Robust  observer‐based‐controller design for uncertain fractional‐order time‐varying‐delay systems

Boukal, Yassine; Darouach, Mohamed; Zasadzinski, Michel; Radhy, Nour-Eddine

doi:10.1002/rnc.5638

Cited by 8 publications

(3 citation statements)

References 48 publications

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“…Observers have been applied in many FO system studies to address the issue of unavailability of state measurements. In some studies, the observer for FO linear systems with different constraints had been considered [22][23][24][25][26]. Other studies have employed nonlinear observers to estimate unmeasured states for nonlinear FO systems [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Observer‐based adaptive controller for a class of fractional‐order uncertain systems subject to unknown input and output quantizers and input nonlinearities

Rahmani Nooshabadi,

Shahrokhi,

Malek

2024

Math Methods in App Sciences

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This work addresses design of an adaptive controller for nonlinear fractional‐order (FO) systems in the strict‐feedback form. The system is subject to unknown dynamics, unavailable state variables, quantized input and output, and input nonlinearity. The fuzzy logic system (FLS) is used to estimate the unknown dynamics, and instead of updating all the regressor weights, only the maximum of their norms is updated, which significantly reduces the computational load. Limitations imposed by data transmission bandwidth have been addressed by incorporating sector‐bounded quantizers, which include both logarithmic and hysteresis quantizers at the system input and output, and their errors have been considered in the controller design. It is assumed that system states are not measured. To estimate the system states, a linear observer has been used. Because of output quantization, the continuous output signal is not available, and therefore the observer has been designed based on the quantized output signal. In addition, the constraints of input nonlinearities, including symmetric and asymmetric saturation, backlash, hysteresis, and dead‐zone, have been considered in the controller design. Input nonlinearity and input quantization have been investigated simultaneously, which makes the analysis more challenging. Moreover, it is assumed that the type of input nonlinearity and its characteristics are not known, which makes the controller design more difficult. These problems have been resolved by using two novel adaptive laws. The adaptive backstepping method and the direct Lyapunov stability analysis have been used to construct the controller, and a nonlinear modified FO filter is used to avoid the explosion of complexity occurring in the traditional backstepping technique. Stability of the closed loop system has been established, and it has been shown that the tracking and state estimation errors converge to a small neighborhood of the origin. Finally, the proposed controller performance has been demonstrated via three simulation examples.

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Section: Introductionmentioning

confidence: 99%

Observer‐based adaptive controller for a class of fractional‐order uncertain systems subject to unknown input and output quantizers and input nonlinearities

Rahmani Nooshabadi,

Shahrokhi,

Malek

2024

Math Methods in App Sciences

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“…However, time delay are common (e.g., in states, inputs, and/or outputs) and estimators designed for the ODE without delay can destabilize if applied when delays are introduced. Consequently, the problem of designing stable or optimal observers for systems with delay has received significant attention in recent years, see References 2,6‐8 and the references therein. Specifically, we consider the problem of designing a state estimator for a delay differential system of the form

\begin{matrix} alignleft \\ align-1right \dot{x} (t) & align-2 = A_{0} x (t) + B w (t) + \sum_{i = 1}^{K} (A_{i} x (t - τ_{i}) + B_{i} w (t - τ_{i})), \\ align-1right z (t) & align-2 = C_{1} x (t) + D_{1} w (t) + \sum_{i = 1}^{K} (C_{1 i} x (t - τ_{i}) + D_{1 i} w (t - τ_{i})), \\ align-1right y (t) & align-2 = C_{2} x (t) + D_{2} w (t) + \sum_{i = 1}^{K} (C_{2 i} x (t - τ_{i}) + D_{2 i} w (t - τ_{i})), \\ align-1right x (s) & align-2 =... \end{matrix}

…”

Section: Introductionmentioning

confidence: 99%

H_∞‐optimal observer design for systems with multiple delays in states, inputs and outputs: A PIE approach

