A sum of squares approach for polynomial fuzzy observer design for polynomial fuzzy systems with unknown inputs

Chibani, Ali; Chadli, Mohammed; Braïek, Naceur Benhadj

doi:10.1007/s12555-014-0406-8

Cited by 42 publications

(16 citation statements)

References 25 publications

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“…In this paper, based on the concept of the SOS technique, the observer synthesis conditions are obtained in the following theorems.Theorem Considering system , the estimation error with the observer (19) approaches zero asymptotically if there exist matrices N ( y ), G , L ( y ), F , E ( y ), O and a symmetric matrix O satisfying the following conditions:

A ((), y) - italicFCA ((), y) - L ((), y) C - N ((), y) = 0

B - italicFCB - G = 0

D - italicFCD = 0

{(italicCD)}^{- 1} italicCA ((), y) - E ((), y) = 0

{(italicCD)}^{- 1} italicCB - O = 0

{v_{1}}^{T} ((), P - ε_{1} I) v_{1} is SOS

- {v_{2}}^{T} ((), N^{T} ((), y) P + italicPN ((), y) - ε_{2} ((), y) I) v_{2} is SOS

Proof From , we have

\overset{y}{true} = C \overset{\overset{x}{true} = italicCA ((), y) \overset{x}{true} + italicCBu + italicCD T_{a}}{true}

…”

Section: Observer Designmentioning

confidence: 99%

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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A ((), y) - italicFCA ((), y) - L ((), y) C - N ((), y) = 0

B - italicFCB - G = 0

D - italicFCD = 0

{(italicCD)}^{- 1} italicCA ((), y) - E ((), y) = 0

{(italicCD)}^{- 1} italicCB - O = 0

{v_{1}}^{T} ((), P - ε_{1} I) v_{1} is SOS

- {v_{2}}^{T} ((), N^{T} ((), y) P + italicPN ((), y) - ε_{2} ((), y) I) v_{2} is SOS

Proof From , we have

\overset{y}{true} = C \overset{\overset{x}{true} = italicCA ((), y) \overset{x}{true} + italicCBu + italicCD T_{a}}{true}

…”

Section: Observer Designmentioning

confidence: 99%

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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“…LMI‐based algorithms for SOF problems have been published: similarity transformation, the min/max algorithm, the LMI methods, and the cone complementary linearization . Some results on the H ∞ or mixed H 2 / H ∞ SOF design are those by Kau et al, Qiu et al, and Jeung and Lee, and a polynomial fuzzy observer via constant Lyapunov function was proposed in the work of Chibani et al…”

Section: Introductionmentioning

confidence: 99%

Polynomial static output feedback H_∞ control via homogeneous Lyapunov functions

Liu

2019

Intl J Robust & Nonlinear

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Summary In this paper, we study a polynomial static output feedback (SOF) stabilization problem with H∞ performance via a homogeneous polynomial Lyapunov function (HPLF). It is shown that the quadratic stability ascertaining the existence of a single constant Lyapunov function becomes a special case. With the HPLF, the proposal is based on a relaxed two‐step sum of square (SOS) construction where a stabilizing polynomial state feedback gain K(x) is returned at the first stage and then the obtained K(x) gain is fed back to the second stage, achieving the SOF closed‐loop stabilization of the underlying polynomial fuzzy control systems. The SOS equations obtained thus effectively serve as a sufficient condition for synthesizing the SOF controllers that guarantee polynomial fuzzy systems stabilization. To demonstrate the effectiveness of the proposed polynomial fuzzy SOF H∞ control, benchmark examples are provided for the new approach.

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“…For the purpose of increasing the safety and reliability of networked controlled systems, fault diagnosis research and their applications to a wide range of industrial and commercial processes have been the subjects of intensive investigations over the past two decades [9,10,11,12]. Many fruitful results for a variety of systems have been reported [13,14,15,16,17,18,19,20,21]. …”

Section: Introductionmentioning

confidence: 99%

Event-Triggered Fault Estimation for Stochastic Systems over Multi-Hop Relay Networks with Randomly Occurring Sensor Nonlinearities and Packet Dropouts

2018

Sensors

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Wireless sensors have many new applications where remote estimation is essential. Considering that a remote estimator is located far away from the process and the wireless transmission distance of sensor nodes is limited, sensor nodes always forward data packets to the remote estimator through a series of relays over a multi-hop link. In this paper, we consider a network with sensor nodes and relay nodes where the relay nodes can forward the estimated values to the remote estimator. An event-triggered remote estimator of state and fault with the corresponding data-forwarding scheme is investigated for stochastic systems subject to both randomly occurring nonlinearity and randomly occurring packet dropouts governed by Bernoulli-distributed sequences to achieve a trade-off between estimation accuracy and energy consumption. Recursive Riccati-like matrix equations are established to calculate the estimator gain to minimize an upper bound of the estimator error covariance. Subsequently, a sufficient condition and data-forwarding scheme are presented under which the error covariance is mean-square bounded in the multi-hop links with random packet dropouts. Furthermore, implementation issues of the theoretical results are discussed where a new data-forwarding communication protocol is designed. Finally, the effectiveness of the proposed algorithms and communication protocol are extensively evaluated using an experimental platform that was established for performance evaluation with a sensor and two relay nodes.

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A sum of squares approach for polynomial fuzzy observer design for polynomial fuzzy systems with unknown inputs

Cited by 42 publications

References 25 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

Polynomial static output feedback H_∞ control via homogeneous Lyapunov functions

Event-Triggered Fault Estimation for Stochastic Systems over Multi-Hop Relay Networks with Randomly Occurring Sensor Nonlinearities and Packet Dropouts

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A sum of squares approach for polynomial fuzzy observer design for polynomial fuzzy systems with unknown inputs

Cited by 42 publications

References 25 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

Polynomial static output feedback H∞ control via homogeneous Lyapunov functions

Event-Triggered Fault Estimation for Stochastic Systems over Multi-Hop Relay Networks with Randomly Occurring Sensor Nonlinearities and Packet Dropouts

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Polynomial static output feedback H_∞ control via homogeneous Lyapunov functions