On the computation of flat outputs for nonlinear control systems

Franke, Matthias; Röbenack, Klaus

doi:10.23919/ecc.2013.6669771

Cited by 16 publications

(16 citation statements)

References 17 publications

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“…Matrices with entries in differential operators play a key role in solving Serre's conjecture (Cluzeau and Quadrat, 2013;Fabianska and Quadrat, 2007;Lam, 1978;Logar and Sturmfels, 1992;Youla and Pickel, 1984) and thus are of interest in pure mathematics. Their occurence in applications such as control theory underlines this interest as well and motivates our work (see, e.g., the works of Franke and Röbenack (2013), Fritzsche et al (2016), Lévine (2011), Middeke (2011), Newman (1972) or Zhou and Labahn (2014) and the references therein). In this paper, we investigate polynomial matrices with meromorphic entries in the differential operator d dt which leads to non-commutative operations.…”

Section: Introductionsupporting

confidence: 52%

On Hyper–Regularity and Unimodularity of Ore Polynomial Matrices

Fritzsche

Röbenack

2018

International Journal of Applied Mathematics and Computer Science

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We investigate Ore polynomial matrices, i. e., matrices with polynomial entries in d/dt whose coefficients are meromorphic functions in t and as such constitute a non-commutative ring. In particular, we study the properties of hyper-regularity and unimodularity of such matrices and derive conditions which make it possible to efficiently check for these characteristics. In addition, this approach enables computation of hyper-regular left and right and unimodular inverses.

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Section: Introductionsupporting

confidence: 52%

On Hyper–Regularity and Unimodularity of Ore Polynomial Matrices

Fritzsche

Röbenack

2018

International Journal of Applied Mathematics and Computer Science

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“…Considering a linear system, controllability conditions differential flatness and vice versa [43]. Methods of determining flat outputs and the mapping function h flat , respectively, are currently being researched, and the interested reader is referred to [19,51,52] and the references therein. Moreover, the construction of so-called flat inputs (i.e., reconstructed inputs based on the given output function (Equation (2))) was shown for SISO systems and a limited set of multi-input and multi-output (MIMO) cases [53].…”

Section: Flat Output Identificationmentioning

confidence: 99%

“…Therefore, to comply with condition given in Equation (6), the dimension of the flat output vector must be 2 as well. Inspecting the system of differential equations in Equation (19) one might observe that x 4 does not appear on the right side of any of the differential equations. The corresponding node in the digraph (see Figure 4a) represents a dead end (i.e., no edge from x 4 ∈ V to {x 1 , x 2 , x 3 } ∈ V), and therefore, must be part of the flat output.…”

Section: Differential Flatness Propertymentioning

confidence: 99%

“…Please also note that while optimizing the flat output trajectory, the number of continuous optimization variables is reduced to the number of flat outputs, i.e., an additional reduction of computational costs as compared to standard nonlinear programming techniques with control and state variable discretization [18]. Methods based on differential flatness have been heavily used in research and industry-primarily in the design of open-loop controllers and the planning of state trajectories in (electro)mechanical systems [19]. In the case of the MBDoE technique, strategies exploiting differential flatness have barely been considered [15,16,20,21], and-to our knowledge-have not been applied to model selection problems under uncertainty before.…”

Section: Introductionmentioning

confidence: 99%

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Robust Model Selection: Flatness-Based Optimal Experimental Design for a Biocatalytic Reaction

Schulze

Schenkendorf

2020

Processes

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Considering the competitive and strongly regulated pharmaceutical industry, mathematical modeling and process systems engineering might be useful tools for implementing quality by design (QbD) and quality by control (QbC) strategies for low-cost but high-quality drugs. However, a crucial task in modeling (bio)pharmaceutical manufacturing processes is the reliable identification of model candidates from a set of various model hypotheses. To identify the best experimental design suitable for a reliable model selection and system identification is challenging for nonlinear (bio)pharmaceutical process models in general. This paper is the first to exploit differential flatness for model selection problems under uncertainty, and thus translates the model selection problem to advanced concepts of systems theory and controllability aspects, respectively. Here, the optimal controls for improved model selection trajectories are expressed analytically with low computational costs. We further demonstrate the impact of parameter uncertainties on the differential flatness-based method and provide an effective robustification strategy with the point estimate method for uncertainty quantification. In a simulation study, we consider a biocatalytic reaction step simulating the carboligation of aldehydes, where we successfully derive optimal controls for improved model selection trajectories under uncertainty.

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“…Hinsichtlich Flachheit wurde (24) auch in [6] mit einem alternativen Zugang, basierend auf Polynomial-Matrizen ähnlich der Vorgehensweise in [11] untersucht.…”

Section: Brockett-integratorunclassified

Eine Normalform für eine spezielle Klasse flacher nichtlinearer Mehrgrößensysteme in Pfaffscher Systemdarstellung

Schöberl

Schlacher

2014

At - Automatisierungstechnik

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Zusammenfassung:In diesem Beitrag betrachten wir nichtlineare Mehrgröẞensysteme und benutzen die sogenannte Pfaffsche Systemdarstellung zur Analyse von Normalformen. Es ist bekannt, dass für Systeme, welche mittels statischer Rückführung exakt linearisierbar sind, eine spezielle Dreiecksdarstellung basierend auf den adaptierten Koordinaten entsprechender involutiver Distributionen existiert. Auch für Systeme, die mittels statischer Rückführung nicht exakt linearisierbar sind, aber welche flach sind und einen flachen Ausgang zulassen, der nicht von Ableitungen der Eingänge abhängt, bietet sich eine ähnliche Normalform an. In diesem Beitrag stellen wir diese Normalform, welche ebenfalls eine Dreiecksstruktur besitzt, vor und geben ein konstruktives Verfahren an, welches flache Systeme (wenn möglich) schrittweise auf diese Dreiecksform transformiert. Diese Normalform beruht nicht auf einer dynamischen Erweiterung sondern ist durch die Verwendung impliziter Differentialgleichungen gekennzeichnet. Drei Beispiele veranschaulichen diese Methodik.Schlüsselwörter: Differentielle Flachheit, nichtlineare Systeme, Pfaffsche Systeme, geometrische Methoden.Abstract: This contribution deals with nonlinear multiinput systems, in particular with the analysis of normal forms in a Pfaffian system representation. It is wellknown that systems that are exactly linearisable by static feedback allow for a special triangular representation in adapted coordinates based on certain involutive distributions. Furthermore, systems that are flat but not exactly linearisable by static feedback can be analyzed us-*Korrespondenzautor: Markus Schöberl, Johannes Kepler Universität Linz, E-

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On the computation of flat outputs for nonlinear control systems

Cited by 16 publications

References 17 publications

On Hyper–Regularity and Unimodularity of Ore Polynomial Matrices

On Hyper–Regularity and Unimodularity of Ore Polynomial Matrices

Robust Model Selection: Flatness-Based Optimal Experimental Design for a Biocatalytic Reaction

Eine Normalform für eine spezielle Klasse flacher nichtlinearer Mehrgrößensysteme in Pfaffscher Systemdarstellung

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