system of ordinary differential equations with a noise of special type acting to the control parameter. As the cost functional the probability of the final state vector to enter to a…
We discuss first order optimality conditions for geometric optimization problems with Neumann boundary conditions and boundary observation. The methods we develop here are applicable to large classes of state systems or cost functionals.…
In this paper, we focus on a method based on optimal control to address the optimization problem. The objective is to find the optimal solution that minimizes the objective function. We transform the optimization problem into optimal…
The paper analyzes a Lagrangian system which is controlled by directly assigning some of the coordinates as functions of time, by means of frictionless constraints. In a natural system of coordinates, the equations of motions contain terms…
We deal with regular Lagrangian constrained systems which are invariant under the action of a symmetry group. Fixing a connection on the higher-order principal bundle where the Lagrangian and the (independent) constraints are defined, the…
We geometrically describe optimal control problems in terms of Morse families in the Hamiltonian framework. These geometric structures allow us to recover the classical first order necessary conditions for optimality and the starting point…
This article contributes to a framework for a computational indirect method based on the Pontryagin maximum principle to efficiently solve a class of state constrained time-optimal control problems in the presence of a time-dependent flow…
Linear time-invariant control systems can be considered as finitely generated modules over the commutative principal ideal ring $\mathbb{R}[\frac{d}{dt}]$ of linear differential operators with respect to the time derivative. The Kalman…
We study the reduction of degrees of freedom for the equations that determine necessary optimality conditions for extrema in an optimal control problem for a multiagent system by exploiting the physical symmetries of agents, where the…
We address the generalized variational problem of Herglotz from an optimal control point of view. Using the theory of optimal control, we derive a generalized Euler-Lagrange equation, a transversality condition, a DuBois-Reymond necessary…
We consider the Lagrange problem of optimal control with unrestricted controls and address the question: under what conditions we can assure optimal controls are bounded? This question is related to the one of Lipschitzian regularity of…
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…
Variational inequalities are an important mathematical tool for modelling free boundary problems that arise in different application areas. Due to the intricate nonsmooth structure of the resulting models, their analysis and optimization is…
We consider a linear-quadratic optimization problem with pointwise bounds on the state for which the constraint is given by the Laplace-Beltrami equation (to have uniqueness we add an lower order term) on a two-dimensional surface . By…
In this paper, a quadratic optimal control problem is considered for second-order parabolic PDEs with homogeneous Dirichlet boundary conditions, in which the "point" control function (depending only on time) constitutes a source term. These…
We obtain a discrete time analog of E. Noether's theorem in Optimal Control, asserting that integrals of motion associated to the discrete time Pontryagin Maximum Principle can be computed from the quasi-invariance properties of the…
In this note, we develop the first-order theory of optimal control problems with box constraints on the control. We emphasize the precise modification of Pontryagin's maximum principle when the admissible control set is compact, the…
In this paper, we study representation formulas for finite-horizon optimal control problems with or without state constraints, unifying two different viewpoints: the Lagrangian and dynamic programming (DP) frameworks. In a recent work [1],…
Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. In this paper we present a method to construct symplectic-momentum integrators for…
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…