An approach to fuzzy control of nonlinear systems: stability and design issues

By Hua O. Wang, Kazuo Tanaka, M. Griffin. 1996

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Optimization

Citations in the corpus

Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Images (2015, background): “We next turn to the task of controlling the classical inverted pendulum system [18, 19] from images.”
Systematic Multimodeling Methodology Applied to an Activated Sludge Reactor Model (2010, unknown): “19 Each vertex deﬁnes a linear submodel and the nonlinear parts are rejected into the weighting functions.”
Stability and Stabilization of Delayed T--S Fuzzy Systems: A Delay Partitioning Approach (2009, background): “928598 mention a few, the problem of stability analysis is investigated in [19], [29], and [31]; stabilizing and H∞ control designs are reported in [4], [5], [15], [22], [28], [40], [45], and [47]; state estimation is addressed in [1], [10], and [46]; reliable control strategies are presented in [34”
Robust Locally-Linear Controllable Embedding (2017, background): “This is the classic problem of controlling an inverted pendulum [16] from 48× 48 pixel images.”
Generalized Value Functions for Large Action Sets (2011, background): “The inverted pendulum problem (Wang et al., 1996) requires balancing a pendulum of unknown length and mass at the upright position by applying forces to the cart to which it is attached.”
On relaxed LMI-based designs for fuzzy regulators and fuzzy observers (2001, methodology): “Consider, as in [ 6 ] and [10]‐[12], the following control input vector:”
Control Design for Interval Type-2 Fuzzy Systems Under Imperfect Premise Matching (2014, background): “Theorem 1 [15]: The FMB control system in the form of (24) is guaranteed to be asymptotically stable if there exist matrices Nj ∈ m×n, j = 1, 2, .”
TP model transformation as a way to LMI-based controller design (2004, result): “This statement is in full accordance with the analytically derived TP model shown in [26] and [27] where the concept of sector nonlinearity is applied.”
Fuzzy Control Systems: Past, Present and Future (2019, methodology): “Although numerous results have been proposed to deal with this source of conservativeness [55]–[61], the most prominent approach relies on Pólya’s theorem.”
Adaptive importance sampling for value function approximation in off-policy reinforcement learning (2009, unknown): “The angle φ and angular velocity φ̇ are updated (Wang et al., 1996) as follows: φt+1 =φt+φ̇t+1∆t, φ̇t+1 =φ̇t+ 9.”
Mode-independent robust stabilization for uncertain Markovian jump nonlinear systems via fuzzy control (2005, methodology): “Based on the parallel distributed compensation (PDC) scheme [3], [14], we consider the following mode-independent fuzzy-control law for the MJFS (5).”
Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach (2000, methodology): “The control design is carried out based on the fuzzy model via the so-called parallel distributed compensation (PDC) scheme [19], [ 22 ].”
Non-Parametric Approximate Linear Programming for MDPs (2011, background): “The inverted pendulum problem (Wang et al., 1996) requires balancing a pendulum of unknown length and mass at the upright position by applying forces to the cart to which it is attached.”
New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI (2003, methodology): “…for the quadratic stability of the T-S fuzzy systems in the sense of Lyapunov in a series of papers (Takagi & Sugeno, 1993; Tanaka & Sano, 1994; Wang, Tanaka, & Gri8n, 1996; Tanaka & Kosaki, 1997; Tanaka, Ikeda, & Wang, 1998a, b) by considering a Lyapunov function of the sub-fuzzy systems of…”