Generalized feedback approach to singular quadratic optimization of nonlinear systems

This work presents a solution to the quadratic regulator problem for a class of nonlinear systems in the case when the cost function depends only on the plant output. It is shown that the optimal solution to this problem requires the inclusion in the class of admissible control signals not only piecewise continuous signals but also impulsive inputs and their derivatives, i.e. higher order distributions. The resulting control law further referred to as generalized control law gives optimal feedback solution. The theory presented contains (a) a rigorous formulation of mathematical models for nonlinear systems admitting both regular and impulsive inputs, (b) design of the generalized quadratic regulator which, along with optimality, simultaneously ensures global system stabilization, and (c) an approximation of the generalized regulator by high gain feedback