Optimal Control and Observation Locations  for Time-Varying Systems on a Finite-Time Horizon

Wu, Xueran; Jacob, Birgit; Elbern, Hendrik

doi:10.1137/15m1014759

Cited by 23 publications

(16 citation statements)

References 29 publications

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“…This part of the paper is an abbreviated and revised version of the results first presented in [14,38]. Similar results have recently also been reported in [49].…”

Section: Introductionsupporting

confidence: 78%

Numerical solution of the infinite-dimensional LQR problem and the associated Riccati differential equations

Benner

Mena

2018

Journal of Numerical Mathematics

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Abstract:The numerical analysis of linear quadratic regulator design problems for parabolic partial differential equations requires solving Riccati equations. In the finite time horizon case, the Riccati differential equation (RDE) arises. The coefficient matrices of the resulting RDE often have a given structure, e.g., sparse, or low-rank. The associated RDE usually is quite stiff, so that implicit schemes should be used in this situation. In this paper, we derive efficient numerical methods for solving RDEs capable of exploiting this structure, which are based on a matrix-valued implementation of the BDF and Rosenbrock methods. We show that these methods are suitable for large-scale problems by working only on approximate low-rank factors of the solutions. We also incorporate step size and order control in our numerical algorithms for solving RDEs. In addition, we show that within a Galerkin projection framework the solutions of the finite-dimensional RDEs converge in the strong operator topology to the solutions of the infinite-dimensional RDEs. Numerical experiments show the performance of the proposed methods.

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“…This part of the paper is an abbreviated and revised version of the results first presented in [14,38]. Similar results have recently also been reported in [49].…”

Section: Introductionsupporting

confidence: 78%

Numerical solution of the infinite-dimensional LQR problem and the associated Riccati differential equations

Benner

Mena

2018

Journal of Numerical Mathematics

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“…For expository reasons we assume δd is a constant over time and the observation operator H(t) mapping the state space to the observation space is a 1 × 2N g time-invariant matrix. In the paper by [46], the convergence of the numerical solution based on the above splitting and dicretization method to the original solution of the partial differential equation ( 36) has been proved.…”

Section: Examplementioning

confidence: 99%

“…The advanced concept of targeted observations has been popularized during the FASTEX campaign (e.g [28], [43]). Theoretical studies are presented, for example by [3], or recently by [2] for a case of study of highly nonlinear dynamics, and [46] for the optimal deployment of observations for time-varying system in a infinite dimensional domain within a finite-time interval. The problem (ii) addressing the benefit assessment of individual observations or types of measurements has been investigated by [10] and a sequence of related papers.…”

Section: Introductionmentioning

confidence: 99%

The Assessment of Potential Observability for Joint Chemical States and Emissions in Atmospheric Modelings

Elbern

Jacob

2021

Preprint

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In predictive geophysical model systems, uncertain initial values and model parameters jointly influence the temporal evolution of the system. As for chemistry-transport models, emission rates are at least as important as initial values for model evolution controls. This renders initial-value-only optimization by traditional data assimilation methods as insufficient. However, blindly extending the optimization parameter set jeopardizes the validity of the resulting analysis since the ill-posedness of the inversion task is increased. Hence, it becomes important to assess the potential observability of measurement networks for model state and parameters in atmospheric modelings in advance of the optimization. In this paper, we introduce an approach to quantify the impact of observation networks jointly for initial trace gas state and emission rates for transport-diffusion models extended by emissions. Applying a Kalman smoother as underlying assimilation technique, we develop a quantitative assessment method to evaluate the potential observability and the sensitivity of observation networks to initial values and emission rates. For practical applications, we derive an ensemble based version of the approach and give several elementary experiments for illustration.

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“…This methodology has been generalized for the 3-dimensional EURAD-IM (European Air pollution Dispersion-Inverse Model) and applied to a field campaign with airship borne measurements by Goris and Elbern (2015). While that paper describes an approach to optimize an atmospheric chemistry observation network, 35 both in terms of individual compounds to be observed with preference and their location, the assessment of the information potential of an established and mainly fixed observation network, like for example the AIRNow AQir Quality Monitor Maps (http://www.airnow.gov/index.cfm?action=airnow.pointmaps) in the US or from the European Environment Agency (http://www.eea.europa.eu/data-and-maps/explore-interactive-maps#c5=&c0=5&b_start=0) needs a different algorithmic approach. Most measurement devices monitor concentrations hourly or half-hourly.…”

Section: Introductionmentioning

confidence: 99%

The degree of freedom for signal assessment of measurement networks for joint chemical state and emission analysis

Elbern

Jacob

2017

Preprint

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Abstract. The Degree of Freedom for Signal (DFS) is generalized and applied to estimate the potential observability of observation networks for augmented model state and parameter estimations. The control of predictive geophysical model systems by measurements is dependent on a sufficient observational basis. Control parameters may include prognostic state variables, mostly the initial values, and insufficiently known model parameters, to which the simulation is sensitive. As for chemistrytransport models, emission rates are at least as important as initial values for model evolution control. Extending the optimisa-5 tion parameter set must be met by observation networks, which allows for controlling the entire optimisation task. In this paper, we introduce a DFS based approach with respect to address both, emission rates and initial value observability. By applying a Kalman smoother, a quantitative assessment method on the efficiency of observation configurations is developed based on the singular value decomposition. For practical reasons an ensemble based version is derived for covariance modelling. The observability analysis tool can be generalized to additional model parameters.

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Optimal Control and Observation Locations for Time-Varying Systems on a Finite-Time Horizon

Cited by 23 publications

References 29 publications

Numerical solution of the infinite-dimensional LQR problem and the associated Riccati differential equations

Numerical solution of the infinite-dimensional LQR problem and the associated Riccati differential equations

The Assessment of Potential Observability for Joint Chemical States and Emissions in Atmospheric Modelings

The degree of freedom for signal assessment of measurement networks for joint chemical state and emission analysis

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