Arbitrary-Order Approximate Solution to Integral State Equation for Generalized Affine Nonlinear Systems

Compared with affine system, the generalized affine system is one more universal nonlinear control system, in which both state variables and control variables are nonlinear. In this paper, from the differential equation of generalized affine nonlinear system, the solution of its homogeneous equation is obtained. The differential equation is converted to the fully equivalent integral equation by the method of variation of parameters. Therefore, the recursion formula of the approximate solution to integral equation is given by heuristic method. And then based on the recursion formula, the arbitrary-order approximate series solution to integral equation is obtained. And the theory of integral equation is employed to prove the convergence.