Avoiding Unmeasured Premise Variables in Designing Unknown Input Observers for Takagi–Sugeno Fuzzy Systems

Dequidt

Transactions of the Institute of Measurement and Control

et al. 2020

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This paper is concerned with the nonlinear tracking control design for robot manipulators. In spite of the rich literature in the field, the problem has not yet been addressed adequately due to the lack of an effective control design. Using a descriptor fuzzy model-based framework, we propose a new approach to design a feedback-feedforward control scheme for robot manipulators in a general form. The goal is to guarantee a small level of an [Formula: see text] gain specification to improve the tracking performance while significantly reducing the numerical complexity for real-time implementation. Based on Lyapunov stability arguments, the control design is formulated as a convex optimization problem involving linear matrix inequalities. Numerical experiments performed with a high-fidelity manipulator benchmark model, embedded in the Simscape MultibodyTM environment, demonstrate the effectiveness of the proposed control solution over existing standard approaches.

Section: Feedback-feedforward Structure For Tracking Controlmentioning

confidence: 97%

Fuzzy descriptor tracking control with guaranteed L∞ error-bound for robot manipulators

Dequidt

Transactions of the Institute of Measurement and Control

et al. 2020

Self Cite

Intl J Robust & Nonlinear

“…where L(𝛼) is defined in (8). Based on the error dynamics (9), and given that P > 0, define the following Lyapunov candidate function…”

Section: Lemmamentioning

confidence: 99%

“…, with e(t 0 ) = e 0 . Thus, V(e), defined in (18), is a Lyapunov function that certifies the exponential stability of the zero equilibrium of system ( 9) and, consequently, of system (8). ▪…”

Section: Lemmamentioning

confidence: 99%

A sufficient condition to design unknown input observers for nonlinear systems with arbitrary relative degree

Coutinho

Bessa

Xie

et al. 2022

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This article addresses the problem of state and unknown inputs (UIs) estimation for nonlinear systems with arbitrary relative degree with respect to the UIs.For this purpose, a novel nonlinear unknown input observer (UIO) is proposed, which is able to decouple the UIs by using the derivatives of the output signal. The error dynamics is attained by an exact handling and a factorization of its gradient to obtain a local polytopic representation suitable for input-affine nonlinear systems. For that representation, a novel design condition based on convex optimization and linear matrix inequalities is proposed to exponentially stabilize the estimation error and to guarantee the validity of the proposed nonlinear UIO. Numerical simulations indicate the effectiveness of the proposed approach for different classes of nonlinear systems, for which the UIs could be totally decoupled from the state estimation.

“…Since both nonlinear functions 𝜙(x k , u k ) and 𝜓(x k ) are continuously differentiable with respect to x k , whose gradients are respectively defined as ]. Using the sector nonlinearity approach [10, Chapter 2], an equivalent N-TS fuzzy descriptor representation (6) with eight fuzzy rules (r = 8) can be obtained for the nonlinear descriptor system (49). A convex bounded set representation can be determined for K(𝛽) and M(𝜃) in ( 13) with 16 and four vertices, respectively.…”

Section: Algorithm 1 Observer Design Proceduresmentioning

confidence: 99%

“…13 The estimation errors of both the state and the UI can be minimized by optimizing a guaranteed 𝓁 ∞ -gain performance. Moreover, the proposed N-TS fuzzy observer design does not require any specific rank condition for UI decoupling as in References [20,21,44,49]. Hence, our systematic LMI-based observer design framework can be applied to a large class of descriptor systems with UIs and unmeasured nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

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

Intl J Robust & Nonlinear

Campos

Guerra

et al. 2021

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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.