Stabilization of uncertain nonlinear systems using approximate partial feedback linearization

Abstract

Feedback linearizaiton is one of the most representative methodologies for nonlinear control. To apply the feedback linearization method in nonlinear system, there are some restrictions such as controllability and involutivity. Thus, to overcome this restrictions, many efforts have been made during the last decade. Among them, the approximate feedback linearization method has been one of the dominant approaches where the system is not restricted to involutivity. However, the problems of conventional approximate feedback linearization is rigorous controllability condition and nonlinear term as perturbation after transformation. In this situation, partial feedback linearization can be good solution to relax rigorous controllability condition. In many real processes, nonlinear systems have uncertainties. And sometimes uncertainties have an effect on stability of nonlinear system. In that case, we can compensate uncertainties of the nonlinear system using appropriately designed controller. In this thesis, we propose an approximate partial feedback linearization method to analyze the nonlinear systems which cannot be applied conventional partial feedback linearization. By our proposed method, nonlinear system is partially feedback linearized without loss of relative degree. In addition, nonlinear system is given flexibility in choosing diffeomorphism because nonlinear system is not restricted partial involutivity condition. And, we propose appropriately designed controller for approximate partially feedback linearized system. Our controller guarantees asymptotic stability of the system and shows better performance than conventional controller where transformed system has high gain nonlinear term. And then, we extend the our result to uncertain nonlinear systems. Thus, we present controller to stabilize approximate partially feedback linearized system from uncertain nonlinear systems. Our results are verified by simulation and compared with other results.