Behavioral Systems Theory: A Survey

Zerz, Eva

doi:10.2478/v10006-008-0024-9

Cited by 9 publications

(7 citation statements)

References 30 publications

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“…This is always a left R-module itself, and one can show that its dual space [11]). Further examples of signal spaces for various kinds of operators may be found in [18], [11], and [19] and the references therein.…”

Section: A Ore Polynomialsmentioning

confidence: 99%

A toolbox for the analysis of linear systems with delays

Antritter

Middeke

2011

IEEE Conference on Decision and Control and European Control Conference

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This paper considers linear time varying control systems with delays. Roughly speaking, a so called π-flat output of such a system, if it exists, allows to parameterize the states and inputs of the system using derivatives and delays of the π-flat output. Additionally, also predictions of the π-flat output are allowed, which are characterized by a prediction operator π. We present a toolbox for the computer algebra system Maple, which implements the algorithm recently been proposed in [1] for the computation of π-flat outputputs. We also give an equivalent description of hyper-regularity of polynomial matrices using one-sided inverses. This allowed us to replace the transformation to Smith-Jacobson form by the efficient method of row-/column-reduction for checking hyper-regularity. The implementation of the toolbox is illustrated and its application is explained by means of examples.

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Section: A Ore Polynomialsmentioning

confidence: 99%

A toolbox for the analysis of linear systems with delays

Antritter

Middeke

2011

IEEE Conference on Decision and Control and European Control Conference

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“…In certain situations, particularly when the degradation of the performances is critical, fault tolerance should be achieved by modifying both the set point of the process and the control parameters in a way that releases constraints on the actuators. Then, the new operating points allow the system to recover performances as close as possible to the nominal ones (Aubrun et al, 2003;Zerz, 2008).…”

Section: Performance Analysis Principlementioning

confidence: 99%

Performance evaluation based fault tolerant control with actuator saturation avoidance

Boussaid¹,

Aubrun²,

Abdelkrim³

et al. 2011

International Journal of Applied Mathematics and Computer Science

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In this paper, a new approach regarding a reconfigured system is proposed to improve the performance of an active fault tolerant control system. The system performance is evaluated with an intelligent index of performance. The reconfiguration mechanism is based on a model predictive controller and reference trajectory management techniques. When an actuator fault occurs in the system, a new degraded reference trajectory is generated and the controller calculates new admissible controls. A constraint set and cost function are established to avoid actuator saturation and reduce the control energy spent in closed loop dynamics. The effectiveness of the proposed method is illustrated using a hydrothermal system subject to actuator faults and constraints on actuator dynamic ranges.

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“…The notion of power in modeling was introduced by Willems (1986) and later studied by Willems (2007) and Zerz (2008a). The power of a model is defined as the ability of the constructed model to describe the given behavior, i.e., the given data, but as anything little else as possible.…”

Section: Notes On the Power Of A Modelmentioning

confidence: 99%

“…Section 4 deals with the inverse problem of modeling the forward and backward solution space of a system, and Section 5 combines the results of the previous sections into a single algorithm. Lastly, in Section 6, following the behavioral framework of Antoulas and Willems (1993), Markovsky et al (2006), Willems (1986;, or Zerz (2008a;2008b;2011), we study the conditions under which the constructed system is most powerful. Section 7 concludes the paper.…”

Section: Introductionmentioning

confidence: 99%

Construction of Algebraic and Difference Equations with a Prescribed Solution Space

Moysis

Karampetakis

2017

International Journal of Applied Mathematics and Computer Science

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This paper studies the solution space of systems of algebraic and difference equations, given as auto-regressive (AR) representations A(σ)β(k) = 0, where σ denotes the shift forward operator and A(σ) is a regular polynomial matrix. The solution space of such systems consists of forward and backward propagating solutions, over a finite time horizon. This solution space can be constructed from knowledge of the finite and infinite elementary divisor structure of A(σ). This work deals with the inverse problem of constructing a family of polynomial matrices A(σ) such that the system A(σ)β(k) = 0 satisfies some given forward and backward behavior. Initially, the connection between the backward behavior of an AR representation and the forward behavior of its dual system is showcased. This result is used to construct a system satisfying a certain backward behavior. By combining this result with the method provided by Gohberg et al. (2009) for constructing a system with a forward behavior, an algorithm is proposed for computing a system satisfying the prescribed forward and backward behavior.

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Behavioral Systems Theory: A Survey

Cited by 9 publications

References 30 publications

A toolbox for the analysis of linear systems with delays

A toolbox for the analysis of linear systems with delays

Performance evaluation based fault tolerant control with actuator saturation avoidance

Construction of Algebraic and Difference Equations with a Prescribed Solution Space

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