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This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and…

Systems and Control · Computer Science 2018-11-16 Siddharth H. Nair , Ravi N. Banavar

On the 3-dimensional fractional-order Toda lattice with two controls The main purpose of this paper is to study the fractional-order system with Caputo derivative associated to 3-dimensional Toda lattice with two controls. For this…

Dynamical Systems · Mathematics 2025-07-29 Mihai Ivan

We study the regional controllability problem for delayed fractional control systems through the use of the standard Caputo derivative. First, we recall several fundamental results and introduce the family of fractional-order systems under…

Optimization and Control · Mathematics 2022-12-22 Touria Karite , Adil Khazari , Delfim F. M. Torres

The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an It\^o type stochastic differential equation with control process entering both in the drift and the…

Optimization and Control · Mathematics 2020-06-05 Richard Archibald , Feng Bao , Jiongmin Yong , Tao Zhou

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…

Numerical Analysis · Mathematics 2016-12-22 John P. Hollkamp , Mihir Sen , Fabio Semperlotti

In this research paper, we examine an optimal control problem involving a dynamical system governed by a nonlinear Caputo fractional time-delay state equation. The primary objective of this study is to obtain the necessary conditions for…

Optimization and Control · Mathematics 2024-01-31 Jasarat J. Gasimov , Nazim I. Mahmudov

The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…

Optimization and Control · Mathematics 2023-10-18 Giovanni Colombo , Boris S. Mordukhovich , Dao Nguyen , Trang Nguyen

The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…

Optimization and Control · Mathematics 2008-10-09 S. Ober-Bloebaum , O. Junge , J. E. Marsden

In this paper, we employ a reduced basis method for solving the PDE constrained optimization problem governed by a fractional parabolic equation with the fractional derivative in time from order beta in (0,1) is defined by Caputo fractional…

Optimization and Control · Mathematics 2019-10-21 Arezou Rezazadeh , Mahmoud Mahmoudi , Majid Darehmiraki

In this paper, we study the numerical approximation of a system of PDEs with fractional time derivatives. This system is derived from an optimal control problem for a time-fractional Fokker-Planck equation with time dependent drift by…

Numerical Analysis · Mathematics 2020-06-08 Fabio Camilli , Serikbolsyn Duisembay , Qing Tang

A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…

Optimization and Control · Mathematics 2022-11-24 Bui Trong Kien , Bui Ngoc Muoi , Ching-Feng Wen , Jen-Chih Yao

For terminal value problems of fractional differential equations of order $\alpha \in (0,1)$ that use Caputo derivatives, shooting methods are a well developed and investigated approach. Based on recently established analytic properties of…

Numerical Analysis · Mathematics 2023-10-03 Kai Diethelm , Frank Uhlig

We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…

Analysis of PDEs · Mathematics 2019-08-05 Moulay Rchid Sidi Ammi , Ismail Jamiai , Delfim F. M. Torres

This paper presents an efficient numerical technique for solving multi-dimensional fractional optimal control problems using fractional-order generalized Bernoulli wavelets. The numerical results obtained by this method have been compared…

Optimization and Control · Mathematics 2023-10-13 Akanksha Singh , S. Saha Ray

We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral. Main results give fractional Euler-Lagrange type equations and…

Optimization and Control · Mathematics 2011-11-11 Ricardo Almeida , Shakoor Pooseh , Delfim F. M. Torres

In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of…

Numerical Analysis · Mathematics 2025-10-20 Leszczynski Jacek , Ciesielski Mariusz

This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…

Optimization and Control · Mathematics 2019-07-26 Sebastian Engel , Philip Trautmann , Boris Vexler

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

A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique,…

Optimization and Control · Mathematics 2016-07-01 J. J. Trujillo , V. M. Ungureanu

We propose a direct numerical method for the solution of an optimal control problem governed by a two-side space-fractional diffusion equation. The presented method contains two main steps. In the first step, the space variable is…

Optimization and Control · Mathematics 2019-01-29 Mushtaq Salh Ali , Mostafa Shamsi , Hassan Khosravian-Arab , Delfim F. M. Torres , Farid Bozorgnia