HYBRID OPTIMAL CONTROL PROBLEMS FOR A CLASS OF SEMILINEAR PARABOLIC EQUATIONS

被引：6

作者：

Court, Sebastien ^{[1
]}

Kunisch, Karl ^{[1
,2
]}

Pfeiffer, Laurent ^{[1
]}

机构：

[1] Karl Franzens Univ Graz, Inst Math & Sci Comp, Heinrichstr 36, A-8010 Graz, Austria

[2] Austrian Acad Sci, Radon Inst, Altenberger Str 69, A-4040 Linz, Austria

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2018年 / 11卷 / 06期

基金：

欧盟地平线“2020”; 奥地利科学基金会;

关键词：

Hybrid optimal control problems; semilinear parabolic equations; PDE-constrained optimization; optimality conditions; transversality conditions; REACTION-DIFFUSION EQUATIONS; POINTWISE STATE CONSTRAINTS; TIME-OPTIMAL CONTROL; 2ND-ORDER ANALYSIS; PRINCIPLE; SYSTEM;

D O I：

10.3934/dcdss.2018060

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A class of optimal control problems of hybrid nature governed by semilinear parabolic equations is considered. These problems involve the optimization of switching times at which the dynamics, the integral cost, and the bounds on the control may change. First- and second-order optimality conditions are derived. The analysis is based on a reformulation involving a judiciously chosen transformation of the time domains. For autonomous systems and a time-independent integral cost, we prove that the Hamiltonian is constant in time when evaluated along the optimal controls and trajectories. A numerical example is provided.

引用

页码：1031 / 1060

页数：30

共 29 条

[1]

Anita S, 2011, MODEL SIMUL SCI ENG, P1

[2]

[Anonymous], 2010, Graduate studies in Mathematics

[3]

[Anonymous], 1968, Amer. Math. Soc., Transl. Math. Monographs

[4] Optimal boundary control of a system of reaction diffusion equations [J].