Related papers: Geometric reduction in optimal control theory with…
We consider some generalizations of the classical nonholonomic integrator and give a geometric approach to characterize controllability for these systems. We use Stokes' theorem and results from complex analysis to obtain necessary and…
We address optimal control problems on the space of measures for an objective containing a smooth functional and an optimal transport regularization. That is, the quadratic Monge-Kantorovich distance between a given prior measure and the…
Many physically important mechanical systems may be described with a Lie group $G$ as configuration space. According to the well-known Noether's theorem, underlying symmetries of the Lie group may be used to considerably reduce the…
Pontryagin's Maximum Principle is an outstanding result for solving optimal control problems by means of optimizing a specific function on some particular variables, the so called controls. However, this is not always enough for solving all…
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…
Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic…
Geometric optimal control utilizes tools from differential geometry to analyze the structure of a problem to determine the control and state trajectories to reach a desired outcome while minimizing some cost function. For a controlled…
We extend Noether's theorem to the setting of multisymplectic geometry by exhibiting a correspondence between conserved quantities and continuous symmetries on a multi-Hamiltonian system. We show that a homotopy co-momentum map interacts…
In this paper, we consider a geometric formalism for optimal control of underactuated mechanical systems. Our techniques are an adaptation of the classical Skinner and Rusk approach for the case of Lagrangian dynamics with higher-order…
Optimal control problems without control costs in general do not possess solutions due to the lack of coercivity. However, unilateral constraints together with the assumption of existence of strictly positive solutions of a pre-adjoint…
A Lie system is a non-autonomous system of first-order ordinary differential equations describing the integral curves of a non-autonomous vector field taking values in a finite-dimensional real Lie algebra of vector fields, a so-called…
Symmetries have proven to be important ingredients in the analysis of neural networks. So far their use has mostly been implicit or seemingly coincidental. We undertake a systematic study of the role that symmetry plays. In particular, we…
We study control systems invariant under a Lie group with application to the problem of nonlinear trajectory planning. A theory of symmetry reduction of exterior differential systems is employed to demonstrate how symmetry reduction and…
Initially introduced in the framework of quantum control, the so-called "monotonic algorithms" have demonstrated excellent numerical performance when dealing with bilinear optimal control problems. This paper presents a unified formulation…
In recent papers it has been suggested that human locomotion may be modeled as an inverse optimal control problem. In this paradigm, the trajectories are assumed to be solutions of an optimal control problem that has to be determined. We…
A deeper understanding of nonequilibrium phenomena is needed to reveal the principles governing natural and synthetic molecular machines. Recent work has shown that when a thermodynamic system is driven from equilibrium then, in the linear…
In the framework of renormalization-group improved cosmologies, we use the Noether symmetry approach to get exact and general integration of the matter-dominated cosmological equations. This is performed by using an expression of…
In this paper we study the sub-Finsler geometry as a time-optimal control problem. In particular, we consider non-smooth and non-strictly convex sub-Finsler structures associated with the Heisenberg, Grushin, and Martinet distributions.…
We compare the performances of symplectic and non-symplectic integrators for the computation of normal geodesics and conjugate points in sub-Riemannian geometry at the example of the Martinet case. For this case study we consider first the…
It is broadly known that Lie point symmetries and their subcase, Noether symmetries, can be used as a geometric criterion to select alternative theories of gravity. Here, we use Noether symmetries as a selection criterion to distinguish…