Mohammad Mehdi Arefi

PhD Thesis Defense Session

Abstract:

In this thesis, first, an adaptive robust stabilization algorithm is presented for a class of nonlinear systems with mismatched uncertainties. In this regard, a new controller based on the Lyapunov stability theory is proposed in order to covercome the problem of stabilizing nonlinear time-varying systems with mismatched uncertainties. This method is such that the stability of the closed-loop system is guaranteed in the absence of triangularity assumption. The proposed approach leads to asymptotic convergence of the states of the closed-loop system to zero for unknown but bounded uncertainties. Then, this method is modified so that all the signals in the closed-loop system are uniformly ultimately bounded. Numerical simulation for two different examples, and also for synchronization of time-varying Rossler systems shows the effectiveness of the given algorithm. Next, a method for stabilization of nonlinear systems with non-parametric mismatched uncertainties is introduced. This method is also based on Lyapunov stability theory, and the uncertainty of the system is approximated via an adaptive neural network. The method can be applied to Multi-input systems. Numerical simulations on a vertical take-off and landing helicopter and also two numerical examples show that the presented algorithm has a good performance in the face of mismatched uncertainties. 
 Finally, the previous algorithm is developed for the systems when all the states are not available. To this end, an observer-based stabilization algorithm based on strictly positive real (SPR)-Lyapunov design is presented. Results show that if the SPR condition is satisfied, one can apply the stabilization algorithm using available outputs.    

Date: August 20, 2011,    Time: 10:00
Place: Electrical Engineering Department, Room 305.