Related papers: The Herglotz principle and vakonomic dynamics
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…
The theory of quantum optomechanics is reconstructed from first principles by finding a Lagrangian from light's equation of motion and then proceeding to the Hamiltonian. The nonlinear terms, including the quadratic and higher-order…
A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an application, we prove that discrete Lagrangian dynamics on a Lie…
For a class of nonequilibrium systems, called driven lattice gases, we study what happens when two systems are kept in contact and allowed to exchange particles with the total number of particles conserved. Both for attractive and repulsive…
In this paper, we present a geometric framework for the reachability analysis of attitude control systems. We model the attitude dynamics on the product manifold $\mathrm{SO}(3) \times \mathbb{R}^3$ and introduce a novel parametrized family…
We propose a neural network approach to model general interaction dynamics and an adjoint based stochastic gradient descent algorithm to calibrate its parameters. The parameter calibration problem is considered as optimal control problem…
This paper gives a brief contact-geometric account of the Pontryagin maximum principle. We show that key notions in the Pontryagin maximum principle---such as the separating hyperplanes, costate, necessary condition, and normal/abnormal…
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…
The paper presents an approach to studying optimal control problems in the space of nonnegative measures with dynamics given by a nonlocal balance law. This approach relies on transforming the balance law into a continuity equation in the…
It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher's Information Matrix. In this work we…
The aim of this work is to study, from an intrinsic and geometric point of view, second-order constrained variational problems on Lie algebroids, that is, optimization problems defined by a cost functional which depends on higher-order…
In this paper, we extend the well-known Noether theorem for Lagrangian systems to contact Lagrangian systems. We introduce a classification of infinitesimal symmetries and obtain the corresponding dissipated quantities. We notice that in…
This paper introduces a new global dynamics and chaos indicator based on the method of Lagrangian Descriptor apt for discriminating ordered and deterministic chaotic motions in multidimensional systems. The selected implementation of this…
This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with…
We consider Lagrangian systems in the limit of infinitely many particles. It is shown that the corresponding discrete action functionals Gamma-converge to a continuum action functional acting on probability measures of particle…
In this paper we consider a nonlinear system of PDEs coupling the viscous Cahn-Hilliard-Oono equation with dynamic boundary conditions enjoying a similar structure on the boundary. After proving well-posedness of the corresponding initial…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
We consider a stochastic control problem which is composed of a controlled stochastic differential equation, and whose associated cost functional is defined through a controlled backward stochastic differential equation. Under appropriate…
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…
We study the time-optimal robust control of a two-level quantum system subjected to field inhomogeneities. We apply the Pontryagin Maximum Principle and we introduce a reduced space onto which the optimal dynamics is projected down. This…