Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems

Heiland J, Zuazua Iriondo E (2021)

Publication Language: English

Publication Status: Accepted

Publication Type: Journal article

Future Publication Type: Journal article

Publication year: 2021

Journal

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

Book Volume: 59

Pages Range: 3600-3624

Journal Issue: 5

URI: https://dcn.nat.fau.eu/wp-content/uploads/heiland-zuazua.pdf

DOI: 10.1137/20M1356105

Open Access Link: https://dcn.nat.fau.eu/wp-content/uploads/heiland-zuazua.pdf

Abstract

The concept of turnpike connects the solution of long but finite time horizon optimal control problems with steady state optimal controls. A key ingredient of the analysis of turnpike phenomena is the linear quadratic regulator problem and the convergence of the solution of the associated differential Riccati equation as the terminal time approaches infinity. This convergence has been investigated in linear systems theory in the 1980s. We extend classical system theoretic results for the investigation of turnpike properties of standard state space systems and descriptor systems. We present conditions for turnpike phenomena in the non detectable case and for impulse controllable descriptor systems. For the latter, in line with the theory for standard linear systems,we establish existence and convergence of solutions to a generalized differential Riccati equation.

Authors with CRIS profile

Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Additional Organisation(s)

Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Max-Planck-Institut für Dynamik komplexer technischer Systeme / Max Planck Institute for Dynamics of Complex Technical Systems DE Germany (DE)

How to cite

APA:

Heiland, J., & Zuazua Iriondo, E. (2021). Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems. SIAM Journal on Control and Optimization, 59(5), 3600-3624. https://doi.org/10.1137/20M1356105

MLA:

Heiland, Jan, and Enrique Zuazua Iriondo. "Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems." SIAM Journal on Control and Optimization 59.5 (2021): 3600-3624.

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