(A) study on extended feedback linearization of nonlinear systems

Abstract

Since the discovery of the exact condition under which a nonlinear system can be linearized by static-state feedback and coordinate transformation in the early 1980s, feedback linearization has been one of the actively studied nonlinear control methodologies in the last decades. Feedback linearization has two approaches in its own: input-state and input-output approaches. The input-state linearization achieves the fully linearized system from input-tostate under rather restrictive conditions - controllability and involutivity. The input-output linearization allows the systems to be linearized from input-to-output while leaving some parts of the systems untouched by the controller in general. The untouched parts are called the internal dynamics. However, it is very unrealistic to expect the practical systems to be exactly linearized. Thus, the immediate interest is the approximate solutions to the problem of linearizing nonlinear systems. We propose a controller which semi-globally stabilizes a class of approximately linearizable systems. Moreover, the computation in obtaining a diffeormophism for the given system usually requires to solve n partial differential equations (PDEs). We show that in some cases, this computational burden can be reduced to solve only single PDE with the proposed controller. The issue with input-output linearization is the requirement of well-defined relative degree and asymptotically or exponentially stable zero dynamics. In our study, we consider a class of systems which violates these conditions and propose a stabilizing controller. In practical systems, there are always some parameter uncertainty, model uncertainty, noise exogenous signals, etc. Thus, we propose a feedback linearizing controller with a dynamic diffeomorphism to treat a class of uncertain nonlinear systems that have unknown constant parameters and some model uncertainty. With the proposed method, we analytically show that some of uncertain systems which possess the ...