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

[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.

[学科分类] 自动化工程

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