A Decoupling Approach for Observer-Based Controller Design of T–S Fuzzy System With Unknown Premise Variables

Xie, Wen‐Bo; Liu, Bing; Bu, Lin-Wei; Wang, Yulong; Zhang, Jian

doi:10.1109/tfuzz.2020.3006572

Cited by 51 publications

(17 citation statements)

References 39 publications

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“…The singular redundancy representation has been exploited for control and observer designs of TS fuzzy descriptor systems with linear consequents. 23,36,48 However, fuzzy observer design using the N-TS fuzzy form (7) has not yet been reported in the open literature. This singular model reformulation allows for an effective treatment of the nonlinear descriptor matrix (x k ) in (1), especially in the context of TS fuzzy observer design with unmeasured premise variables.…”

Section: Description Of N-ts Fuzzy Descriptor Systemsmentioning

confidence: 99%

“…Hence, the variable 𝜒 k can be viewed as an estimate of x k + 1 . The key idea to introduce the virtual variable 𝜒 k into the observer structure ( 8) is to guarantee the consistency between the proposed observer form and the singular redundancy representation (7), which allows avoiding any special structure of the observer gain ℒ (h). Hence, a convex observer design framework with a reduced degree of conservatism can be achieved.…”

Section: N-ts Fuzzy Observer Structure and Useful Lemmasmentioning

confidence: 99%

“…1 Hence, state estimation for dynamical systems is a fundamental problem in control theory and applications. To this end, numerous approaches have been proposed to design full-order or reduced-order observers, with or without unknown inputs (UIs), for both linear and nonlinear systems, see References [2][3][4][5][6][7] and references therein. Since the pioneer work on linear time-invariant systems, 8 numerous extensions have been developed for nonlinear cases.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Takagi–Sugeno fuzzy observer design for nonlinear descriptor systems with unmeasured premise variables and unknown inputs

Nguyen

Campos

Guerra

et al. 2021

Intl J Robust & Nonlinear

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This article presents a new observer design framework for a class of nonlinear descriptor systems with unknown but bounded inputs. In the presence of unmeasured nonlinearities, that is, premise variables, designing nonlinear observers is known as particularly challenging. To solve this problem, we rewrite the nonlinear descriptor system in the form of a Takagi-Sugeno (TS) fuzzy model with nonlinear consequents. This model reformulation enables an effective use of the differential mean value theorem to deal with the mismatching terms involved in the estimation error dynamics. These nonlinear terms, issued from the unmeasured nonlinearities of the descriptor system, cause a major technical difficulty for TS fuzzy-model-based observer design. The descriptor form is treated through a singular redundancy representation. For observer design, we introduce into the Luenberger-like observer structure a virtual variable aiming at estimating the one-step ahead state. This variable introduction allows for free-structure decision variables involved in the observer design to further reduce the conservatism. Using Lyapunov-based arguments, the observer design is reformulated as an optimization problem under linear matrix inequalities with a single line search parameter. The estimation error bounds of both the state and the unknown input can be minimized by means of a guaranteed 𝓁 ∞ -gain performance level. The interests of the new 𝓁 ∞ TS fuzzy observer design are clearly illustrated with two physically motivated examples.

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Section: Description Of N-ts Fuzzy Descriptor Systemsmentioning

confidence: 99%

Section: N-ts Fuzzy Observer Structure and Useful Lemmasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Takagi–Sugeno fuzzy observer design for nonlinear descriptor systems with unmeasured premise variables and unknown inputs

Nguyen

Campos

Guerra

et al. 2021

Intl J Robust & Nonlinear

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“…In (1), q = q ev ∈ R 3 is the coordinate, M = M a ∈ R 3×3 is a symmetric positive definite inertia matrix, C = C a ∈ R 3×3 denotes the matrix of centripetal and Coriolis forces, and G = G a ∈ R 3 is the gravitational torque. d = − 1 2 P T d a ∈ R 3 represents usually uncertain external disturbances (the external disturbances are assumed to be continuous and bounded, and then the disturbances can be dealt with through bounded stability without designing an observer [8].). τ = 1 2 P T τ a ∈ R 3 denotes the control input.…”

