Piecewise Fuzzy Model Construction and Controller Design based on Piecewise Lyapunov Function

2007 ◽  
Author(s):  
Hiroshi Ohtake ◽  
Kazuo Tanaka ◽  
Hua O. Wang
Keyword(s):  
Lyapunov Function ◽  
Controller Design ◽  
Fuzzy Model ◽  
Model Construction ◽  
Piecewise Lyapunov Function

Switching Model Construction and Stability Analysis for Nonlinear Systems

2006 ◽  
Vol 10 (1) ◽  
pp. 3-10 ◽  
Author(s):  
Hiroshi Ohtake ◽  
◽  
Kazuo Tanaka
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Fuzzy Model ◽  
Function Approach ◽  
Model Construction ◽  
Switching Model ◽  
Piecewise Lyapunov Function ◽  
System A ◽  
The Stability

This paper presents switching model construction and stability analysis for a class of nonlinear systems. A switching fuzzy model newly developed in this paper is employed to represent the dynamics of a nonlinear system. A key feature of the switching fuzzy model construction is to find the so-called minimum distance sector by solving a nonlinear optimization problem. Next, we discuss the stability of a switching fuzzy model. To take advantage of the switching fuzzy model, we introduce a piecewise Lyapunov function that mirrors its structure. We show that the piecewise Lyapunov function approach provides less conservative results for the typical quadratic Lyapunov function approach. Illustrative examples demonstrate the utility of the switching model construction and the stability analysis.

Switching Fuzzy Model Construction and Controller Design for Dynamical Systems with Input Nonlinearity

2008 ◽  
Vol 12 (6) ◽  
pp. 537-545 ◽  
Author(s):  
Hiroshi Ohtake ◽  
◽  
Kazuo Tanaka
Keyword(s):  
Dynamical Systems ◽  
State Feedback ◽  
Controller Design ◽  
Fuzzy Model ◽  
Construction Method ◽  
Model Construction ◽  
Dynamic State ◽  
Membership Functions ◽  
Input Nonlinearity ◽  
Control Approach

Fuzzy model-based control mainly deals with dynamical systems which affinely depend on control inputs. In this paper, dynamical systems which is permitted to have nonlinearity not only in the states, but also in the inputs is considered. Input nonlinearity makes a nonlinear system complicated and makes the number of fuzzy model rules increase. Thus, switching fuzzy control approach is employed. Firstly, the switching fuzzy model construction with arbitrary linear dividing planes, which is an extension of the ordinary switching fuzzy model construction method with dividing planes corresponding to quadrants, is introduced. Secondly, by applying the switching fuzzy model construction method to the dynamical system with input nonlinearity, the switching fuzzy model with membership functions which depend on control inputs is constructed. Finally, by utilizing the dynamic state feedback control approach, we show that membership functions which depend on control inputs can be calculated. Moreover, by employing augmented system approach, the switching fuzzy dynamic state feedback controller design conditions based on the switching Lyapunov function are derived in terms of linear matrix inequalities. A design example illustrates the utility of this approach.

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