Global Exact Tracking for Uncertain Systems Using Output-Feedback Sliding Mode Control

Nunes, Eduardo V. L.; Hsu, Liu; Lizarralde, Fernando

doi:10.1109/tac.2009.2013042

Cited by 34 publications

(18 citation statements)

References 14 publications

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“…The proposed hybrid estimator consists of a convex combination of the estimates

{\overset{ξ}{true}}_{o}

{\overset{σ}{true}}_{o}

in provided by the HGO and the RED estimates

{\overset{ξ}{true}}_{r}

{\overset{σ}{true}}_{r}

in according to (see Figure ):

\begin{matrix} leftalign \\ rightalign-odd ξ ̂ & align-even : = α MathClass-open(σ ̃ MathClass-close) {ξ ̂}_{o} + [1 - α MathClass-open(σ ̃ MathClass-close)] {ξ ̂}_{r}, & rightalign-label (23) \end{matrix}

\begin{matrix} leftalign \\ rightalign-odd σ ̂ & align-even : = α MathClass-open(σ ̃ MathClass-close) {σ ̂}_{o} + [1 - α MathClass-open(σ ̃ MathClass-close)] {σ ̂}_{r}, & rightalign-label (24) \end{matrix}

where

\overset{σ}{true} MathClass-rel= {\overset{σ}{true}}_{r} MathClass-bin- {\overset{σ}{true}}_{o}

is the difference between both estimators. The switching function

α (\overset{σ}{true})

is a continuous modulation, which assumes values in the interval [0,1] and allows the controller to smoothly change from one estimator to the other .…”

Section: Hybrid Estimation Schemementioning

confidence: 99%

“…The switching function˛. Q / is a continuous modulation, which assumes values in the interval OE0, 1 and allows the controller to smoothly change from one estimator to the other [22,23]. The underlying idea of the proposed controller is, first to drive the error state into an invariant compact set D R WD ¹x e W jx e j 6 Rº, for all R > 0, where the convergence of the RED can be guaranteed and an upper boundĄ for the hybrid estimation error Q x e can be determined, and then to ensure that after some finite time, only the RED is used to estimate the ideal sliding variable Sx e .…”

Section: Hybrid Estimation Scheme Designmentioning

confidence: 99%

“…Now, given any W , we have two possibilities: W <! 22 .0/j. Note that, it is always possible to find an exponential decaying term, which is an upper bound for the earlier affine time function, that is, t= 2 C j N W .0/ 2!…”

Section: (C) Norm Bound For Vmentioning

confidence: 99%

“…or W >!22 . Considering the latter case, Dˇ1e 1 t and let N W D W C 1 = 1 , for some positive constant 1 and someˇ1 2 K 1 .…”

mentioning

confidence: 99%

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Peaking free output‐feedback exact tracking of uncertain nonlinear systems via dwell‐time and norm observers

Oliveira

Peixoto

Hsu

2011

Intl J Robust & Nonlinear

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SUMMARY The control of uncertain nonlinear systems by high‐gain observer based output feedback is addressed. Two tracking sliding mode controllers are designed for a broad class of uncertain nonlinear systems with arbitrary relative degree and unmatched polynomial nonlinearities in the unmeasured states. The proposed strategies are based either on dwell‐time for control activation or on simple norm state observers to remove the peaking phenomenon related with high‐gain observers, depending on the nonlinearity growth conditions. In contrast with previous works, exact tracking is also achieved by means of a switching strategy based on locally exact differentiators. Global or semi‐global stability is proved by using Lyapunov theory and on small‐gain analysis. Simulations show that the proposed methodologies provide better and uniform transient behavior, larger regions of attraction, performance recovery with significantly smaller observer gains and good robustness properties with respect to exogenous disturbances and measurement noise. Copyright © 2011 John Wiley & Sons, Ltd.

