A Sum-of-Squares Approach to Modeling and Control of Nonlinear Dynamical Systems With Polynomial Fuzzy Systems

2009 ◽  
Vol 17 (4) ◽  
pp. 911-922 ◽  
Author(s):  
K. Tanaka ◽  
H. Yoshida ◽  
H. Ohtake ◽  
H.O. Wang
Keyword(s):  
Dynamical Systems ◽  
Fuzzy Systems ◽  
Nonlinear Dynamical Systems ◽  
Sum Of Squares ◽  
Nonlinear Dynamical ◽  
Modeling And Control ◽  
Polynomial Fuzzy Systems ◽  
And Control

scholarly journals Modeling and Control of Power and Energy Produced by a Synchronous Generator Using Polynomial Fuzzy Systems and Sum-of-Squares Approach

2021 ◽  
Author(s):  
Parisa Ansari Bonab ◽  
Seyyed Mohammad Hosseini Rostami ◽  
Ahmad Jafari ◽  
Babak Sheikhi ◽  
Jin Wang ◽  
...  
Keyword(s):  
Power Systems ◽  
Control Strategy ◽  
Fuzzy Systems ◽  
Fuzzy Model ◽  
Synchronous Generator ◽  
Sum Of Squares ◽  
Effective Control ◽  
Modeling And Control ◽  
Polynomial Fuzzy Systems ◽  
And Control

The synchronous generator, as the main component of power systems, plays a key role in these system’s stability. Therefore, utilizing the most effective control strategy for modeling and control the synchronous generator results in the best outcomes in power systems’ performances. The advantage of using a powerful controller is to have the synchronous generator modeled and controlled as well as its main task i.e. stabilizing power systems. Since the synchronous generator is known as a complicated nonlinear system, modeling and control of it is a difficult task. This paper presents a sum of squares (SOS) approach to modeling and control the synchronous generator using polynomial fuzzy systems. This method as an efficacious control strategy has numerous superiorities to the well-known T–S fuzzy controller, due to the control framework is a polynomial fuzzy model, which is more general and effectual than the well-known T–S fuzzy model. In this case, a polynomial Lyapunov function is used for analyzing the stability of the polynomial fuzzy system. Then, the number of rules in a polynomial fuzzy model is less than in a T-S fuzzy model. Besides, derived stability conditions are represented in terms of the SOS approach, which can be numerically solved via the recently developed SOSTOOLS. This approach avoids the difficulty of solving LMI (Linear Matrix Inequality). The Effectiveness of the proposed control strategy is verified by using the third-part Matlab toolbox, SOSTOOLS.

scholarly journals Integral observability operators of nonlinear dynamical systems

2003 ◽  
Vol 2003 (55) ◽  
pp. 3519-3538
Author(s):  
Yury V. Zaika
Keyword(s):  
Dynamical Systems ◽  
Duality Theory ◽  
Phase State ◽  
Nonlinear Dynamical Systems ◽  
Functional Dependence ◽  
Integral Operators ◽  
Nonlinear Dynamical ◽  
Linear Problems ◽  
And Control ◽  
Nonlinear Observability

In terms of functional dependence, the description of observable functions in nonlinear dynamical systems, which are analytic with respect to phase variables, is obtained. For processing of measurements, integral operators are used, which provide certain noise stability of operation of phase state reconstruction. The analogue of the duality theory known for linear problems of observation and control is developed. Computing schemes for nonlinear observability problem are proposed.

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