Related papers: Order Reduction of Optimal Control Systems
In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the…
The first-order optimality conditions for a generic nonlinear optimization problem are generated as part of the terminal transversality conditions of an optimal control problem. It is shown that the Lagrangian of the optimization problem is…
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…
It has been shown recently that optimal control problems with the dynamical constraint given by a second order system admit a regular Lagrangian formulation. This implies that the optimality conditions can be obtained in a new form based on…
In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an…
We consider the class of control systems where the differential equation, state and control system are described by polynomials. Given a set of trajectories and a class of Lagrangians, we are interested to find a Lagrangian in this class…
The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…
In this work, we analyse the discretisation of a recently proposed new Lagrangian approach to optimal control problems of affine-controlled second-order differential equations with cost functions quadratic in the controls. We propose exact…
We are interested in optimally driving a dynamical system that can be influenced by exogenous noises. This is generally called a Stochastic Optimal Control (SOC) problem and the Dynamic Programming (DP) principle is the natural way of…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
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…
In the context of optimal control, we consider the inverse problem of Lagrangian identification given system dynamics and optimal trajectories. Many of its theoretical and practical aspects are still open. Potential applications are very…
In this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equations. The cost functional contains a term that measures the size of the support of the control, which is the so-called…
In the contest of optimal control problems, regularity results for optima are known when addressing fiber-strictly convex Lagrangian. For infinite time horizons, or for settings with infinite dimensional dynamics, the equivalence between…
In this work, we propose and study a new approach to formulate the optimal control problem of second-order differential equations, with a particular interest in those derived from force-controlled Lagrangian systems. The formulation results…
This paper proposes an algorithmic technique for a class of optimal control problems where it is easy to compute a pointwise minimizer of the Hamiltonian associated with every applied control. The algorithm operates in the space of relaxed…
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…
We propose a mean-field optimal control problem for the parameter identification of a given pattern. The cost functional is based on the Wasserstein distance between the probability measures of the modeled and the desired patterns. The…
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 consider a nonlinear system, affine with respect to an unbounded control $u$ which is allowed to range in a closed cone. To this system we associate a Bolza type minimum problem, with a Lagrangian having sublinear growth with respect to…