Generation of stable oscillations in uncertain nonlinear systems with matched and unmatched uncertainties

Hakimi, Ali Reza; Binazadeh, Tahereh

doi:10.1080/00207179.2017.1364427

Cited by 17 publications

(11 citation statements)

References 29 publications

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“…Neglecting the delay can yield poor performances and even instability of the controlled systems (Binazadeh and Yousefi, 2017, 2018). On the other hand, uncertainties in the plant models are basically unavoidable due to external disturbances, parameter variations, idealizations, and simplifications in the modeling procedure (Skogestad and Postlethwaite, 2007; Hakimi and Binazadeh, 2019). Thus, it is necessary to consider time delays and modeling uncertainties for the problem of simultaneous stabilization.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous stabilization of a collection of uncertain discrete-time systems with time-varying state-delay via discrete-time sliding mode control

Dastaviz

Binazadeh

2019

Journal of Vibration and Control

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This paper considers the simultaneous stabilization problem which concerns finding a single controller to simultaneously stabilize a finite collection of discrete-time nonlinear systems with time-varying state delay and norm-bounded uncertainties. For this purpose, a simultaneously stabilizing discrete-time sliding mode controller (DT-SMC) is synthesized. Based on the delay-dependent Lyapunov–Krasovskii functional method, sufficient conditions are derived which guarantee the existence of a common sliding surface in terms of a nonconvex feasibility problem. The cone complementarity linearization approach is exploited to transform the nonconvex conditions into a convex optimization problem. Finally, the robust simultaneously stabilizing DT-SMC is designed in order to draw the closed-loop trajectories of each system onto the common sliding surface in finite time and to maintain it thereafter. The effectiveness of the proposed method is investigated by simulation of a practical example.

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Section: Introductionmentioning

confidence: 99%

Simultaneous stabilization of a collection of uncertain discrete-time systems with time-varying state-delay via discrete-time sliding mode control

Dastaviz

Binazadeh

2019

Journal of Vibration and Control

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“…To achieve a robust manner in the face of matched uncertainties, the combination of Lyapunov redesign and backstepping methods was proposed by Hakimi and Binazadeh to generate robust limit cycles in uncertain systems. This method was developed by Hakimi and Binazadeh to design a robust limit cycle controller in the presence of both matched and unmatched uncertainties in nonlinear SISO systems. Similar studies has been done by Gómez‐Estern et al, Aguilar‐Ibañez et al, and Hakimi and Binazadeh .…”

Section: Introductionmentioning

confidence: 99%

“…Second, the system under study is in the standard strict feedback form. Third, the control input is characterized in such a way that creates just one limit cycle in the phase trajectories of the closed‐loop system …”

Section: Introductionmentioning

confidence: 99%

“…Third, the control input is characterized in such a way that creates just one limit cycle in the phase trajectories of the closed-loop system. 15,16,21 Many practical systems have been modeled as multiple-input multiple-output (MIMO) systems and not necessarily in the standard strict feedback form. Such systems include an important class of dynamic systems, for example, multilink robots and quadrotors.…”

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confidence: 99%

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Sustained oscillations in MIMO nonlinear systems through limit cycle shaping

Hakimi

Binazadeh

2019

Intl J Robust & Nonlinear

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Summary This paper studies on generating periodic behaviors through shaping stable limit cycles in multiple‐input‐multiple‐output nonlinear systems. For this purpose, first, limit cycles are shaped with respect to the desired sustained oscillations of the system's outputs. Then, the Lyapunov analyses, which are appropriate for stability analysis of invariant sets, are employed to design the control law and conclude the asymptotic convergence toward the predefined limit cycles. The problem is studied in two cases. In the first case, some assumptions in the mathematical model are assumed that leads to simplification in the design procedure. In the second case, the design procedure is discussed in more general cases. Finally, the validity and performance of the proposed method for shaping limit cycles with different geometric shapes are illustrated by computer simulations for practical and numerical examples.

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“…Furthermore, some dynamics of the system may not be considered due to model simplification or their small impact. In addition to parametric uncertainty and unmodelled dynamics, the effect of external disturbances on mechanical systems is unavoidable [12,13]. These factors together, which are called uncertainties in this paper, can affect the desired performance of the system or may lead to instability.…”

Section: Introductionmentioning

confidence: 99%

Robust control approach for handling matched and/or unmatched uncertainties in port‐controlled Hamiltonian systems

Binazadeh

Karimi

Tavakolpour-Saleh

2019

IET cyber-systems robotics

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Generation of stable oscillations in uncertain nonlinear systems with matched and unmatched uncertainties

Cited by 17 publications

References 29 publications

Simultaneous stabilization of a collection of uncertain discrete-time systems with time-varying state-delay via discrete-time sliding mode control

Simultaneous stabilization of a collection of uncertain discrete-time systems with time-varying state-delay via discrete-time sliding mode control

Sustained oscillations in MIMO nonlinear systems through limit cycle shaping

Robust control approach for handling matched and/or unmatched uncertainties in port‐controlled Hamiltonian systems

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