We propose a dynamic augmentation scheme for the asymptotic solution of the nonlinear algebraic loops arising in well-known input saturated feedbacks typically designed by solving linear matrix inequalities (LMIs). We prove that the existing approach based on dynamic augmentation, which replaces the static loop by a dynamic one through the introduction of a sufficiently small time constant, works under some restrictive sufficient well-posedness conditions, requiring the existence of a diagonal Lyapunov matrix. However it can fail in general, even when the algebraic loop is well-posed. Then, we propose a novel approach whose effectiveness is guaranteed whenever well-posedness holds. We also show how this augmentation allows preserving the guaranteed region of attraction with Lyapunov-based designs, as long as a gain parameter is sufficiently large. We finally propose an adaptive version of the scheme where this parameter is adjusted online. Simulation results show the effectiveness of the proposed solutions.

Solving nonlinear algebraic loops arising in input-saturated feedbacks / Blanchini, F.; Giordano, G.; Riz, F.; Zaccarian, L.. - In: IEEE TRANSACTIONS ON AUTOMATIC CONTROL. - ISSN 0018-9286. - 2022:(2022). [10.1109/TAC.2022.3170858]

Solving nonlinear algebraic loops arising in input-saturated feedbacks

Giordano G.;Riz F.;Zaccarian L.
2022-01-01

Abstract

We propose a dynamic augmentation scheme for the asymptotic solution of the nonlinear algebraic loops arising in well-known input saturated feedbacks typically designed by solving linear matrix inequalities (LMIs). We prove that the existing approach based on dynamic augmentation, which replaces the static loop by a dynamic one through the introduction of a sufficiently small time constant, works under some restrictive sufficient well-posedness conditions, requiring the existence of a diagonal Lyapunov matrix. However it can fail in general, even when the algebraic loop is well-posed. Then, we propose a novel approach whose effectiveness is guaranteed whenever well-posedness holds. We also show how this augmentation allows preserving the guaranteed region of attraction with Lyapunov-based designs, as long as a gain parameter is sufficiently large. We finally propose an adaptive version of the scheme where this parameter is adjusted online. Simulation results show the effectiveness of the proposed solutions.
Blanchini, F.; Giordano, G.; Riz, F.; Zaccarian, L.
Solving nonlinear algebraic loops arising in input-saturated feedbacks / Blanchini, F.; Giordano, G.; Riz, F.; Zaccarian, L.. - In: IEEE TRANSACTIONS ON AUTOMATIC CONTROL. - ISSN 0018-9286. - 2022:(2022). [10.1109/TAC.2022.3170858]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/347759
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