Related papers: Symmetries in left-invariant optimal control probl…
Left-invariant optimal control problems on Lie groups form an important class of problems with big symmetry group. They are interesting from the theoretical point of view since they often can be completely studied, and general features can…
In this work we study the invariant optimal control problem on Lie groupoids. We show that any invariant optimal control problem on a Lie groupoid reduces to its co-adjoint Lie algebroid. In the final section of the paper, we present an…
In this work, we study an optimal control problem for a multi-agent system modeled by an undirected formation graph with nodes describing the kinematics of each agent, given by a left-invariant control system on a Lie group. The agents…
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…
In this paper we study reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent control systems, with partial symmetry breaking cost functions. Our approach emphasizes the role of…
Necessary conditions for existence of normal extremals in optimal control of systems subject to nonholonomic constraints are derived as solutions of a constrained second order variational problems. In this work, a geometric interpretation…
We extend the second Noether theorem to optimal control problems which are invariant under symmetries depending upon k arbitrary functions of the independent variable and their derivatives up to some order m. As far as we consider a…
We investigate symmetry reduction of optimal control problems for left-invariant control systems on Lie groups, with partial symmetry breaking cost functions. Our approach emphasizes the role of variational principles and considers a…
We study the reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent control systems, with partial symmetry breaking cost functions for continuous-time and discrete-time systems. We…
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…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
This paper addresses the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems enjoy certain…
This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to…
This paper studies the reduction by symmetry of variational problems on Lie groups and Riemannian homogeneous spaces. We derive the reduced equations of motion in the case of Lie groups endowed with a left-invariant metric, and on Lie…
The problem of finding optimal curves (the longest arcs) for sub-Lorentzian structures is an optimal control problem with an unbounded control set and a concave cost functional. The question of existence of an optimal solution is nontrivial…
The paper presents the geometry of Lie algebroids and its applications to optimal control. The first part deals with the theory of Lie algebroids, connections on Lie algebroids and dynamical systems defined on Lie algebroids (mainly…
This paper studies symmetric constrained linear-quadratic optimal control problems and their parametric solutions. The parametric solution of such a problem is a piecewise-affine feedback law that can be equivalently expressed as a set of…
In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…
The purpose of this paper is to use the framework of Lie algebroids to study optimal control problems for affine connection control systems on Lie groups. In this context, the equations for critical trajectories of the problem are…
The paper discusses various aspects of time-optimal control of quantum spin systems, modelled as right-invariant systems on a compact Lie group G. The main results are the reduction of such a system to an equivalent system on a homogeneous…