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Title: A convex penalty for switching control of partial differential equations

Journal Article · · Systems & Control Letters
 [1];  [2];  [2];  [3]
  1. Univ. of Duisburg-Essen, Essen (Germany)
  2. Karl-Franzens-Univ. Graz, Graz (Austria)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
+ Show Author Affiliations

A convex penalty for promoting switching controls for partial differential equations is introduced; such controls consist of an arbitrary number of components of which at most one should be simultaneously active. Using a Moreau–Yosida approximation, a family of approximating problems is obtained that is amenable to solution by a semismooth Newton method. In conclusion, the efficiency of this approach and the structure of the obtained controls are demonstrated by numerical examples.

Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1266013
Journal Information:
Systems & Control Letters, Vol. 89; ISSN 0167-6911
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 12 works
Citation information provided by
Web of Science

References (14)

Parabolic Control Problems in Measure Spaces with Sparse Solutions journal January 2013
Switching control journal January 2011
Relaxation methods for mixed-integer optimal control of partial differential equations journal November 2012
Optimal Switching for Ordinary Differential Equations journal January 1984
Stability Criteria for Switched and Hybrid Systems journal January 2007
Modeling and Analysis of Modal Switching in Networked Transport Systems journal August 2008
Optimal switching for partial differential equations I journal March 1989
Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces journal January 2011
Stability of Switched Linear Hyperbolic Systems by Lyapunov Techniques journal August 2014
Optimal control of a diffusion/reaction/switching system journal January 2013
Robust null controllability for heat equations with unknown switching control mode journal April 2014
Local Existence of Strong Solutions to the 3D Zakharov-Kuznetsov Equation in a Bounded Domain journal August 2013
Optimal switching boundary control of a string to rest in finite time journal April 2008
Optimal control of switched distributed parameter systems with spatially scheduled actuators journal February 2009

Cited By (4)

Stationarity conditions and constraint qualifications for mathematical programs with switching constraints: With applications to either-or-constrained programming journal March 2019
Optimal control problems with control complementarity constraints: existence results, optimality conditions, and a penalty method journal May 2019
Hybrid Optimal Control Problems for a Class of Semilinear Parabolic Equations preprint January 2016
A Hybrid Finite-Dimensional RHC for Stabilization of Time-Varying Parabolic Equations preprint January 2019

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Related Subjects

97 MATHEMATICS AND COMPUTING
optimal control
switching control
partial differential equations
nonsmooth optimization
convex analysis
semi-smooth Newton method