Nonlinearity quantification for the optimal state feedback controller

It is an important question whether nonlinear controller design is needed for a particular application or whether linear controllers are sufficient to achieve the desired control goals. The present paper introduces the closed-loop optimal control law (OCL) nonlinearity measure, a new tool that provides a scheme to quantify the degree of nonlinearity of an optimal state feedback controller for a given control problem. The method builds upon the Optimal Control Structure (OCS) method introduced by Stack and Doyle III [9]. The new closed-loop OCL method is compared to the OCS approach and numerical examples illustrate the theoretical results.