Optimal Volterra kernels for nonlinear controllers

This paper presents a method for designing Volterra kernels for nonlinear controllers which minimize an analytic cost functional. Expressions for the kernels are obtained as well as an estimate of the radius of convergence of the resulting controller. First, a general unconstrained minimization problem on Banach spaces is stated and solved. The function to be minimized is assumed to be analytic in two variables: a parameter and a minimizing variable. The minimizing variable is found as an analytic function of the parameter. This function is found recursively in series form. The theory of polynomial operators is used to represent each analytic series. Next, by appropriately identifying the variables in the minimization problem with signals in a nonlinear control system, the results are applied to obtain Volterra kernels for a nonlinear controller.