A Study on SOS-based Stability Analysis of Fuzzy Tracking Control for Nonlinear Systems
- A Study on SOS-based Stability Analysis of Fuzzy Tracking Control for Nonlinear Systems
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- In this thesis, we propose a fuzzy tracking control design method for nonlinear system with external disturbance. The fuzzy controller is developed to track the reference model and to reduce the tracking error as small as possible. The Takagi-Sugeno (T-S) fuzzy model is used to represent nonlinear system dynamics and to design the fuzzy controller. Based on Lyapunov's direct method, the model reference tracking control scheme based on the augmented system is proposed. To prove the stability for augmented system, the sufficient condition is derived in terms of a state-dependent nonlinear matrix inequality which converted into a sum-of-squares (SOS) optimization problem. The main point of the proposed approach is to obtain the stability conditions under nonlinear matrix inequality for the nonlinear system dynamics and to solve the nonlinear matrix inequality using the SOS convex optimization techniques. Lastly, a simulation result is given to illustrate tracking performance of the proposed method.
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