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“…The proposed hybrid estimator consists of a convex combination of the estimates

{\overset{ξ}{true}}_{o}

{\overset{σ}{true}}_{o}

in provided by the HGO and the RED estimates

{\overset{ξ}{true}}_{r}

{\overset{σ}{true}}_{r}

in according to (see Figure ):

\begin{matrix} leftalign \\ rightalign-odd ξ ̂ & align-even : = α MathClass-open(σ ̃ MathClass-close) {ξ ̂}_{o} + [1 - α MathClass-open(σ ̃ MathClass-close)] {ξ ̂}_{r}, & rightalign-label (23) \end{matrix}

\begin{matrix} leftalign \\ rightalign-odd σ ̂ & align-even : = α MathClass-open(σ ̃ MathClass-close) {σ ̂}_{o} + [1 - α MathClass-open(σ ̃ MathClass-close)] {σ ̂}_{r}, & rightalign-label (24) \end{matrix}

where

\overset{σ}{true} MathClass-rel= {\overset{σ}{true}}_{r} MathClass-bin- {\overset{σ}{true}}_{o}

is the difference between both estimators. The switching function

α (\overset{σ}{true})

is a continuous modulation, which assumes values in the interval [0,1] and allows the controller to smoothly change from one estimator to the other .…”

Section: Hybrid Estimation Schemementioning

confidence: 99%

Section: Hybrid Estimation Scheme Designmentioning

confidence: 99%

Section: (C) Norm Bound For Vmentioning

confidence: 99%

“…or W >!22 . Considering the latter case, Dˇ1e 1 t and let N W D W C 1 = 1 , for some positive constant 1 and someˇ1 2 K 1 .…”

mentioning

confidence: 99%

See 2 more Smart Citations

Peaking free output‐feedback exact tracking of uncertain nonlinear systems via dwell‐time and norm observers

Oliveira

Peixoto

Hsu

2011

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…Moreover, it must taken into account that only some form of local/semiglobal closed-loop stability can be guaranteed because of the assumption of uniformly constant Lipschitz bounds for the derivatives up to the nth order. Therefore, especially for high dimensional systems, a good control scheme would be based on the intelligent use of differentiator as well as of old-fashioned differentiator free techniques [10].…”

Section: Introductionmentioning

confidence: 99%

Adaptive tracking of sinusoids with unknown frequencies for some classes of SISO non‐minimum phase systems

Bartolini

Estrada

Punta

2016

Adaptive Control & Signal

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In this paper, the output-tracking problem for a class of non-affine nonlinear systems with unstable zero-dynamics is addressed. The system output must track a signal, which is the sum of a known number of sinusoids with unknown frequencies amplitudes and phases. The non-minimum phase nature of the considered systems prevents the direct tracking by standard sliding mode methods, which are known to generate unstable behaviors of the internal dynamics. The proposed method relies on the properties of differentially flat systems under mild assumptions relevant to the relation between the original output and a suitably designed flat output. As a result, the original problem is transformed into a state-tracking problem for invertible stable systems, where any internal state turns out to be bounded. Because of the uncertainty in the frequencies and in the parameters defining the relationship between system output and flat states, adaptive indirect methods are applied.

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Output feedback sliding‐mode control with unmatched disturbances, an ISS approach

Aparicio

Castaños

2016

Intl J Robust & Nonlinear

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The robustness properties of a first-order sliding-mode controller are combined with those of an added linear term in order to obtain a closed loop that shows input-to-state stability with respect to matched and unmatched disturbances, of which an upper bound might not be known, using only output information. The output under consideration can have any relative degree. Also, a transformation of the state into a novel output normal form is presented. The zero dynamics are considered unstable and perturbed, so a methodology for defining an observer and a virtual control for it is presented.

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Global Exact Tracking for Uncertain Systems Using Output-Feedback Sliding Mode Control

Cited by 34 publications

References 14 publications

Peaking free output‐feedback exact tracking of uncertain nonlinear systems via dwell‐time and norm observers

Peaking free output‐feedback exact tracking of uncertain nonlinear systems via dwell‐time and norm observers

Adaptive tracking of sinusoids with unknown frequencies for some classes of SISO non‐minimum phase systems

Output feedback sliding‐mode control with unmatched disturbances, an ISS approach

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