Control of uncertain nonlinear systems based on observers and estimators

Jiang, Tiantian; Huang, Chaodong; Guo, Lei

doi:10.1016/j.automatica.2015.06.012

Cited by 104 publications

(67 citation statements)

References 25 publications

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“…Moreover, the state could be bounded in many practical control systems such as those for faults diagnosis . Finally, since the observer is usually designed for feedback purpose, we can use observer‐based feedback to make the state be bounded …”

Section: Problem Formulationmentioning

confidence: 99%

“…For this reason, ensuring normal operation for a control system under various uncertainties becomes a central issue in control theory. In recent years, the control approaches with estimation/compensation of uncertainty to force the system to satisfy desired performance have been substantially developed for the control of uncertain systems . The effectiveness of such control strategies lies in large part in the observer design, which is used not only to recover the state but also the uncertainty.…”

Section: Introductionmentioning

confidence: 99%

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Observers and observability for uncertain nonlinear systems: A necessary and sufficient condition

Bai

Chen

Huang

et al. 2019

Intl J Robust & Nonlinear

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Summary In this paper, observers and observability for uncertain nonlinear systems are systematically discussed. It is shown that for the convergence of a large class of observers, featured with the augment state to estimate the uncertainty, it requires not only the observability condition for the augment matrix pair but, more importantly, requires a structural condition first proposed in this paper. Furthermore, it is demonstrated that the combination of this structural condition and the observability of the augment matrix pair is a necessary and sufficient condition for the convergence of the observers and the observability of the original uncertain nonlinear systems. This implies that both the structural condition and the observability condition of the augment matrix pair reveal essential feature of the observing problems for uncertain nonlinear systems. In addition, for unobservable uncertain nonlinear systems, which do not satisfy this necessary and sufficient condition, the biased estimation error is explicitly presented, which can be used to evaluate the estimation performance of this class of observers. The numerical simulations for three typical examples are carried out to validate our theoretical analysis.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Observers and observability for uncertain nonlinear systems: A necessary and sufficient condition

Bai

Chen

Huang

et al. 2019

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…Remark The traditional ADRC approach needs to have a nominal value of unknown control coefficient b , which is specified in Assumption in this paper. However, an adaptive projected gradient method is developed in to estimate b without a priori estimate. Therefore, it would be interesting and challenging to generalize some adaptive way like the algorithm in to the stochastic counterpart of systems considered in this paper.…”

Section: Active Disturbance Rejection Control With Constant Gain Extementioning

confidence: 99%

“…However, an adaptive projected gradient method is developed in to estimate b without a priori estimate. Therefore, it would be interesting and challenging to generalize some adaptive way like the algorithm in to the stochastic counterpart of systems considered in this paper.…”

Section: Active Disturbance Rejection Control With Constant Gain Extementioning

confidence: 99%

“…The convergence of linear ESO, which is proposed in in terms of bandwidth, is discussed in . The linear ADRC has been addressed for different systems like those for control and disturbance unmatched systems , lower triangular systems , and the system without known nominal control parameter . In particular, linear ADRC with adaptive gain ESO is investigated in and extended state filter is addressed for filtering problem of general discrete nonlinear uncertain systems in .…”

Section: Introductionmentioning

confidence: 99%

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Active disturbance rejection control approach to output‐feedback stabilization of lower triangular nonlinear systems with stochastic uncertainty

Guo

2016

Intl J Robust & Nonlinear

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Summary In this paper, we apply the active disturbance rejection control approach to output‐feedback stabilization for uncertain lower triangular nonlinear systems with stochastic inverse dynamics and stochastic disturbance. We first design an extended state observer (ESO) to estimate both unmeasured states and stochastic total disturbance that includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance, and uncertainty caused by the deviation of control parameter from its nominal value. The stochastic total disturbance is then compensated in the feedback loop. The constant gain and the time‐varying gain are used in ESO design separately. The mean square practical stability for the closed‐loop system with constant gain ESO and the mean square asymptotic stability with time‐varying gain ESO are developed, respectively. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output‐feedback control scheme. Copyright © 2016 John Wiley & Sons, Ltd.

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References

2019

Estimation of Stochastic Processes With Stationary Increments and Cointegrated Sequences

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Control of uncertain nonlinear systems based on observers and estimators

Cited by 104 publications

References 25 publications

Observers and observability for uncertain nonlinear systems: A necessary and sufficient condition

Observers and observability for uncertain nonlinear systems: A necessary and sufficient condition

Active disturbance rejection control approach to output‐feedback stabilization of lower triangular nonlinear systems with stochastic uncertainty

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