Peet

Sun

et al. 2023

Intl J Robust & Nonlinear

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This article investigates the H ∞ -optimal estimation problem of a class of linear system with delays in states, disturbance input, and outputs. The estimator uses an extended Luenberger estimator format which estimates both the present and history states. The estimator is designed using an equivalent Partial Integral Equation (PIE) representation of the coupled nominal system. The advantage of the resulting PIE representation is compact and delay free-obviating the need for commonly used bounding technique such as integral inequalities which typically introduces conservatism into the resulting optimization problem. The H ∞ -optimal estimator synthesis problem is then reformulated as a Linear Partial Inequality (LPI)-a form of convex optimization using operator variables and inequlities. Such LPI-based optimization problems can be solved using semidefinite programming via the PIETOOLS toolbox in Matlab. Compared with previous work, the proposed method simplifies the analysis and computation process and resulting in observers which are non-conservtism to 4 decimal places when compared with Pad é-based ODE observer design methodologies. Numerical examples and simulation results are given to illustrate the effectiveness and scalability of the proposed approach.

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“…By using the FO Razumikhin theorem, Sau et al (2020) studied the problem of passivity analysis of FO neural networks with a bounded time-varying delay and Chen et al (2020) discussed the asymptotic stability and stabilization of FO linear systems with time-varying structured uncertainties and time-varying delay in form of two new delay-dependent and order-dependent LMI-based criteria. In addition, other control ideas can also be added to the stability analysis, such as robust H∞ observer based control (Boukal et al (2021)), fuzzy observer based control (Duan and Li (2018)), guaranteed cost control (Chen et al (2021)), and FO proportional integral control (Ghorbani and Tavakoli-Kakhki (2020)).…”

Section: Introductionmentioning

confidence: 99%

Delay-dependent and order-dependent stability and stabilization analysis of variable fractional order uncertain differential systems with time-varying delay via linear matrix inequality approach

Wang

Zhou

Shi

et al. 2022

Journal of Vibration and Control

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This paper concentrates on the robust stability and stabilization analysis of variable fractional order uncertain differential systems with time-varying delay. Firstly, by using a suitable Lyapunov–Krasovskii function and constructing an appropriate variable fractional order inequality, a novel delay-dependent and order-dependent stability theorem of the nominal systems is proposed. Then, based on the above stability conditions, the robust delay-dependent and order-dependent stability conditions for the uncertain systems are discussed. Moreover, in order to stabilize the nominal and uncertain systems, state feedback controllers are also derived with the help of the presented stability criteria. All the results are in the form of linear matrix inequalities. Finally, two numerical examples are provided to verify the effectiveness of the introduced theoretical formulation.

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Robust observer‐based‐controller design for uncertain fractional‐order time‐varying‐delay systems

Cited by 8 publications

References 48 publications

Observer‐based adaptive controller for a class of fractional‐order uncertain systems subject to unknown input and output quantizers and input nonlinearities

Observer‐based adaptive controller for a class of fractional‐order uncertain systems subject to unknown input and output quantizers and input nonlinearities

H_∞‐optimal observer design for systems with multiple delays in states, inputs and outputs: A PIE approach

Delay-dependent and order-dependent stability and stabilization analysis of variable fractional order uncertain differential systems with time-varying delay via linear matrix inequality approach

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Robust observer‐based‐controller design for uncertain fractional‐order time‐varying‐delay systems

Cited by 8 publications

References 48 publications

Observer‐based adaptive controller for a class of fractional‐order uncertain systems subject to unknown input and output quantizers and input nonlinearities

Observer‐based adaptive controller for a class of fractional‐order uncertain systems subject to unknown input and output quantizers and input nonlinearities

H∞‐optimal observer design for systems with multiple delays in states, inputs and outputs: A PIE approach

Delay-dependent and order-dependent stability and stabilization analysis of variable fractional order uncertain differential systems with time-varying delay via linear matrix inequality approach

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H_∞‐optimal observer design for systems with multiple delays in states, inputs and outputs: A PIE approach