Optimization methods for solving bang-bang control problems with state constraints and the verification of sufficient conditions

We consider bang-bang control problems with state inequality constraints. It is shown that the control problem induces an optimization problem where the optimization vector consists of all switching times of the bang-bang control and junction times with boundary arcs. The induced optimization proble...

Full description

Saved in:
Bibliographic Details
Main Authors: Maurer, H., Altrogge, I., Goris, N.
Format: Conference Proceeding
Language:English
Subjects:
Bang-bang control
Cancer
Constraint optimization
Feedback
Medical treatment
Optimal control
Optimization methods
Process control
Sufficient conditions
Testing
Online Access:Request full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider bang-bang control problems with state inequality constraints. It is shown that the control problem induces an optimization problem where the optimization vector consists of all switching times of the bang-bang control and junction times with boundary arcs. The induced optimization problem is a generalization of the one studied in [1], [19]. [20], [22] for bang-bang controls without state constraints. We develop second order sufficient conditions (SSC) for the state-constrained control problem which require that (1) the SSC for the induced optimization problem are satisfied and (2) additional conditions for the switching function hold at switching and junction times. An optimization algorithm is presented which simultaneously carries out the second-order test. The algorithm is illustrated on a numerical example in cancer chemotherapy.
ISSN:0191-2216
DOI:10.1109/CDC.2005.1582275