Journal Articles IEEE Transactions on Automatic Control Year : 2024

Incremental stabilization of cascade nonlinear systems and harmonic regulation: a forwarding-based design

Abstract

In this work, we address the problem of designing a control law for a system in feedforward form to be globally incrementally exponentially stable. To do that, we develop an incremental version of the so-called forwarding mod{LgV} approach. Then, we apply such a control design to the problem of compensating matched disturbances assumed to be given by the superimposition of a finite number of harmonics with unknown amplitude. For this, we propose a dynamic controller made of L linear oscillators processing the regulation error and a stabilizer making the closed-loop system incrementally globally exponentially stable, uniformly with respect to the external signals. This guarantees that the closed-loop system asymptotically converges to a periodic trajectory having the first L-Fourier coefficients of the error to be zero. Then, we specialize our design for the class of linear systems with a scalar nonlinearity and of minimum-phase systems possessing contractive zero dynamics.
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Dates and versions

hal-04410732 , version 1 (23-01-2024)

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Cite

Mattia Giaccagli, Daniele Astolfi, Vincent Andrieu, Lorenzo Marconi. Incremental stabilization of cascade nonlinear systems and harmonic regulation: a forwarding-based design. IEEE Transactions on Automatic Control, 2024, 69 (7), pp.4828-4835. ⟨10.1109/TAC.2024.3358985⟩. ⟨hal-04410732⟩
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