Smooth and Analytic Normal and Canonical Forms for Strict Feedforward Systems

Tall, Issa Amadou; Respondek, Witold

doi:10.1109/cdc.2005.1582823

Cited by 9 publications

(4 citation statements)

References 39 publications

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“…, ξn) is a scalar nonlinearity verifying f1(0) = 0. Referring to the recent publications [9], [11], [10], the dynamics of many Hamiltonian mechanical systems can be transformed into (1) by changing the coordinates and applying a linearizing state feedback. However, when the input is not completely known, the linearization of the last state with respect to the control input is not possible.…”

Section: Theorem 1 Consider Systemmentioning

confidence: 99%

“…It is worth mentioning that the stabilization algorithm given by the statement of Theorem could be generalized to controllable feedforward systems of the following form:

\begin{matrix} {\overset{ξ}{true}}_{1} = f_{1} (ξ_{2} ​, ξ_{3} ​, ξ_{4} ​, \dots, ξ_{n}), \\ {\overset{ξ}{true}}_{i} = ξ_{i + 1} ​, 2 \leq i \leq n - 1, \\ {\overset{ξ}{true}}_{n} = D (u) . \end{matrix}

where f 1 ( ξ 2 , ξ 3 , ξ 4 , … , ξ n ) is a scalar nonlinearity verifying f 1 (0) = 0. Referring to the recent publications , , , the dynamics of many Hamiltonian mechanical systems can be transformed into by changing the coordinates and applying a linearizing state feedback. However, when the input is not completely known, the linearization of the last state with respect to the control input is not possible.…”

Section: Feedforward Systems Subject To Symmetric Dead‐zone Inputsmentioning

confidence: 99%

“…The reader is also referred to other extensive contributions, that can be traced in [2][3][4][5][6][7][8]. For recent developments on linearizability of feedforward systems and their equivalence to some normal forms, see [9][10][11], and the references therein.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Adaptive and Robust Stabilization of Feedforward Nonlinear Systems Driven by Symmetric and Non‐symmetric Dead‐zone Inputs

Ibrir¹,

Su²

2014

Asian Journal of Control

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The stabilization of feedforward nonlinear systems subject to hard-input nonlinearities is a challenging problem due to the presence of input uncertainties. This paper deals with adaptive control of a class of feedforward nonlinear systems driven by unknown dead-zone inputs. The unknown dead-zone input nonlinearity is assumed to be either symmetric or non-symmetric. The control design is based on the combination of the invariant-manifold stabilization technique with the classical adaptive and robust compensation methods. Simulation results showed that the presence of the dead-zone inputs in the system dynamics can be handled even for arbitrary large dead-zone parameters.

show abstract

Section: Theorem 1 Consider Systemmentioning

confidence: 99%

“…It is worth mentioning that the stabilization algorithm given by the statement of Theorem could be generalized to controllable feedforward systems of the following form:

\begin{matrix} {\overset{ξ}{true}}_{1} = f_{1} (ξ_{2} ​, ξ_{3} ​, ξ_{4} ​, \dots, ξ_{n}), \\ {\overset{ξ}{true}}_{i} = ξ_{i + 1} ​, 2 \leq i \leq n - 1, \\ {\overset{ξ}{true}}_{n} = D (u) . \end{matrix}

Section: Feedforward Systems Subject To Symmetric Dead‐zone Inputsmentioning

confidence: 99%

See 1 more Smart Citation

Adaptive and Robust Stabilization of Feedforward Nonlinear Systems Driven by Symmetric and Non‐symmetric Dead‐zone Inputs

Ibrir¹,

Su²

2014

Asian Journal of Control

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show abstract

“…where F is the applied control input, m 1 and m 2 are the masses of the cart and the pendulum, respectively, l is the length of the pendulum, q 1 is the displacement of the cart, and q 2 is the rotation angle of the pendulum. It has been shown in Tall and Respondek [2005] that for −π/2 < q 2 < π/2, the feedback controller:…”

Section: Semi-global Stabilization Of the Pendulum-cart Systemmentioning

confidence: 99%