State estimation of unknown input polynomial systems: A sum of squares approach

Chibani, Ali; Chadli, Mohammed; Belhaouane, Mohamed Moez; Braeik, Naceur Benhadj

doi:10.1109/med.2014.6961543

Cited by 7 publications

(6 citation statements)

References 28 publications

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“…Recently, a new method for modeling the nonlinear systems so‐called the polynomial system has been introduced in Chibani et al and Saat . The polynomial system can model the original nonlinear system in the format of the linear system with the system matrices being polynomial matrices.…”

Section: Introductionmentioning

confidence: 99%

“…Additionally, with the support of SOS technique and SOS Tool in MATLAB, the controller and observer design for the polynomial system become easier and more effective. In past few years, there were a large number of studies focusing on controller and observer design for the polynomial system . For example, a polynomial observer was synthesized for the polynomial system with unknown inputs, in which the effects of the unknown inputs were completely eliminated and the unmeasurable states were estimated asymptotically.…”

Section: Introductionmentioning

confidence: 99%

“…In past few years, there were a large number of studies focusing on controller and observer design for the polynomial system . For example, a polynomial observer was synthesized for the polynomial system with unknown inputs, in which the effects of the unknown inputs were completely eliminated and the unmeasurable states were estimated asymptotically. Moreover, an approach to design an observer‐based controller for the uncertain polynomial system was investigated in Vu et al, where both unknown states and uncertainties were estimated, then feed‐backed to the controller to stabilize the system.…”

Section: Introductionmentioning

confidence: 99%

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A novel nonlinear observer‐based LQ control system design for wind energy conversion systems with single measurement

Duc

2019

Wind Energy

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The issue of tracking the optimal power for wind energy conversion systems (WECSs) via regulating the rotor speed of the generator is taken into account in this study. Additionally, a novel polynomial observer is proposed for estimating not only aerodynamic torque in WECSs but also d‐axis and electromagnetic torque. Therefore, in this new approach, only the rotor speed of the generator is required to be measured instead of measuring all state variables. With the new observer form, the aerodynamic torque does not need to satisfy any constraints, which are mandatory in the previous methods. It should be noted that this methodology has not been investigated for the WECSs in any previous papers. To design a complete control system, a linear optimal control method cooperated with the polynomial observer is employed to track the optimal trajectory of a generator. Moreover, in this paper, the permanent magnet synchronous generator is used. In addition, on the basis of the Lyapunov theory and sum‐of‐square (SOS) technique, the conditions for observer synthesis are derived in the main theorems. Finally, the simulation results are provided to prove the effectiveness and merit of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A novel nonlinear observer‐based LQ control system design for wind energy conversion systems with single measurement

Duc

2019

Wind Energy

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“…However, the T-S fuzzy system only represented exactly the nonlinear system within a compact set of state variables within a specific range. Recently, a new method for modelling the nonlinear system, so-called polynomial system [5,6], was investigated. The polynomial systems were expressed as a format of a linear system with the entries of system matrices being the polynomials.…”

Section: Introductionmentioning

confidence: 99%

“…Due to the effectiveness of the polynomial system in modelling the non-linear system, there are a large number of studies, recently, paying attention to design the observer and controller for the polynomial systems [5,6,[8][9][10][11][12][13][14][15][16]. For example, an observer was designed for the polynomial system to estimate the states asymptotically and eliminate the impact of unknown inputs [5]. Moreover, a H ∞ based feedback controller was synthesised for polynomial system [8] to minimise the ratio of the energy of the output and disturbance.…”

Section: Introductionmentioning

confidence: 99%

Observer‐based controller synthesis for uncertain polynomial systems

Wang

2018

IET Control Theory & Applications

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A Polynomial Decentralized Controller Design for a Large-Scale Nonlinear System: SOS Approach

2022

IEEE Access

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This paper proposes a novel approach for designing a decentralized controller to stabilize the large-scale nonlinear system. Unlike the previous studies, the polynomial system framework is employed to model the nonlinear large-scale system to decrease not only the modeling error but also the complexity and computational load significantly. Especially, in case the large-scale nonlinear systems consist of nonpolynomial forms (such as sine, cosine, and so on), synthesizing the controller for this system becomes much more challenging. By putting non-polynomial terms inside the matrices, a new approach for designing a decentralized polynomial controller is presented to eliminate the impacts of nonlinear terms and stabilize the system. Based on Lyapunov methodology, the conditions for synthesizing a decentralized polynomial controller expressed under the framework of Sum-of-Square (SOS) are derived in the main theorems. Finally, the effectiveness and superiority of the proposed method are demonstrated in two illustrative examples.INDEX TERMS Large-scale nonlinear system, polynomial system, polynomial decentralized controller design, SOS.

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State estimation of unknown input polynomial systems: A sum of squares approach

Cited by 7 publications

References 28 publications

A novel nonlinear observer‐based LQ control system design for wind energy conversion systems with single measurement

A novel nonlinear observer‐based LQ control system design for wind energy conversion systems with single measurement

Observer‐based controller synthesis for uncertain polynomial systems

A Polynomial Decentralized Controller Design for a Large-Scale Nonlinear System: SOS Approach

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