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This paper aims to establish second order necessary conditions for optimal control in quantum stochastic systems. We employ a variational approach, analogous to methods in classical stochastic control, to analyze systems governed by quantum…

Optimization and Control · Mathematics 2026-03-17 Penghui Wang , Shan Wang

We consider control-linear left-invariant time-optimal problems on step 2 Carnot groups with strictly convex set of control parameters (in particular, sub-Finsler problems). We describe all linear-in-momenta Casimirs on the dual of the Lie…

Optimization and Control · Mathematics 2020-03-18 Yuri L. Sachkov

The main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach. The control system is governed by a stochastic…

Optimization and Control · Mathematics 2016-11-09 Hélène Frankowska , Haisen Zhang , Xu Zhang

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…

Differential Geometry · Mathematics 2013-02-26 Liviu Popescu

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

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…

Optimization and Control · Mathematics 2007-05-23 M. Chyba , N. E. Leonard , E. D. Sontag

The present paper extends the classical second-order variational problem of Herglotz type to the more general context of the Euclidean sphere S^n following variational and optimal control approaches. The relation between the Hamiltonian…

Differential Geometry · Mathematics 2018-11-13 L. Machado , L. Abrunheiro , N. Martins

In recent years, much effort in designing numerical methods for the simulation and optimization of mechanical systems has been put into schemes which are structure preserving. One particular class are variational integrators which are…

Optimization and Control · Mathematics 2015-05-08 Cédric M. Campos , Sina Ober-Blöbaum , Emmanuel Trélat

We study local controllability and optimal control problems for invertible discrete-time control systems. We present second order necessary conditions for optimality and sufficient conditions for local controllability. The conditions are…

Optimization and Control · Mathematics 2013-01-30 M. Barbero-Liñán , B. Jakubczyk

Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…

Optimization and Control · Mathematics 2018-02-13 Laurent Pfeiffer

In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition.…

Optimization and Control · Mathematics 2016-11-17 Islam I. Hussein , Melvin Leok , Amit K. Sanyal , Anthony M. Bloch

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…

Optimization and Control · Mathematics 2024-11-26 Ghorbanali Haghighatdoost

In this paper we study optimal control problems for nonholonomic systems defined on Lie algebroids by using quasi-velocities. We consider both kinematic, i.e. systems whose cost functional depends only on position and velocities, and…

Optimization and Control · Mathematics 2015-05-27 L. Abrunheiro , M. Camarinha , J. F. Cariñena , J. Clemente-Gallardo , E. Martínez , P. Santos

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…

Optimization and Control · Mathematics 2022-07-15 Efstratios Stratoglou , Alexandre Anahory Simoes , Leonardo J. Colombo

In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition.…

Optimization and Control · Mathematics 2007-12-31 Anthony M. Bloch , Islam I. Hussein , Melvin Leok , Amit K. Sanyal

This paper is concerned with second-order optimality conditions for Tikhonov regularized optimal control problems governed by the obstacle problem. Using a simple observation that allows to characterize the structure of optimal controls on…

Optimization and Control · Mathematics 2019-06-24 Constantin Christof , Gerd Wachsmuth

This paper analyzes the optimal control problem of cubic polynomials on compact Lie groups from a Hamiltonian point of view and its symmetries. The dynamics of the problem is described by a presymplectic formalism associated with the…

Optimization and Control · Mathematics 2015-05-27 L. Abrunheiro , M. Camarinha , J. Clemente-Gallardo

In this manuscript, we consider a control system governed by a general ordinary differential equation on a Riemannian manifold, with its endpoints satisfying some inequalities and equalities, and its control constrained to a closed convex…

Optimization and Control · Mathematics 2020-11-06 Li Deng

Isoperimetric problems consist in minimizing or maximizing a cost functional subject to an integral constraint. In this work, we present two fractional isoperimetric problems where the Lagrangian depends on a combined Caputo derivative of…

Optimization and Control · Mathematics 2017-01-17 Dina Tavares , Ricardo Almeida , Delfim F. M. Torres

We develop a Poisson Hamiltonian formulation of Pontryagin dynamics for optimal control of mechanical systems on Lie groupoids. The reduced dynamics is formulated intrinsically on the dual Lie algebroid endowed with its canonical linear…

Optimization and Control · Mathematics 2026-02-25 Ghorbanali Haghighatdoost