Approximate normal forms of nonlinear systems

A method is presented to solve the approximate linearization problem of nonlinear control systems. The problem is reduced to the solution of a set of linear equations as follows. First, the generalized homological equations are derived. By introducing an appropriate basis for expressing higher degree monomials in the vector field, a set of equations linear in the coefficients of the monomials are found. An exact solution to this set of equations is not always possible. A least-squares solution is proposed that minimizes in a statistical sense the error in the approximation