Related papers: Morse families in optimal control problems
In this paper we consider the Hamiltonian formulation of the equations of incompressible ideal fluid flow from the point of view of optimal control theory. The equations are compared to the finite symmetric rigid body equations analyzed…
Optimal control problems for underactuated mechanical systems can be seen as a higher-order variational problem subject to higher-order constraints (that is, when the Lagrangian function and the constraints depend on higher-order…
In this paper we study, from a variational and geometrical point of view, second-order variational problems on Lie groupoids and the construction of variational integrators for optimal control problems. First, we develop variational…
A new relation among a class of optimal control systems and Lagrangian systems with symmetry is discussed. It will be shown that a family of solutions of optimal control systems whose control equation are obtained by means of a group action…
We study a trajectory-planning problem whose solution path evolves by means of a Lie group action and passes near a designated set of target positions at particular times. This is a higher-order variational problem in optimal control,…
Infinite horizon open loop optimal control problems for semilinear parabolic equations are investigated. The controls are subject to a cost-functional which promotes sparsity in time. The focus is put on deriving first order optimality…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
This paper concerns a first-order algorithmic technique for a class of optimal control problems defined on switched-mode hybrid systems. The salient feature of the algorithm is that it avoids the computation of Fr\'echet or G\^ateaux…
We consider an optimal control problem for the obstacle problem with an elliptic variational inequality. The obstacle function which is the control function is assumed in $H^{2}$. We use an approximate technique to introduce a family of…
In this paper, we present a framework for solving continuous optimal control problems when the true system dynamics are approximated through an imperfect model. We derive a control strategy by applying Pontryagin's Minimum Principle to the…
In this work we deal with the optimal design and optimal control of structures undergoing large rotations. In other words, we show how to find the corresponding initial configuration and the corresponding set of multiple load parameters in…
We study a time minimization problem on the group of motions of a plane with admissible control in a half-disk. The considered control system describes a model of a car that can move forward on a plane and turn in place. Optimal…
Given a submersion $\pi:Q \to M$ with an Ehresmann connection $\mathcal{H}$, we describe how to solve Hamiltonian systems on $M$ by lifting our problem to $Q$. Furthermore, we show that all solutions of these lifted Hamiltonian systems can…
A class of optimal control problems of hybrid nature governed by semilinear parabolic equations is considered. These problems involve the optimization of switching times at which the dynamics, the integral cost, and the bounds on the…
In this work, we extend Aubry-Mather theory to the case of control systems with nonholonomic constraints. In this framework, we consider an optimal control problem where admissible trajectories are solutions of a control-affine equation.…
Motivated by the control of invasive biological populations, we consider a class of optimization problems for moving sets $t\mapsto \Omega(t)\subset\mathbb{R}^2$. Given an initial set $\Omega_0$, the goal is to minimize the area of the…
This paper addresses the optimal control problem of finite-horizon discrete-time nonlinear systems under state and control constraints. A novel numerical algorithm based on optimal control theory is proposed to achieve superior…
Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization maps can be conveniently lifted to the…
We discuss the use of Dirac structures to obtain a better understanding of the geometry of a class of optimal control problems and their reduction by symmetries. In particular we will show how to extend the reduction of Dirac structures…
This paper formulates an optimal control problem for a system of rigid bodies that are connected by ball joints and immersed in an irrotational and incompressible fluid. The rigid bodies can translate and rotate in three-dimensional space,…