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We develop aspects of geometric control theory on Lie groups G which may be infinite dimensional, and on smooth G-manifolds M modelled on locally convex spaces. As a tool, we discuss existence and uniqueness questions for differential…

Functional Analysis · Mathematics 2022-08-25 Helge Glockner , Joachim Hilgert

Several new invariants for Lie algebroids have been discovered recently. We give an overview of these invariants and establish several relationships between them.

Differential Geometry · Mathematics 2007-05-23 Rui L. Fernandes

We study deformations of Lie groupoids by means of the cohomology which controls them. This cohomology turns out to provide an intrinsic model for the cohomology of a Lie groupoid with values in its adjoint representation. We prove several…

Differential Geometry · Mathematics 2020-11-19 Marius Crainic , João Nuno Mestre , Ivan Struchiner

We consider control systems governed by nonlinear O.D.E.'s that are affine in the time-derivative du/dt of the control u. The latter is allowed to be an integrable, possibly of unbounded variation function, which gives the system an…

Optimization and Control · Mathematics 2014-11-07 M. Soledad Aronna , Franco Rampazzo

In this paper we study an optimal control problem (OCP) associated to a linear elliptic equation {on a bounded domain $\Omega$}. The matrix-valued coefficients A of such systems is our control taken in L2 which in particular may comprise…

Optimization and Control · Mathematics 2013-06-12 Thierry Horsin , Peter I. Kogut

The paper studies optimal control problem described by higher order evolution differential inclusions (DFIs) with endpoint and state constraints. In the term of Euler-Lagrange type inclusion is derived sufficient condition of optimality for…

Optimization and Control · Mathematics 2020-09-17 Elimhan N. Mahmudov

We consider a differential quasivariational inequality for which we state and prove the continuous dependence of the solution with respect to the data. This convergence result allows us to prove the existence of at least one optimal pair…

Analysis of PDEs · Mathematics 2020-09-10 Mircea Sofonea , Julieta Bollati , Domingo A. Tarzia

We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain…

Numerical Analysis · Mathematics 2021-06-18 Susanne C. Brenner , Li-yeng Sung , Winnifried Wollner

Optimal quantum control of continuous variable systems poses a formidable computational challenge because of the high-dimensional character of the system dynamics. The framework of quantum invariants can significantly reduce the complexity…

An optimal control problem driven by an ordinary differential equation under continuous state constraints is considered in this study. From an operational point of view, we introduce a discrete state constraints optimal control problem and…

Optimization and Control · Mathematics 2018-12-04 Shuzhen Yang

Let G be a Lie groupoid with Lie algebroid g. It is known that, unlike in the case of Lie groups, not every subalgebroid of g can be integrated by a subgroupoid of G. In this paper we study conditions on the invariant foliation defined by a…

Differential Geometry · Mathematics 2007-05-23 I. Moerdijk , J. Mrcun

We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove the strong convergence…

Analysis of PDEs · Mathematics 2013-09-20 Mahdi Boukrouche , Domingo A. Tarzia

This paper studies a time optimal control problem with control constraints of the rectangular type for the linear multi-input time-varying ordinary differential equations. The aims of this study are to establish certain necessary and…

Optimization and Control · Mathematics 2016-11-25 Can Zhang

We analyze discrete optimal control problems and their connection with back propagation and deep learning. We consider in particular the symmetric representation of the discrete rigid body equations developed via optimal control analysis…

Optimization and Control · Mathematics 2024-04-11 Anthony M. Bloch , Peter E. Crouch , Tudor S. Ratiu

We discuss the problem of the existence of a regular invariant Lagrangian for a given system of invariant second-order differential equations on a Lie group $G$, using approaches based on the Helmholtz conditions. Although we deal with the…

Differential Geometry · Mathematics 2008-04-21 M. Crampin , T. Mestdag

Inspired by flight characteristics captured from live Monarch butterflies, an optimal control problem is presented while accounting the effects of low-frequency flapping and abdomen undulation. A flapping-wing aerial vehicle is modeled as…

Optimization and Control · Mathematics 2021-07-19 Tejaswi K. C. , Taeyoung Lee

In an infinite-horizon optimal control problem the stability of the adjoint variable implying the vanishing of the adjoint variable at infinity along optimal solution.

Optimization and Control · Mathematics 2010-12-17 Dmitry Khlopin

In the paper we study the following problem: given a Hamilton-Jacobi equation where the Hamiltonian is convex with respect to the last variable, are there any optimal control problems representing it? In other words, we search for an…

Optimization and Control · Mathematics 2015-07-07 Arkadiusz Misztela

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…

Optimization and Control · Mathematics 2015-06-04 Fernando Jimenez , Marin Kobilarov , David Martin de Diego

In this survey, we present a geometric description of Lagrangian and Hamiltonian Mechanics on Lie algebroids. The flexibility of the Lie algebroid formalism allows us to analyze systems subject to nonholonomic constraints, mechanical…

Mathematical Physics · Physics 2007-05-23 Jorge Cortes , Manuel de Leon , Juan C. Marrero , D. Martin de Diego , Eduardo Martinez