Long time versus steady state optimal control

Porretta A, Zuazua E (2013)

Publication Type: Journal article

Publication year: 2013

Journal

SIAM Journal on Control and Optimization Society for Industrial and Applied Mathematics

Book Volume: 51

Pages Range: 4242-4273

Journal Issue: 6

DOI: 10.1137/130907239

Abstract

This paper analyzes the convergence of optimal control problems for an evolution equation in a finite time-horizon [0, T] toward the limit steady state ones as T ?8. We focus on linear problems. We first consider linear time-independent finite-dimensional systems and show that the optimal controls and states exponentially converge in the transient time (as T tends to infinity) to the ones of the corresponding steady state model. For this to occur suitable observability assumptions need to be imposed. We then extend the results to infinite-dimensional systems including the linear heat and wave equations with distributed controls. Copyright © 2013 Society for Industrial and Applied Mathematics.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Università degli Studi di Roma 'Tor Vergata' IT Italy (IT) Basque Center of Applied Mathematics (BCAM) ES Spain (ES)

How to cite

APA:

Porretta, A., & Zuazua, E. (2013). Long time versus steady state optimal control. SIAM Journal on Control and Optimization, 51(6), 4242-4273. https://doi.org/10.1137/130907239

MLA:

Porretta, Alessio, and Enrique Zuazua. "Long time versus steady state optimal control." SIAM Journal on Control and Optimization 51.6 (2013): 4242-4273.

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