A modified SDRE design for the nonlinear benchmark problem with a stability proof

An approximation to the SDRE control law for the non-linear benchmark problem is developed, which is a solution of an optimal control problem. Although the SDRE solution of the non-linear benchmark problem was derived using the tools of optimal control, the SDRE control law is not the solution of any optimal control problem. The new control law is obtained by approximating the existing SDRE control law in the least square sense from the class of control laws that are of the form required for them to be solutions of optimal control problems. Using the sum of squares tools the optimality criterion is calculated. As a byproduct, the stability of the approximating control law is established over a subset of the non-linear benchmark problem´s state space.