A Unified Pseudospectral Framework for Nonlinear Controller and Observer Design

Gong, Qi; Ross, I. Michael; Kang, Wei

doi:10.1109/acc.2007.4282898

Cited by 7 publications

(4 citation statements)

References 27 publications

(45 reference statements)

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“…where the gains 𝐿 𝑖 are determined by solving a set of LMI involving ℎ the Lipschitz constant of term (20).…”

Section: Fractional Order Fuzzy Observer Synthesismentioning

confidence: 99%

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Synthesis of Fractional Order Fuzzy Observer for a Fractional Order Takagi-Sugeno Model With Unmeasurable Premise Variables

DJEDDI,

AMIEUR,

HANNACHI

et al. 2024

RRST-EE

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In this article, we present a novel approach: a fractional-order fuzzy observer, an extension of the Thau-Luenberger observer, specifically designed for nonlinear systems characterized by commensurate non-integer order Takagi-Sugeno models. This work makes significant contributions in two key areas. Firstly, both the activation functions of the model and the Lipschitz fractional-order fuzzy observer are dependent on unmeasurable variables, particularly the system's state. Secondly, our proposed fuzzy observer explicitly incorporates the system's initial conditions. The stability conditions of the fractional-order fuzzy observer are expressed through Bilinear Matrix Inequalities, which are then converted into linear matrix inequalities (LMIs). Subsequently, numerical simulations are conducted to demonstrate the efficacy of our proposed estimator.

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“…where the gains 𝐿 𝑖 are determined by solving a set of LMI involving ℎ the Lipschitz constant of term (20).…”

Section: Fractional Order Fuzzy Observer Synthesismentioning

confidence: 99%

“…The selection of an appropriate gain matrix, meeting the stability criterion for estimation error dynamics, frequently necessitates a trial-and-error approach. This endeavor can pose challenges and, in certain instances, may be unachievable, particularly for high-order systems [19,20].…”

Section: Introductionmentioning

confidence: 99%

Synthesis of Fractional Order Fuzzy Observer for a Fractional Order Takagi-Sugeno Model With Unmeasurable Premise Variables

DJEDDI,

AMIEUR,

HANNACHI

et al. 2024

RRST-EE

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“…NCSs possess many advantages over traditional systems including easy installation and maintenance, decreased wiring weight and cost, and so on. [24][25][26] However, NCSs also induce a series of network-induced phenomena such as communication delays, packet dropout, data quantization, and distortion. [27][28][29] Generally speaking, when the signal information of spacecraft formation dynamic systems is transmitted between star sensor, orbit module, and actuator module over the digital communication network, it inevitably induces quantization errors which will bring essential difficulties and challenges to the state tracking control problems in a networked environment.…”

Section: Introductionmentioning

confidence: 99%

Optimal sliding mode tracking control of spacecraft formation flying with limited data communication

Liu

Cao

et al. 2018

Advances in Mechanical Engineering

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This article deals with the optimal tracking control problem for spacecraft formation flying via a sliding mode approach in the presence of external disturbances and signal quantization, where both state quantization and input quantization are considered. First, the Gauss pseudospectral method is adopted to solve the multi-objective optimization problem, where performance optimization, thruster amplitude constraints, and collision avoidance are simultaneously taken into consideration. Second, a novel quantized sliding mode control strategy is developed by employing a dynamic logarithmic quantizer to track the obtained optimal trajectories of relative position and velocity. In this design, the quantizer parameters are input into the designed controller to compensate for the signal quantization effects. Under the proposed robust quantized sliding mode control strategy, the resulting closed-loop control system is asymptotically stable with satisfying performance multi-objective constraints. Finally, a simulation example is presented to show the effectiveness of the proposed control design scheme.

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“…The idea is illustrates in the following diagram. For the details on building a unified framework by PS methods, the readers are referred to [17].…”

Section: E Closed-loop Implementationmentioning

confidence: 99%