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We first prove the equivalence of two definitions of Riemann-Liouville fractional integral on time scales, then by the concept of fractional derivative of Riemann-Liouville on time scales, we introduce fractional Sobolev spaces,…

Classical Analysis and ODEs · Mathematics 2022-05-27 Xing Hu , Yongkun Li

Appropriate time discretization is crucial for real-time applications of numerical optimal control, such as nonlinear model predictive control. However, if the discretization error strongly depends on the applied control input, meeting…

Optimization and Control · Mathematics 2024-09-17 Amon Lahr , Filip Tronarp , Nathanael Bosch , Jonathan Schmidt , Philipp Hennig , Melanie N. Zeilinger

We consider a class of closed loop stochastic optimal control problems in finite time horizon, in which the cost is an expectation conditional on the event that the process has not exited a given bounded domain. An important difficulty is…

Optimization and Control · Mathematics 2019-12-19 Yves Achdou , Mathieu Laurière , Pierre-Louis Lions

This article deals with variational optimal-control problems on time scales in the presence of delay in the state variables. The problem is considered on a time scale unifying the discrete, the continuous and the quantum cases. Two examples…

Dynamical Systems · Mathematics 2009-12-15 Thabet Abdeljawad , Fahd Jarad , Dumitru Baleanu

We study a linear-quadratic optimal control problem involving a parabolic equation with fractional diffusion and Caputo fractional time derivative of orders $s \in (0,1)$ and $\gamma \in (0,1]$, respectively. The spatial fractional…

Optimization and Control · Mathematics 2015-04-02 Harbir Antil , Enrique Otarola , Abner J. Salgado

The paper investigates data-driven output-feedback predictive control of linear systems subject to stochastic disturbances. The scheme relies on the recursive solution of a suitable data-driven reformulation of a stochastic Optimal Control…

Systems and Control · Electrical Eng. & Systems 2022-12-16 Guanru Pan , Ruchuan Ou , Timm Faulwasser

In this paper, we consider a diffusion equation with fractional-time derivative with nonsingular Mittag-Leffler kernel in Hilbert spaces. Existence and uniqueness of solution are proved by means of a spectral argument. The existence of…

Analysis of PDEs · Mathematics 2017-11-27 J. D. Djida , G. M. Mophou , I. Area

We consider an optimal control problem governed by a class of boundary value problem with the spectral Dirichlet fractional Laplacian. Some sufficient condition for the existence of optimal processes is stated. The proof of the main result…

Analysis of PDEs · Mathematics 2017-12-29 Dorota Bors

In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order $\alpha\in(0,1)$ in time. The…

Numerical Analysis · Mathematics 2017-12-22 Bangti Jin , Buyang Li , Zhi Zhou

This paper shows that the optimal policy and value functions of a Markov Decision Process (MDP), either discounted or not, can be captured by a finite-horizon undiscounted Optimal Control Problem (OCP), even if based on an inexact model.…

Systems and Control · Electrical Eng. & Systems 2023-02-08 Arash Bahari Kordabad , Mario Zanon , Sebastien Gros

We introduce a discrete-time fractional calculus of variations on the time scale $h\mathbb{Z}$, $h > 0$. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and…

Optimization and Control · Mathematics 2010-10-29 Nuno R. O. Bastos , Rui A. C. Ferreira , Delfim F. M. Torres

While it is known that one can consider the Cauchy problem for evolution equations with Caputo derivatives, the situation for the initial value problems for the Riemann-Liouville derivatives is less understood. In this paper we propose new…

Analysis of PDEs · Mathematics 2022-06-28 Erkinjon Karimov , Michael Ruzhansky , Niyaz Tokmagambetov

Fractional systems with Riemann-Liouville derivatives are considered. The initial memory value problem is posed and studied. We obtain explicit steering laws with respect to the values of the fractional integrals of the state variables. The…

Optimization and Control · Mathematics 2010-10-29 Dorota Mozyrska , Delfim F. M. Torres

An effective form of the Variation Evolving Method (VEM), which originates from the continuous-time dynamics stability theory, is developed for the classic time-optimal control problem with control constraint. Within the mathematic…

Systems and Control · Computer Science 2017-11-09 Sheng Zhang , Wei-Qi Qian

We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators. Main…

Classical Analysis and ODEs · Mathematics 2019-02-19 Thabet Abdeljawad , Raziye Mert , Delfim F. M. Torres

In this paper, we discuss a new general formulation of fractional optimal control problems whose performance index is in the fractional integral form and the dynamics are given by a set of fractional differential equations in the Caputo…

Optimization and Control · Mathematics 2016-08-24 H. M. Ali , F. Lobo Pereira , S. M. A. Gama

We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They…

Optimization and Control · Mathematics 2010-10-28 Nuno R. O. Bastos , Rui A. C. Ferreira , Delfim F. M. Torres

We introduce a numerical method, based on modified hat functions, for solving a class of fractional optimal control problems. In our scheme, the control and the fractional derivative of the state function are considered as linear…

Optimization and Control · Mathematics 2019-05-29 Somayeh Nemati , Pedro M. Lima , Delfim F. M. Torres

The first order optimality conditions of optimal control problems (OCPs) can be regarded as boundary value problems for Hamiltonian systems. Variational or symplectic discretisation methods are classically known for their excellent long…

Optimization and Control · Mathematics 2021-11-24 Christian Offen , Sina Ober-Blöbaum

This paper considers the class of deterministic continuous-time optimal control problems (OCPs) with piecewise-affine (PWA) vector field, polynomial Lagrangian and semialgebraic input and state constraints. The OCP is first relaxed as an…

Optimization and Control · Mathematics 2012-11-15 M. Rasheed Abdalmoaty , Didier Henrion , Luis Rodrigues