Regional Enlarged Controllability of Semilinear Systems with Constraints on the Gradient: Approaches and Simulations

Journal of control, automation and electrical systems

article

Karite, T.¹  Boutoulout, A.¹  El Alaoui, F. Z.¹ 

[1] MACS Laboratory, Department of Mathematics and Computer Science, Institute of Sciences, Moulay Ismail University

关键词: Distributed systems;    Parabolic systems;    Regional controllability;    Gradient;    Sub-differential;    Lagrangian multiplier;    Semilinear systems;    Minimum energy;    Uzawa algorithm;   

DOI  :  10.1007/s40313-019-00460-3

学科分类：自动化工程

来源: Springer

【 摘 要 】

The aim of this paper is to study the constrained gradient controllability problem governed by parabolic evolution equations. The purpose is to find and compute the control u that steers the gradient state from an initial gradient one $$\nabla y_{_{0}}$$ ∇ y 0 to a gradient vector supposed to be unknown between two defined levels $$\alpha (\cdot )$$ α ( · ) and $$\beta (\cdot )$$ β ( · ) , only on a subregion $$\omega $$ ω of the system evolution domain $$\varOmega $$ Ω . The obtained results have been proved via two approaches: The first one is based on sub-differential techniques, while the second one is based on Lagrangian multipliers. An algorithm is given on the basis of Uzawa algorithm, and numerical results are established.

【 授权许可】

CC BY