Luenberger Observers for Nonlinear Controlled Systems
Author: Pauline Bernard, 56th IEEE Conference on Decision an Control (CDC 2017)
We show how the (original) Luenberger methodology presented in [1] for autonomous linear systems can be used to design causal observers for controlled non linear systems. Their implementation relies on the resolution of a time-varying PDE, the solutions of which transform the dynamics into linear asymptotically stable ones. We prove the existence and injectivity (after a certain time) of such transformations, under a differential observability assumption. We also show on practical examples how this PDE can be solved and how the observability assumption can be checked.
BibTeX:
@Proceedings{,
author = {Bernard, Pauline},
title = {Luenberger Observers for Nonlinear Controlled Systems},
booktitle = {Luenberger Observers for Nonlinear Controlled Systems},
address = {Melbourne},
year = {2017},
abstract = {We show how the (original) Luenberger methodology presented in [1] for autonomous linear systems can be used to design causal observers for controlled non linear systems. Their implementation relies on the resolution of a time-varying PDE, the solutions of which transform the dynamics into linear asymptotically stable ones. We prove the existence and injectivity (after a certain time) of such transformations, under a differential observability assumption. We also show on practical examples how this PDE can be solved and how the observability assumption can be checked.}, }
We show how the (original) Luenberger methodology presented in [1] for autonomous linear systems can be used to design causal observers for controlled non linear systems. Their implementation relies on the resolution of a time-varying PDE, the solutions of which transform the dynamics into linear asymptotically stable ones. We prove the existence and injectivity (after a certain time) of such transformations, under a differential observability assumption. We also show on practical examples how this PDE can be solved and how the observability assumption can be checked.
BibTeX:
@Proceedings{,
author = {Bernard, Pauline},
title = {Luenberger Observers for Nonlinear Controlled Systems},
booktitle = {Luenberger Observers for Nonlinear Controlled Systems},
address = {Melbourne},
year = {2017},
abstract = {We show how the (original) Luenberger methodology presented in [1] for autonomous linear systems can be used to design causal observers for controlled non linear systems. Their implementation relies on the resolution of a time-varying PDE, the solutions of which transform the dynamics into linear asymptotically stable ones. We prove the existence and injectivity (after a certain time) of such transformations, under a differential observability assumption. We also show on practical examples how this PDE can be solved and how the observability assumption can be checked.}, }