Section: Spacecraft Attitude Tracking Error Modelmentioning

confidence: 99%

Command Filter-Based Control for Spacecraft Attitude Tracking With Pre-Defined Maximum Settling Time Guaranteed

Gao

2021

IEEE Access

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For the on-orbit service spacecraft attitude tracking task with external disturbances, considering the limited capacity of its actuators and high control performance required, an improved performance constraint control algorithm based on command filters is proposed in this paper. For the proposed control algorithm, before the theoretical control signal is transmitted to the actuator, it needs to be filtered by the command filter. This filter can constrain the rate, magnitude, and bandwidth of the signals, smooth the command signals and avoid peak interference. In terms of performance constraints, inspired by the performance constraint curve, this paper uses the determined points to re-design a new performance constraint function, which shows the maximum settling time parameters, allowing designers to pre-defined this limited time of the closed-loop system according to needs. Therefore, the maximum settling time of the actual closed-loop system will be less than the pre-defined maximum settling time. The controller based on the command filter is designed, and on this basis, the corresponding performanceconstrained control algorithm with pre-defined maximum settling time guaranteed is proposed. Through the proof and simulation, the rationality and effectiveness of the proposed controller are further demonstrated.

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“…Then the overall fast subsystem of T‐S fuzzy form can be obtained

{\dot{x}}_{2 f} = \sum_{i = 1}^{r} h_{i} (x_{1}) [A_{f, i} x_{2 f} (t) + B_{f, i} u_{f} (t)],

where

h_{i} (x_{1} (t)) = 𝕏_{i} [x_{1} (t)] / \sum_{i = 1}^{r} 𝕏_{i} [x_{1} (t)]

is the membership function,

𝕏_{i} [x_{1} (t)]

represents the grade of membership of x 1 ( t ) in

𝕏_{i}

\sum_{i = 1}^{r} h_{i} (x_{1} (t)) = 1

. Thus, based on the approach of PDC, 18,43 the fast subproblem can be converted to solving the linear regulation problems of r ‐tuple fuzzy fast subsystems.…”

Section: Rl‐fuzzy‐based Composite Suboptimal Controller Design and Performance Analysismentioning

confidence: 99%

Suboptimal control for nonlinear slow‐fast coupled systems using reinforcement learning and Takagi–Sugeno fuzzy methods

Liu

Yang

Luo

et al. 2021

Adaptive Control & Signal

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Summary In this article, by using singular perturbation theory, reinforcement learning (RL), and Takagi–Sugeno (T‐S) fuzzy methods, a RL‐fuzzy‐based composite suboptimal control method is proposed for nonlinear slow‐fast coupled systems (SFCSs) with unknown slow dynamics. First, the SFCSs is decomposed into slow and fast subsystems and the original optimal control problem is reduced to two subproblems. Then, for the slow subsystem, a nonlinear coordinate transformation is introduced to transform the nonquadratic slow utility function into the quadratic form. Unmeasurable virtual slow subsystem state is reconstructed by the state measurements of original system and slow controller design algorithm is proposed in the framework of RL by utilizing the actor‐critic neural networks to approximate the controller and cost function. For the fast subsystem, T‐S fuzzy model is established and state measurements of the original system are exploited to reconstruct the unmeasurable fast subsystem state. Fast controller is designed with the approach of parallel distributed compensation. The obtained slow and fast controllers form the composite suboptimal controller for the original SFCSs. Considering the state reconstruction error, convergence of the slow controller design algorithm, suboptimality of the composite controller, and stability of the closed‐loop SFCSs are analyzed. Finally, the effectiveness of our proposed method is illustrated by examples.

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A Decoupling Approach for Observer-Based Controller Design of T–S Fuzzy System With Unknown Premise Variables

Cited by 51 publications

References 39 publications

Takagi–Sugeno fuzzy observer design for nonlinear descriptor systems with unmeasured premise variables and unknown inputs

Takagi–Sugeno fuzzy observer design for nonlinear descriptor systems with unmeasured premise variables and unknown inputs

Command Filter-Based Control for Spacecraft Attitude Tracking With Pre-Defined Maximum Settling Time Guaranteed

Suboptimal control for nonlinear slow‐fast coupled systems using reinforcement learning and Takagi–Sugeno fuzzy methods

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