Related papers: Discrete variational integrators and optimal contr…
Here an original idea is suggested to prove the existence of optimal control for some types of non- linear problems. The obtained results can be considered as individual existence theorems (in some sense).
We provide a fast and simple method to solve fractional variational problems with dependence on Hadamard fractional derivatives. Using a relation between the Hadamard fractional operator and a sum involving integer-order derivatives, we…
In this paper we consider discrete time stochastic optimal control problems over infinite and finite time horizons. We show that for a large class of such problems the Taylor polynomials of the solutions to the associated Dynamic…
In this article we show the crucial role of elliptic regularity theory for the development of efficient numerical methods for the solution of some variational problems. Here we focus to a class of elliptic multiobjective optimal control…
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…
This paper traces the strong relations between experimental design and control, such as the use of optimal inputs to obtain precise parameter estimation in dynamical systems and the introduction of suitably designed perturbations in…
In this work we refer to motivations, applications, and relations of control theory with other areas of mathematics. We present a brief historical review of optimal control theory, from its roots in the calculus of variations and the…
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete…
A piecewise constant Mayer cost function is used to model optimal control problems in which the state space is partitioned into several regions, each having its own Mayer cost value. In such a context, the standard numerical methods used in…
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of application are studied, in particular,…
We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…
We develop a simple and accurate method to solve fractional variational and fractional optimal control problems with dependence on Caputo and Riemann-Liouville operators. Using known formulas for computing fractional derivatives of…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
We use a computer algebra system to compute, in an efficient way, optimal control variational symmetries up to a gauge term. The symmetries are then used to obtain families of Noether's first integrals, possibly in the presence of…
To tackle the difficulties faced by both stochastic dynamic programming and scenario tree methods, we present some variational approach for numerical solution of stochastic optimal control problems. We consider two different interpretations…
Appropriate time discretization is crucial for real-time applications of numerical optimal control, such as nonlinear model predictive control. However, if the discretization error strongly depends on the applied control input, meeting…
In this paper we present a general framework that allows one to study discretization of certain dynamical systems. This generalizes earlier work on discretization of Lagrangian and Hamiltonian systems on tangent bundles and cotangent…
We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators,…
A new method for the optimal solutions is proposed. Originating from the continuous-time dynamics stability theory in the control field, the optimal solution is anticipated to be obtained in an asymptotically evolving way. By introducing a…
In this paper, we consider optimization problems with $L^0$-cost of the controls. Here, we take the support of the control as independent optimization variable. Topological derivatives of the corresponding value function with respect to…