On stabilizability of switched differential algebraic equations

Wijnbergen, Paul; Jeeninga, Mark; Trenn, Stephan

doi:10.1016/j.ifacol.2020.12.2580

Cited by 4 publications

(2 citation statements)

References 16 publications

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“…Several structural properties of switched DAEs have been studied recently such as controllability by [4], stability/stabilizability by [5][6][7][8] and observability/detectability by [9][10][11]. Impulse-controllability has been studied in the non-swtiched case [12][13][14][15] and in the switched case in [2] for fixed switching signals.…”

Section: Introductionmentioning

confidence: 99%

Impulse-controllability of system classes of switched differential algebraic equations

Wijnbergen

Trenn

2022

Preprint

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In this paper impulse controllability of system classes containing switched DAEs is studied. We introduce several notions of impulse-controllability of system classes and provide a characterization of strong impulse-controllability of system classes generated by arbitrary switching signals. In the case of a system class generated by switching signals with a fixed mode sequence it is shown that either all or almost all systems are impulse-controllable, or that all or almost all systems are impulse-uncontrollable. Sufficient conditions for all systems to be impulse-controllable or impulse-uncontrollable are presented. Furthermore, it is observed that although all systems are impulse-controllable, the input achieving impulse-free solutions might still depend on the switching times in the future, which causes some causality issues. Therefore, the concept of (quasi-) causal impulse-controllability is introduced and system classes which are (quasi-) causal are characterized. Finally necessary and sufficient conditions for a system class to be causal given some dwell-time are stated.

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Section: Introductionmentioning

confidence: 99%

Impulse-controllability of system classes of switched differential algebraic equations

Wijnbergen

Trenn

2022

Preprint

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“…The literature on optimal control of non-switched DAEs is quite mature, (besides the already mentioned literature) see e.g., [9]- [12], and several structural properties of switched DAEs have been investigated recently [13], [14]. Also results on optimal control of switched ordinary differential equations have appeared e.g., [15].…”

Section: Introductionmentioning

confidence: 99%

Optimal control of DAEs with unconstrained terminal costs

Wijnbergen

Trenn

2021

2021 60th IEEE Conference on Decision and Control (CDC)

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This paper is concerned with the linear quadratic optimal control problem for impulse controllable differential algebraic equations on a bounded half open interval. Regarding the cost functional, a general positive semi-definite weight matrix is considered in the terminal cost. It is shown that for this problem, there generally does not exist an input that minimizes the cost functional. First it is shown that the problem can be reduced to finding an input to an index-1 DAE that minimizes a different quadratic cost functional. Second, necessary and sufficient conditions in terms of matrix equations are given for the existence of an optimal control.

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Impulse-controllability of system classes of switched differential algebraic equations

Wijnbergen,

Trenn

2023

Math. Control Signals Syst.

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In this paper, impulse-controllability of system classes containing switched DAEs is studied. We introduce several notions of impulse-controllability of system classes and provide a characterization of strong impulse-controllability of system classes generated by arbitrary switching signals. For a system class generated by switching signals with a fixed-mode sequence, it is shown that either almost all systems are impulse-controllable, or almost all systems are impulse-uncontrollable. Sufficient conditions for all systems in this system class to be impulse-controllable or impulse-uncontrollable are presented. Furthermore, it is observed that even if all systems in a system class are impulse-controllable, knowledge of all the switching times is generally necessary to construct an input that ensures impulse-free solutions. Consequently, it is impossible to design a controller in real time if the switching times in the future are unknown. This phenomenon can be regarded as a causality issue. Therefore, the concept of (quasi-) causal impulse-controllability is introduced, and system classes which are (quasi-) causal are characterized. Finally, necessary and sufficient conditions for a system class to be causal given some dwell-time are stated.

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On stabilizability of switched differential algebraic equations

Cited by 4 publications

References 16 publications

Impulse-controllability of system classes of switched differential algebraic equations

Impulse-controllability of system classes of switched differential algebraic equations

Optimal control of DAEs with unconstrained terminal costs

Impulse-controllability of system classes of switched differential algebraic equations

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