Optimal control of a fractional diffusion equation with state constraints

Mophou, Gisèle; N’Guérékata, Gaston M.

doi:10.1016/j.camwa.2011.04.044

Cited by 62 publications

(35 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, the notion of controllability plays a central role in the study of the theory of control and optimization. Therefore, there are a lot of works on the controllability, approximate controllability, and optimal control of linear and nonlinear differential and integral systems in various frameworks (see [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Approximate Controllability for Functional Equations with Riemann-Liouville Derivative by Iterative and Approximate Method

Ibrahim

Fan

2017

Journal of Function Spaces

View full text Add to dashboard Cite

We discuss the functional control systems governed by differential equations with Riemann-Liouville fractional derivative in general Banach spaces in the present paper. First we derive the uniqueness and existence of mild solutions for functional differential equations by the approach of fixed point and fractional resolvent under more general settings. Then we present new sufficient conditions for approximate controllability of functional control system by means of the iterative and approximate method. Our results unify and generalize some previous works on this topic.

show abstract

Section: Introductionmentioning

confidence: 99%

Approximate Controllability for Functional Equations with Riemann-Liouville Derivative by Iterative and Approximate Method

Ibrahim

Fan

2017

Journal of Function Spaces

View full text Add to dashboard Cite

show abstract

“…Remark 4.1 Note that the convergence of ξ(v n ) to ξ γ (u γ ) can be obtained by proceeding as for the proof of Proposition 3.7 in [35].…”

Section: Study Of the No-regret Control And Low-regret Controlmentioning

confidence: 97%

“…Lemma 2.2 [35] Let f ∈ L 2 (Q) and y ∈ L 2 (Q) be such that D α RL y − y = f. Then Consider the following initial/boundary value problem for the fractional diffusion equation with the left Caputo fractional time derivative:…”

Section: Introductionmentioning

confidence: 99%

Optimal Control for Fractional Diffusion Equations with Incomplete Data

Mophou

2015

J Optim Theory Appl

View full text Add to dashboard Cite

We are concerned with the optimal control of time-fractional diffusion equations with missing boundary condition. Using the notion of no-regret control and least (or low) regret control developed by Lions, we first prove that the least regret control problem associated with the boundary fractional diffusion equation has a unique solution. Then we show that this solution converges to the no-regret control which we characterize by a singular optimality system.

show abstract

“…In the context of partial differential equations (PDEs), problems of this type are often referred to as PDE-constrained optimization problems and have been studied extensively over the last decades (see [37,85] for introductions to the field). Optimal control problems for FDEs have previously been studied in literature such as [2,3,54,55,65,74]. However, they were mostly considering one-dimensional spatial domains, since the direct treatment of higher dimensions was too expensive.…”

Section: Introductionmentioning

confidence: 99%

Fast tensor product solvers for optimization problems with fractional differential equations as constraints

Dolgov

Pearson

Savostyanov

et al. 2016

Applied Mathematics and Computation

View full text Add to dashboard Cite

Fractional differential equations have recently received much attention within computational mathematics and applied science, and their numerical treatment is an important research area as such equations pose substantial challenges to existing algorithms. An optimization problem with constraints given by fractional differential equations is considered, which in its discretized form leads to a high-dimensional tensor equation. To reduce the computation time and storage, the solution is sought in the tensor-train format. We compare three types of solution strategies that employ sophisticated iterative techniques using either preconditioned Krylov solvers or tailored alternating schemes. The competitiveness of these approaches is presented using several examples with constant and variable coefficients.

show abstract

Optimal control of a fractional diffusion equation with state constraints

Cited by 62 publications

References 22 publications

Approximate Controllability for Functional Equations with Riemann-Liouville Derivative by Iterative and Approximate Method

Approximate Controllability for Functional Equations with Riemann-Liouville Derivative by Iterative and Approximate Method

Optimal Control for Fractional Diffusion Equations with Incomplete Data

Fast tensor product solvers for optimization problems with fractional differential equations as constraints

Contact Info

Product

Resources

About