Abstract
We consider tracking control for multi-input multi-output differential-algebraic systems. First, the concept of vector relative degree is generalized for linear systems and we arrive at the novel concept of “truncated vector relative degree”, and we derive a new normal form. Thereafter, we consider a class of nonlinear functional differential-algebraic systems which comprises linear systems with truncated vector relative degree. For this class we introduce a feedback controller which achieves that, for a given sufficiently smooth reference signal, the tracking error evolves within a pre-specified performance funnel.
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Notes
- 1.
In [21] a domain \(\mathcal {D}\subseteq {\mathbb {R}}_{\ge 0}\times {\mathbb {R}}\) is considered, but the generalization to the higher dimensional case is straightforward.
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This work was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft) via the grant BE 6263/1-1.
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Berger, T., Lê, H.H., Reis, T. (2020). Vector Relative Degree and Funnel Control for Differential-Algebraic Systems. In: Reis, T., Grundel, S., Schöps, S. (eds) Progress in Differential-Algebraic Equations II. Differential-Algebraic Equations Forum. Springer, Cham. https://doi.org/10.1007/978-3-030-53905-4_8
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