Approximated feedback linearization of nonlinear systems

Obtaining a linearizing feedback and a coordinate transformation map is very difficult, even though the system is feedback linearizable. It is known that finding a desired transformation map and feedback is equivalent to finding an integrating factor for an annihilating one-form for single input nonlinear systems. It is also known that such an integrating factor can be approximated using the simple CIR method and tensor product splines. In the paper, it is shown that m integrating factors can always be approximated whenever a nonlinear system with m inputs is feedback linearizable. Next, m zero-forms can be constructed by utilizing these m integrating factors and the same methodology in the single input case. Hence, the coordinate transformation map is obtained.